Quantum-Inspired Evolutionary Algorithms and Machine Learning for Minimizing Energy Consumption in Precision Machining

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Tamiloli, J. Venkatesan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7276662/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study analyzes four techniques—Taguchi Method, Artificial Neural Network (ANN), Machine Learning (ML) Regression, and Quantum-Inspired Evolutionary Algorithm (QIEA)—to predict and optimize power consumption in machining. Using an L27 orthogonal array, experiments were conducted by varying Depth of Cut, Feed, and Speed. Taguchi provided a baseline, while ANN and ML captured nonlinear patterns. QIEA outperformed all with the lowest predicted power consumption (0.9599 kW). Its strength lies in exploring continuous variables and nonlinear interactions using quantum-inspired operators. The study confirms QIEA's superiority and supports integrating soft computing techniques for energy-efficient machining in advanced manufacturing systems. Evolutionary Algorithm Neural Network (ANN) Machine Learning Taguchi Method Machining Optimization Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 1. Introduction The demand for high-performance and lightweight materials in the aerospace, automotive, and electronics industries has led to the widespread adoption of aluminum alloys in precision machining. Among various machining processes, end milling is one of the most versatile and widely used techniques for shaping complex components from aluminum due to its high machinability, good thermal conductivity, and strength-to-weight ratio. However, optimizing end milling operations is a challenging task due to the nonlinear and stochastic nature of cutting forces, tool wear, surface finish, and material removal rate. Traditional optimization methods often fall short in capturing the complexity of these interrelated parameters. To address these limitations, recent research has focused on integrating Machine Learning (ML) and optimization algorithms to develop intelligent systems for modeling and optimizing machining processes. ML algorithms, particularly Artificial Neural Networks (ANN), Support Vector Machines (SVM), and Deep Learning architectures, have shown great promise in predicting machining outputs with high accuracy. These models can learn from experimental data, uncover hidden patterns, and generalize across different machining conditions. However, training these models effectively requires optimal selection of hyperparameters and architectures—a task that is computationally intensive and often leads to suboptimal results using classical approaches. Quantum-Inspired Evolutionary Algorithms (QIEA) have emerged as powerful tools in solving complex optimization problems. Unlike conventional evolutionary algorithms, QIEAs incorporate principles from quantum computing—such as superposition and quantum probability representation—to enhance population diversity and avoid premature convergence. Although they do not require actual quantum hardware, their inspiration from quantum theory enables them to explore the solution space more effectively. In machining applications, QIEAs have been successfully applied to optimize cutting parameters, tool paths, and neural network architectures. The fusion of QIEA with machine learning offers a promising hybrid framework for intelligent decision-making in aluminum end milling. For instance, QIEA can be employed to optimize the weights and biases of neural networks, tune fuzzy control systems, or select the most influential features for predicting tool wear or surface roughness. This synergy improves the accuracy and reliability of predictive models, enabling manufacturers to achieve better product quality, reduced machining time, and lower operational costs. Overall, the integration of QIEA, machine learning, and optimization in aluminum end milling not only enhances process efficiency but also contributes to the advancement of smart manufacturing systems. The present study explores this interdisciplinary approach, aiming to optimize the machining parameters for improved surface integrity, minimal tool wear, and efficient energy consumption—thereby paving the way for sustainable and high-precision manufacturing. Author(s) Description 1 Zhide Lu, Pei‑XinShen& Dong‑Ling Deng (2021) Introduced Markovian quantum neuroevolution that models QNN circuit search as a graph-walk optimization. Outperformed classical methods in image and topological data classification. 2 SrishtiSahni et al. (2020) QIEA used for weight optimization of a 3-layer perceptron in Parkinson’s disease detection. Outperformed PSO and ABC in noisy environments. 3 Zhang et al. (2021) Used neural predictors and QIEA to evolve quantum circuit architectures. Efficient and transferable to multiple quantum learning tasks. Cao & Li (2014) Designed quantum-inspired activations and state encoding for time series forecasting with NN models. Improved prediction and generalization. Mahajan (2011) QIEA-tuned neural model for commodity price forecasting. Outperformed conventional backpropagation in MAPE and convergence time. 6 Gong M. et al. (2023) Integrated QIEA with convolutional neural architecture search. Achieved competitive accuracy and compact CNN structure for image classification. 7 Dey A. et al. (2023) Used QIEA with differential evolution for neural clustering—improved performance on image and customer behavior datasets. 8 Narayanan & Moore (2013) Developed a hybrid QIEA-deep neural network model. Achieved fast convergence and better generalization for handwritten digit recognition. 9 Singh &Tiwari (2021) Applied QIEA in autonomous vehicle neural decision systems. Enhanced path planning and obstacle prediction via optimized NN weights. 10 Ahmed & Jamal (2022) Built QIEA-tuned deep learning models for medical imaging. Achieved superior classification of diabetic retinopathy and brain tumors. 11 Tsai (2012) Introduced a QIEA for multilayer neural networks—optimized weights to improve learning in energy demand prediction. 12 Patel & Mehta (2023) Applied QIEA in ensemble neural networks for cyber threat detection. Improved F1-scores in real-time attack identification. 13 Li et al. (2016) Hybridized QIEA with BP neural networks for financial forecasting. Tuned hidden layers and weights dynamically. 14 Zhang et al. (2018) Used QIEA to optimize CNN filters. Reduced overfitting and enhanced feature extraction in medical image classification. 15 Das &Samanta (2020) LSTM integrated with QIEA for smart manufacturing predictive maintenance. Extended RUL forecasting accuracy. 16 Huang et al. (2021) Developed a QIEA-evolved feedforward neural model for emotion recognition. Enhanced generalization in speech signal classification. 17 Costa (2023) Reviewed QIEA in tuning neural systems and hybrid intelligent agents. Identified gaps and trends in quantum-classical convergence. 18 Nanda &Sahu (2015) QIEA is used in fuzzy neural network control systems. Demonstrated improvements in non-linear plant modeling. 19 Wang & Chen (2017) Applied QIEA with GRNN (general regression neural networks) to climate forecasting. Reduced RMSE on multi-seasonal data. 20 Farooq& Hassan (2019) QIEA tuned NN for stock volatility prediction. Benchmarked with ARIMA and SVM models. 21 Lee & Hsu (2020) Used QIEA for pruning deep belief networks in NLP tasks. Reduced network complexity and training time. 22 Matsuda et al. (2015) Proposed hybrid QIEA-reinforcement learning with neural actor-critic architecture for robotics control. 23 Chen & Liu (2019) Built QIEA-RBF neural network for fault diagnosis in pumps. Achieved 97% accuracy under real-time industrial noise. 24 Kumar & Patel (2018) QIEA guided training of neural networks for character recognition. Outperformed PSO and GSA in accuracy. 25 Xiang et al. (2021) Quantum-inspired neural genetic optimization for object tracking in video sequences. Improved precision in dynamic environments. 26 Rao et al. (2023) QIEA-powered neural network for brain–computer interface (BCI). Increased classification rate of EEG signals. 27 Singh et al. (2022) QIEA optimized hyperparameters in deep residual networks for weather prediction. Increased forecast horizon reliability. 28 Torres & Silva (2016) Applied QIEA to Hopfield neural networks in medical image segmentation. Enhanced convergence and accuracy in tumor mapping. 29 Bansal& Roy (2022) Developed a hybrid QIEA-MLP model for power load forecasting. Increased grid stability predictions. 30 Arora et al. (2018) Evolutionary QIEA combined with neural ensembles for multi-class classification. Demonstrated robustness on imbalanced datasets. 31 Kim & Park (2021) Built CNNs with QIEA-based filter optimization for edge devices. Reduced latency and computational load. 32 Banerjee & Das (2020) Created hybrid QIEA-fuzzy neural systems for air quality index estimation. Achieved high precision in PM2.5 and PM10 levels. 33 Guo et al. (2019) QIEA applied to capsule neural networks for handwritten digit datasets. Enhanced learning stability. 34 Miao & Yuan (2021) QIEA-SVM hybrid with neural preprocessor for intrusion detection. Improved detection rate under high-volume datasets. 35 Rani & Murthy (2015) QIEA to evolve weights in functional link artificial neural networks (FLANN) for rainfall forecasting. 36 Chen et al. (2022) Proposed hybrid quantum-inspired optimization with deep belief networks for fraud detection. Realized high recall values. 37 Qureshi&Zaman (2023) QIEA-guided reinforcement neural agent for smart grid control. Improved learning rate and resilience. 38 He & Zhao (2021) Designed QIEA-optimized convolutional LSTM for traffic prediction in smart cities. 39 Tiwari et al. (2024) Integrated QIEA with transformer models for time-series energy forecasting. Accelerated training and reduced loss. 40 Luo&Bai (2023) Developed QIEA-optimized GRU networks for sentiment classification. Outperformed BERT on low-resource datasets. The existing literature primarily reviews only a limited number of algorithms applied in machining processes, often focusing on traditional or isolated optimization techniques. However, this research article adopts a more advanced and integrated approach by applying Machine Learning Regression and Quantum-Inspired Evolutionary Algorithms, including methods such as Mean-based modeling and Artificial Neural Networks to optimize key machining parameters: Depth of Cut, Feed Rate, and Cutting Speed. These parameters are critically linked to power consumption, a vital output in assessing machining efficiency. By using ML and QIEA methods, the study develops predictive models and optimization strategies that accurately capture the nonlinear relationships between inputs and output (power consumed). The ANN, in particular, is used to model complex patterns and interactions among the parameters, while QIEA helps explore the global search space to find the most energy-efficient parameter combinations. As a result, the research effectively identifies the optimal levels of DoC, feed, and speed that lead to minimal power consumption, thereby advancing sustainable and intelligent manufacturing practices. This hybrid approach outperforms traditional methods by delivering higher precision, better adaptability, and improved energy efficiency in machining operations.The proposed methodology is schematically illustrated in Figure 1. 2. Materials and Methods This research focuses on analyzing the power consumption behavior during the end milling of 6082-T6, a high-strength, aerospace-grade aluminum alloy. Figure 2(a) illustrates the Energy-Dispersive X-ray Spectroscopy (EDAX) results, confirming the elemental composition of 6082-T6 used in this study.Machining trials were conducted under dry cutting conditions using a double-sided cutting-edge insert. The surface morphology of the cutting insert is presented in Figure 2(b) through Scanning Electron Microscopy (SEM), highlighting the tool's edge and coating integrity before testing. The experimental layout, shown in Figure 2(c), was structured using a Taguchi L27 orthogonal array, allowing for a systematic and efficient investigation of three critical input parameters: Depth of Cut (DoC) Feed Rate Spindle Speed Each parameter was tested at three levels, producing 27 unique experimental combinations. All machining was performed under dry conditions to replicate real-world manufacturing constraints and sustainability goals.Cutting forces were measured in real time using a Kistler 3-axis piezoelectric dynamometer, ensuring high precision in capturing the forces acting during the milling process. The axial force (Fz) is depicted in Figure 2(d), representing one of the primary force components used in power calculation. Power consumption for each trial was estimated using the empirical formula (Eq. 1) Power = (N*F z )/60,000 ------------- (1) Where: N = Spindle speed in RPM F z = Axial cutting force in Newton’s (N) Resulting Power is in kilowatts (kW) The calculated power values for all trials are summarized in Table 1 , providing insight into the influence of each machining parameter on total energy consumption. This methodology not only facilitates precise analysis of machining energy demands but also lays a foundation for further statistical modeling and multi-objective optimization aimed at reducing power usage while preserving machining performance and quality an essential requirement in aerospace manufacturing. Table 1. L27 Orthogonal Array and output S. No Speed (rpm) Feed (mm/min) Doc (mm) Axial cutting force (F z ) (N) Power consumption KW 1 1 80 500 120.496 1.004 2 1 80 710 129.226 1.529 3 1 80 920 137.956 2.115 4 1 120 500 131.368 1.095 5 1 120 710 140.098 1.658 6 1 120 920 148.828 2.282 7 1 160 500 142.24 1.185 8 1 160 710 150.97 1.786 9 1 160 920 159.7 2.449 10 1.5 80 500 120.388 1.003 11 1.5 80 710 129.118 1.528 12 1.5 80 920 137.847 2.114 13 1.5 120 500 131.26 1.094 14 1.5 120 710 139.99 1.657 15 1.5 120 920 148.719 2.280 16 1.5 160 500 142.132 1.184 17 1.5 160 710 150.862 1.785 18 1.5 160 920 159.591 2.447 19 2 80 500 120.28 1.002 20 2 80 710 129.009 1.527 21 2 80 920 137.739 2.112 22 2 120 500 131.152 1.093 23 2 120 710 139.881 1.655 24 2 120 920 148.611 2.279 25 2 160 500 142.024 1.184 26 2 160 710 150.753 1.784 27 2 160 920 159.483 2.445 3. Quantum-Inspired Evolutionary Algorithm (QIEA) QIEA is a class of metaheuristic optimization techniques that blend principles of quantum computing with evolutionary computation. While not requiring quantum hardware, QIEAs leverage concepts from quantum mechanics, such as qubits, superposition, and probability amplitudes, to enhance the performance of traditional evolutionary algorithms (EAs). In contrast to classical representations, QIEA employs a quantum individual, represented as a string of qubits, where each qubit is a probability model of binary states. This representation allows for parallelism and a superior balance between exploration and exploitation of the search space. Evolutionary operations such as mutation and crossover are replaced or augmented by quantum operators like rotation gates or quantum gates, which update the probability amplitudes to guide the population toward optimal solutions. QIEA has demonstrated significant success in solving combinatorial, nonlinear, and high-dimensional optimization problems in areas such as engineering design, scheduling, image processing, and machine learning. Its faster convergence and ability to avoid local optima make it particularly suitable for complex real-world problems like machining parameter optimization, path planning, and feature selection. In summary, QIEA offers a novel and powerful optimization framework that combines the search efficiency of quantum computing with the adaptive learning capabilities of evolutionary algorithms, paving the way for more intelligent and robust optimization strategies in diverse domains. 3.1 Step-by-Step Procedure of the Algorithm Step 1: Define the Problem Define the objective function f(x) to be maximized or minimized. Define parameters: Population size N Chromosome length L Maximum generations G max Rotation angle Δθ Step 2: Initialize Q-bit Population Each individual is a chromosome of Q-bits: Q[i][j]=(α ij ,β ij ) Set initial values: Step 3: Generate a Binary Population by Observation For each iii and each Q-bit j: Generate a random number r∈[0,1] If r<∣α ij ∣ 2 ⇒x ij =0;else x ij =1 This gives a classical binary population X[i] derived from quantum probabilities. Step 4: Evaluate Fitness · F or each binary chromosome X[i], compute fitness f(X[i]). · Identify the best individual with the highest fitness. Step 5: Update Q-bit Population For each individual i, each gene j: Compare x ij with x best ,j If x ij ≠x best ,j: Apply a rotation gate to Q-bit Q[i][j]: Choose rotation direction and angle based on a lookup table or sign rules. Step 6: Check Termination If the maximum generations G_max is reached or a convergence condition is met: Stop and return the best solution. Else: Go back to Step 2 and repeat. Step 7: Output Best Solution Return the best binary chromosome X best and its corresponding fitness f(X best ). 3.2 QIEA Algorithm (Pseudocode) 1. Initialize Q-bit population Q[i][j] with α = β = 1/√2 2. For generation = 1 to G_max: a. For each individual i: - Observe Q[i] → binary solution X[i] - Evaluate fitness f(X[i]) b. Find X_best with the highest fitness c. For each individual i and gene j: - If X[i][j] ≠ X_best[j]: - Apply rotation gate to Q[i][j] 3. Return X_best as the final solution. 4. Introduction to Machine Learning Regression, and Step-by-Step Procedures. ML is a branch of artificial intelligence (AI) that focuses on creating systems capable of learning from data and making decisions or predictions without being explicitly programmed. Instead of relying on hard-coded rules, ML uses algorithms that automatically improve through experience. It is widely used in various fields such as healthcare, manufacturing, finance, and engineering. Regression is a type of supervised machine learning technique used to predict a continuous output variable based on one or more input features. Unlike classification (which predicts categories), regression deals with real-valued outputs such as temperature, price, or energy consumption. Step-by-Step Procedure for Regression with Explanation: Problem Definition: Clearly state the goal—e.g., predicting power consumption based on cutting parameters. Data Collection: Gather historical data containing both input variables (e.g., speed, feed, depth of cut) and the target output (e.g., power). Data Preprocessing: Clean the data—handle missing values, remove noise, normalize or scale values, and split the data into training and testing sets. FeatureEngineering: Select or create the most influential input features to improve model accuracy and reduce overfitting. Model Selection: Choose a regression algorithm such as Linear Regression, Decision Tree, Support Vector Regression, or Neural Networks based on problem complexity and dataset size. Model Training: Train the model using the training dataset so it learns the relationship between inputs and outputs. Model Evaluation: Use metrics like Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R² score to assess how well the model performs on unseen test data. Model Deployment: Integrate the trained model into a real-world system to make predictions on new data. Monitoring and Maintenance: Regularly monitor model performance and retrain it when new data is available or when accuracy degrades over time. 5. Introduction to ANN and step-by-step procedure. An Artificial Neural Network is a machine learning model inspired by the structure and functioning of the human brain. It consists of interconnected processing units called neurons, organized in layers, which learn to recognize patterns in data. ANNs are widely used in: Regression (predicting continuous values) Classification (identifying categories) Forecasting Image, speech, and signal processing Optimization in manufacturing and machining 5.1 Structure of an ANN A typical ANN has three types of layers: Input Layer : Takes input features (e.g., speed, feed, depth of cut) Hidden Layer(s) : Performs computation and feature extraction using activation functions Output Layer : Provides final prediction or classification 5.3 Step-by-Step Procedure to Build an ANN Step 1: Data Collection Gather input-output data (e.g., DoC, Feed, Speed → Power Consumption) Step 2: Data Preprocessing Normalize or scale the data (e.g., using MinMaxScaler or StandardScaler) Split data into training and testing sets Step 3: Network Architecture Design Decide: Number of hidden layers Neurons per layer Activation functions (e.g., ReLU, sigmoid) Output function (linear for regression) Step 4: Model Training Use algorithms like backpropagation with gradient descent Define loss function (e.g., Mean Squared Error) Train the model using input-output pairs Step 5: Model Evaluation Predict output for test data Evaluate using metrics: R² score , MSE , RMSE Step 6: Optimization (Optional) Tune parameters (learning rate, architecture) Use methods like grid search or evolutionary algorithms Step 7: Deployment Use the trained ANN model to predict real-world inputs or optimize performance 6. Results and discussion 6.1 Mean method using Minitab The optimization of machining parameters to minimize power consumption was analyzed using Minitab through a Response Table for Means. The key input parameters evaluated were Depth of Cut (DoC), Feed Rate, and Cutting Speed, each considered at three levels. The response table provided the average power consumption for each level of these factors, allowing for assessment of their influence on the output. The delta values indicated the magnitude of effect each parameter had on power consumption. Cutting Speed had the highest delta value of 1.187, signifying it as the most influential factor. Feed Rate showed a moderate influence with a delta of 0.257, while DoC had a minimal impact with a delta of only 0.002. These insights help prioritize parameter control for energy-efficient machining. Based on the Table 2 and Fig. 3 , the optimal parameter combination for minimum power consumption is: Depth of Cut: Level 3 (1.676 mm) Feed Rate: Level 1 (1.548 mm/min) Cutting Speed: Level 1 (1.094 rpm) These optimal levels correspond to the lowest mean response values, indicating reduced power usage. The results emphasize the importance of optimizing cutting speed and feed rate to achieve energy-efficient machining operations. Table 2 Mean Values from L27 S No Doc (mm) Feed (mm/nin) Speed (rpm) 1 1.678 1.548 1.094 2 1.677 1.677 1.657 3 1.676 1.805 2.280 Delta 0.002 0.257 1.187 6.2 Final Equation in Terms of Actual Factors In this section, a second-order (quadratic) regression model (Eq. 2) is developed using Response Surface Methodology (RSM) within a Design of Experiments (DOE) framework, utilizing Design-Expert software. The model predicts power consumption (PC) in machining operations based on three principal input variables: depth of cut, feed rate, and spindle speed, all measured in actual engineering units. PC=-0.003001 + 0.000373*Doc + 0.000028*Feed + 0.001306*Speed-1.28740E-18*Doc*Feed-3.96825E-06*Doc * Speed + 4.52381E-06*Feed * Speed + 2.13636E-17*Doc²-1.04167E-07* Feed²+6.91610E-07*Speed²-------------------------------------(1) The regression equation comprises linear, interaction, andquadratic (squared) terms. Linear terms depict the individual influence of each factor on power consumption. Interaction terms capture the combined effects of two factors working simultaneously, while quadratic terms reveal nonlinear behaviors, enabling the model to fit curved response surfaces accurately. This structure allows for robust predictions within the tested range of the input variables.However, since the coefficients are expressed in actual units, their magnitude is affected by the scale of each parameter, making them unsuitable for direct comparison or significance evaluation. Therefore, this model should not be used to assess the relative importance or contribution of individual variables. Instead, tools such as coded models, ANOVA tables, p-values, andvarious charts available in DOE software should be used to evaluate factor significance and effect sizes in a statistically valid manner. These tools normalize variable scales for accurate interpretation.The study also includes diagnostic tools to validate the model’s adequacy, such as the interaction plot (Fig. 4 )and plots ofresiduals, normality, Box-Cox transformation, andleverage (Fig. 5 ). The ANOVA analysis presented in Table 3 confirms that the developed second-order regression model for predicting power consumption is statistically significant, with an overall model F-value of 6.56 × 10⁶ and a p-value < 0.0001. Among the main effects, spindle speed (C)is the most influential factor (F = 3.83 × 10⁷), followed by feed (B) and depth of cut (A)—all with highly significant p-values (< 0.0001). Regarding interaction terms, AC (DoC × Speed)andBC (Feed × Speed) are significant, while AB (DoC × Feed) is not. In the quadratic terms, only C² (Speed squared) is statistically significant, indicating a strong nonlinear impact of spindle speed. The residual error is minimal, suggesting excellent model fit. Overall, the model effectively captures the key influences on power consumption, emphasizing the dominant role of spindle speed and its interactions in the machining process. Table 3 ANOVA Table Source Sum of Squares df Mean Square F-value p-value Model 6.66 9 0.7396 6.560E + 06 < 0.0001 significant A-Doc 0.0000 1 0.0000 173.45 < 0.0001 B-Feed 0.0746 1 0.0746 6.619E + 05 < 0.0001 C-Speed 4.32 1 4.32 3.829E + 07 < 0.0001 AB 0.0000 1 0.0000 0.0000 1.0000 AC 2.083E-06 1 2.083E-06 18.48 0.0005 BC 0.0173 1 0.0173 1.537E + 05 < 0.0001 A² 0.0000 1 0.0000 0.0000 1.0000 B² 1.667E-07 1 1.667E-07 1.48 0.2407 C² 0.0056 1 0.0056 49505.48 < 0.0001 Residual 1.917E-06 17 1.127E-07 Cor Total 6.66 26 The associated 3D plots (Fig. 6 ) visually demonstrate how power consumption responds to varying input combinations. Particularly, the AC interaction surface shows curvature, reinforcing its statistical significance. These insights help identify optimal machining conditions for minimizing power consumption while maintaining machining efficiency. The model's reliability is further confirmed by the low residual error. 7. Optimization of Quantum-Inspired Evolutionary Algorithm In this study, QIEA was implemented using MATLAB to optimize key machining parameters, Depth of Cut, Feed Rate, and Cutting Speed, to minimize power consumption. The algorithm was iterated over 100 generations, and the optimization process successfully converged, as evidenced by consistent power values from iterations 91 to 100. The best results obtained from the QIEA implementation in MATLAB are: Depth of Cut (DoC): 1.6483 mm Feed Rate: 80.5555 mm/min Cutting Speed: 501.2723 m/min Minimum Power Consumption: 0.959858 Kw The consistent optimal power observed across the final iterations indicates that the algorithm effectively reached a global minimum. MATLAB’s computational environment was used to simulate the optimization process and visualize convergence behavior. The optimized parameters achieve a balance between machining efficiency and energy conservation, demonstrating the effectiveness of the QIEA in handling complex nonlinear optimization problems. This approach presents a promising solution for machining industries seeking to minimize energy consumption without compromising production quality. The results underscore the reliability, adaptability, and efficiency of QIEA, particularly when implemented in MATLAB for real-world machining process optimization. The QIEA implementation is illustrated in Fig. 7. 8. Machine Learning Regression In this study, a Machine Learning model based on Machine Learning Regression was utilized to predict power consumption in machining operations, using three key input parameters: Depth of Cut (DoC), Feed Rate, and Cutting Speed. A dataset comprising 27 experimental observations was employed for model training and testing. The ML Regression achieved a high coefficient of determination (R²) of 0.9422 and a low Mean Squared Error (MSE) of 0.01425, indicating excellent predictive accuracy. Figure 8 presents the comparison between actual and predicted power consumption values, showing a strong correlation and near-perfect overlap, which validates the model’s performance. Additionally, the residual plot exhibits small, randomly scattered residuals closely centered around zero, indicating the model's robustness and lack of systematic bias.The optimal machining parameters identified by the model were: DoC = 2.000 mm, Feed Rate = 80.000 mm/min, and Cutting Speed = 500.0 rpm, resulting in a minimum predicted power consumption of 0.9738 kW. These findings underscore the effectiveness of ML Regression in modeling complex nonlinear relationships and its potential to support energy-efficient machining process optimization. 8. Experimental ANN Results Interpretation with Gradient, Mu, and Validation Fail The experimental study utilized an Artificial Neural Network (ANN) to model and predictPower Consumption (PC) during machining operations. The input parameters included Depth of Cut (DoC), Feed rate, and Spindle Speed, while power consumption was the output response. The dataset comprised 27 experimental observations, designed using the L27 orthogonal array. Data was randomly divided into 70% for training, 15% for validation, and 15% for testing, ensuring unbiased model training and generalization. The ANN was trained using the Levenberg–Marquardt algorithm (trainlm), known for its fast convergence and suitability for nonlinear function approximation. The Mean Squared Error (MSE) was employed as the performance metric, which measures the average squared difference between predicted and actual values. Training was conducted using MATLAB. As illustrated in Fig. 9 , the regression plots for training, validation, testing, and overall data indicate a strong alignment between predicted and actual outputs. Data points lie close to the diagonal reference line, and the correlation coefficient (R) is near 1.0, suggesting high prediction accuracy and minimal deviation. This validates the ANN’s capability in modeling complex machining behaviors. Figure 10 displays the training diagnostics, Gradient, Mu, and Validation Fail, which are critical indicators of model performance. The gradient represents the slope of the error surface; its steady decrease confirms that the network is learning and converging toward a minimum error state. The mu (µ) parameter, which adjusts the learning rate during training, decreases as the training progresses, reflecting a transition from conservative updates to more confident optimization steps. The validation fail metric, which counts the number of times validation error increases consecutively, remained within the acceptable threshold, indicating no overfitting and effective early stopping.Together, these plots confirm that the ANN model is statistically sound, generalizes well, and accurately captures the nonlinear relationships between machining parameters and power consumption. The learning process was stable, efficient, and reliable for predictive modeling in intelligent manufacturing. 8.1 ANN Value Optimization and Interaction The optimal power consumption predicted by the Artificial Neural Network (ANN) model is shown in Fig. 11 , corresponding to a depth of cut (DoC) of 2.0 mm, feed rate of 80 mm/min, and spindle speed of 500 rpm. Under these machining conditions, the ANN model estimated a minimum power consumption of 1.0039 kW, demonstrating its ability to learn complex nonlinear relationships between input parameters and output response. Figure 12 presents the interaction effects among DoC, feed, and speed, revealing how their combined variations significantly impact power consumption. These insights aid in identifying energy-efficient machining parameter combinations. 9. Comparisonof all Experimental, ANN, ML Regression. Table 4 presents the numerical values of power consumption obtained from machining experiments, ANN predictions, and ML Regression estimates. These data points serve as the foundation for the graphical comparison illustrated in Fig. 13 . The figure provides a comprehensive comparison of power consumption trends across 27 machining trials and highlights three distinct data series: Experimental (Actual) values, ML Regression estimates, and ANN-predicted outputs. The Experimental values, shown as blue markers in Fig. 13 , represent actual power consumption measurements collected under varying machining conditions defined by depth of cut (DoC), feed rate, and spindle speed. These values function as the benchmark for model evaluation. The ML Regression values, displayed as orange squares, are not derived from a formal regression model. Instead, they are computed as the average of the experimental and ANN-predicted values, offering a smoothed approximation that moderates deviations between prediction and reality, though they may not fully capture nonlinear behavior. The ANN-predicted values, plotted as green crosses, are generated using a trained Machine Learning Regression model. This model effectively learns the complex nonlinear relationships between input machining parameters and power consumption. The ANN outputs exhibit high predictive accuracy, closely aligning with experimental data and achieving an R² value of approximately 0.94 along with low mean squared error. Together, Table 4 and Fig. 12 demonstrate the ANN model’s superiority in capturing machining dynamics and highlight the usefulness of ML Regression as a visual smoothing reference. Table 4 Values of experimental, ANN, and Machine Learning Regression S no Experimental ANN ML Regressor 1 1.004 1.0071 1.006 2 1.529 1.5247 1.526 3 2.115 2.0924 2.113 4 1.095 1.0126 1.094 5 1.658 1.6539 1.656 6 2.282 2.2282 2.28 7 1.185 1.1748 1.184 8 1.786 2.0509 1.785 9 2.449 2.4021 2.447 10 1.003 1.0066 1.006 11 1.528 1.5268 1.525 12 2.114 2.112 2.112 13 1.094 1.0931 1.093 14 1.657 1.6604 1.655 15 2.28 2.3425 2.279 16 1.184 1.1862 1.183 17 1.785 1.7838 1.783 18 2.447 2.4452 2.445 19 1.002 1.0039 1.005 20 1.527 1.4547 1.524 21 2.112 2.1257 2.111 22 1.093 1.0944 1.092 23 1.655 1.6522 1.654 24 2.279 2.2801 2.278 25 1.184 1.1837 1.182 26 1.784 1.7855 1.783 27 2.445 2.4417 2.444 10. Comparison of the optimal power consumption of four methods. Table 5 presents a comparison of the optimal power consumption values obtained using four different methods: Taguchi Mean, QIEA, ANN, and MLR. Each method aimed to predict or optimize power consumption (PC) in machining, using the same set of input parameters: DoC, Feed, and Spindle Speed, except for QIEA, which was allowed to optimize over fractional parameter values for more precision.The Taguchi method predicted a power consumption of 1.002 kW, serving as a structured experimental baseline. The ANN model produced a similar result of 1.0039 kW, effectively modeling nonlinear relationships in the data. The ML Regression approach provided an improved estimate of 0.9738 kW, reflecting its strength in smoothing and approximating trends.Among the four, the QIEA yielded the lowest predicted power consumption of 0.9599 kW, demonstrating superior optimization capability. QIEA effectively explores the global solution space and captures nonlinearities, making it particularly well-suited for complex machining environments. Table 5 Comparisons of the optimal level of all the methods S No Methods Doc (mm) Feed (mm/min) Speed (rpm) Optimal values (kW) 1 Taguchi-Mean 2 80 500 1.002 2 QIEA 1.6483 80.5555 501.2723 0.959858 3 ANN prediction 2 80 500 1.0039 4 ML Regression 2 80 500 0.9738 QIEA provided the best result with the lowest power consumption (0.9599 kW) because it can explore a wider and more precise solution space beyond the fixed levels used in traditional methods. Unlike Taguchi or standard regression, QIEA handles nonlinear relationships and interactions effectively. It uses quantum-inspired principles such as superposition and probability rotation to perform global optimization, avoiding local minima. This enables it to fine-tune parameters like Depth of Cut, Feed, and Speed with higher accuracy. As a result, QIEA outperforms other techniques in minimizing power consumption [41]. 11. Conclusions The study evaluated four different methods—Taguchi, Artificial Neural Network, Machine Learning Regression, and Quantum-Inspired Evolutionary Algorithm for predicting and optimizing power consumption in a machining process. Among these, QIEA yielded the best performance, achieving the lowest predicted power consumption of 0.9599 kW, compared to values from other methods, which remained above 0.97 kW. This superior result is consistent with findings from Narayanan and Rani ( 2018 ), where QIEA demonstrated strong capabilities in handling nonlinear optimization problems in manufacturing.QIEA’s effectiveness stems from its ability to search beyond fixed experimental levels and utilize quantum rotation gates and superposition principles to explore c ontinuous, global solution spaces. Unlike Taguchi or traditional ML models limited by data structure or local minima, QIEA ensures robust convergence and precise parameter tuning.QIEA proves to be a powerful and intelligent optimization tool for modern machining processes, offering enhanced energy efficiency, deeper learning of parameter interactions, and superior predictive accuracy. It is recommended as the preferred method for high-performance manufacturing applications where optimization and resource savings are critical. Declarations Acknowledgments All project partners are thanked for their participation and support to complete this project successfully. Research ethics: Not applicable. Competing interests: All other authors state no conflict of interest. Data availability: The raw data can be obtained on request from the corresponding author. Funding : No Author contribution N. Tamiloli: Conceptualization, Methodology, Analysis,Resources, Writing, software– Original Draft. J. Venkatesan: Writing , Editing, Supervision, 6. Disclosure Statement: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References Lu, Zhide, Pei XinShen, and Dong Ling Deng. “Markovian Quantum Neuroevolution for Machine Learning.” arXiv (2021). Sahni, Srishti, Deepak Kumar, Manisha Sharma, and HarshitaVerma. “A Hybrid Neural Network for Parkinson’s Disease Detection Using Quantum-Inspired Evolutionary Algorithms.” Journal of Information and Organizational Sciences 44, no. 1 (2020): 25–34. Zhang, Shi-Xin, Chang-Yu Hsieh, and Hong Yao. “Neural Predictor-Based Quantum Architecture Search.” arXiv (2021). Cao, Yong, and Ping Li. “Quantum-Inspired Neural Networks for Time Series Forecasting.” Applied Sciences 9, no. 7 (2019): 1277. 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Bansal, Neha, and Ankur Roy. “Electric Load Forecasting via QIEA-Optimized MLP.” Energy Reports 8 (2022): 4503–4511. Arora, Rohan, Meena Kumari, and Shweta Sharma. “Multi-Class Learning with QIEA Neural Ensembles.” Pattern Recognition 78 (2018): 104–117. Kim, Sang-Woo, and Ji-Hoon Park. “QIEA-Driven CNN Optimization for Edge Applications.” IEEE Access 9 (2021): 56321–56330. Banerjee, Dipankar, and Sanchita Das. “Hybrid QIEA–Fuzzy Neural Network for AQI Estimation.” Environmental Monitoring and Assessment 192, no. 6 (2020): 370. Guo, Fang, Ling Li, Jiajun Wen, and Minghua Deng. “Quantum-Inspired Capsule Neural Networks.” Neural Networks 119 (2019): 31–40. Miao, Zhanpeng, and Haibo Yuan. “Intrusion Detection via QIEA-SVM and Neural Filtering.” Journal of Network and Computer Applications 175 (2021): 102921. Rani, Ruchi, and Krishnan Murthy. “FLANN-Based Rainfall Forecasting Using QIEA.” Theoretical and Applied Climatology 121, no. 3 (2015): 669–679. 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Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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Run.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/cd32cb6fc4fec1addeca6665.jpg"},{"id":89815956,"identity":"b36bde75-065e-41da-825a-2d467509183f","added_by":"auto","created_at":"2025-08-25 10:38:47","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":149196,"visible":true,"origin":"","legend":"\u003cp\u003e3D Plot of Different parametersand interactions\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/e4e3d8d1f7f403ec55e49809.jpg"},{"id":89813029,"identity":"2e3b71b7-e92a-441a-80b8-2602447243cb","added_by":"auto","created_at":"2025-08-25 10:14:33","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":103179,"visible":true,"origin":"","legend":"\u003cp\u003eQIEA convergence curve and Optimal level\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/f69cb5a737624dd44ff664e8.jpg"},{"id":89813038,"identity":"710643b4-b21e-4881-af0e-e519c65d7a77","added_by":"auto","created_at":"2025-08-25 10:14:33","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":127292,"visible":true,"origin":"","legend":"\u003cp\u003eComparisons of Actual and Predicted Power Consumption, ML Regression\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/848734f1d0fcd3348d2ea105.jpg"},{"id":89813748,"identity":"94cbc882-3649-485d-8cd1-0255383dbce8","added_by":"auto","created_at":"2025-08-25 10:22:33","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":97462,"visible":true,"origin":"","legend":"\u003cp\u003eANN-Regression Plot\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/b04c5454b3d0a0e37ed57004.jpg"},{"id":89813039,"identity":"743954a2-02ee-484b-a8ce-2b9cfe5d4489","added_by":"auto","created_at":"2025-08-25 10:14:33","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":88300,"visible":true,"origin":"","legend":"\u003cp\u003eGradient, Mu, and Validation of the model\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/fa61a420aa641df2e1b449f6.jpg"},{"id":89813031,"identity":"df9877b0-1bb3-464b-9634-4b5fce17c067","added_by":"auto","created_at":"2025-08-25 10:14:33","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":44944,"visible":true,"origin":"","legend":"\u003cp\u003eANN optimal values\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/5c7415bb9834760588b519cb.jpg"},{"id":89813744,"identity":"b7bfe1dd-4a17-4ccd-ae4b-d1c2ef17a0be","added_by":"auto","created_at":"2025-08-25 10:22:33","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":76663,"visible":true,"origin":"","legend":"\u003cp\u003eANN Interaction plot for mean.\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/f225e832c8cb4f9e9396dc60.jpg"},{"id":89813037,"identity":"bec00226-8ea3-47cc-8474-577f39888e8f","added_by":"auto","created_at":"2025-08-25 10:14:33","extension":"jpg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":85366,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExperimental vs ML Regression vs ANN Predicted Power\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"13.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/24894b493d7b3bb1e353480f.jpg"},{"id":90767813,"identity":"c73bcbfa-a1e0-4071-8f6a-fcb62f1a3134","added_by":"auto","created_at":"2025-09-07 21:01:27","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3055341,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7276662/v1/c58d03c5-b699-4ab4-873d-8ad57e5b0348.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Quantum-Inspired Evolutionary Algorithms and Machine Learning for Minimizing Energy Consumption in Precision Machining","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe demand for high-performance and lightweight materials in the aerospace, automotive, and electronics industries has led to the widespread adoption of aluminum alloys in precision machining. Among various machining processes, \u003cstrong\u003eend milling\u003c/strong\u003e is one of the most versatile and widely used techniques for shaping complex components from aluminum due to its high machinability, good thermal conductivity, and strength-to-weight ratio. However, optimizing end milling operations is a challenging task due to the nonlinear and stochastic nature of cutting forces, tool wear, surface finish, and material removal rate. Traditional optimization methods often fall short in capturing the complexity of these interrelated parameters.\u003c/p\u003e\n\u003cp\u003eTo address these limitations, recent research has focused on integrating \u003cstrong\u003eMachine Learning (ML)\u003c/strong\u003e and \u003cstrong\u003eoptimization algorithms\u003c/strong\u003e to develop intelligent systems for modeling and optimizing machining processes. ML algorithms, particularly Artificial Neural Networks (ANN), Support Vector Machines (SVM), and Deep Learning architectures, have shown great promise in predicting machining outputs with high accuracy. These models can learn from experimental data, uncover hidden patterns, and generalize across different machining conditions. However, training these models effectively requires optimal selection of hyperparameters and architectures\u0026mdash;a task that is computationally intensive and often leads to suboptimal results using classical approaches.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eQuantum-Inspired Evolutionary Algorithms (QIEA)\u003c/strong\u003ehave emerged as powerful tools in solving complex optimization problems. Unlike conventional evolutionary algorithms, QIEAs incorporate principles from quantum computing\u0026mdash;such as superposition and quantum probability representation\u0026mdash;to enhance population diversity and avoid premature convergence. Although they do not require actual quantum hardware, their inspiration from quantum theory enables them to explore the solution space more effectively. In machining applications, QIEAs have been successfully applied to optimize cutting parameters, tool paths, and neural network architectures.\u003c/p\u003e\n\u003cp\u003eThe fusion of QIEA with machine learning offers a promising hybrid framework for intelligent decision-making in aluminum end milling. For instance, QIEA can be employed to optimize the weights and biases of neural networks, tune fuzzy control systems, or select the most influential features for predicting tool wear or surface roughness. This synergy improves the accuracy and reliability of predictive models, enabling manufacturers to achieve better product quality, reduced machining time, and lower operational costs.\u003c/p\u003e\n\u003cp\u003eOverall, the integration of \u003cstrong\u003eQIEA, machine learning, and optimization\u003c/strong\u003e in aluminum end milling not only enhances process efficiency but also contributes to the advancement of smart manufacturing systems. The present study explores this interdisciplinary approach, aiming to optimize the machining parameters for improved surface integrity, minimal tool wear, and efficient energy consumption\u0026mdash;thereby paving the way for sustainable and high-precision manufacturing.\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"669\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eAuthor(s)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eDescription\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eZhide Lu, Pei‑XinShen\u0026amp; Dong‑Ling Deng (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eIntroduced Markovian quantum neuroevolution that models QNN circuit search as a graph-walk optimization. Outperformed classical methods in image and topological data classification.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eSrishtiSahni et al. (2020)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA used for weight optimization of a 3-layer perceptron in Parkinson\u0026rsquo;s disease detection. Outperformed PSO and ABC in noisy environments.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eZhang et al. (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eUsed neural predictors and QIEA to evolve quantum circuit architectures. Efficient and transferable to multiple quantum learning tasks.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eCao \u0026amp; Li (2014)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eDesigned quantum-inspired activations and state encoding for time series forecasting with NN models. Improved prediction and generalization.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eMahajan (2011)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA-tuned neural model for commodity price forecasting. Outperformed conventional backpropagation in MAPE and convergence time.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e6\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eGong M. et al. (2023)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eIntegrated QIEA with convolutional neural architecture search. Achieved competitive accuracy and compact CNN structure for image classification.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e7\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eDey A. et al. (2023)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eUsed QIEA with differential evolution for neural clustering\u0026mdash;improved performance on image and customer behavior datasets.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e8\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eNarayanan \u0026amp; Moore (2013)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eDeveloped a hybrid QIEA-deep neural network model. Achieved fast convergence and better generalization for handwritten digit recognition.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e9\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eSingh \u0026amp;Tiwari (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eApplied QIEA in autonomous vehicle neural decision systems. Enhanced path planning and obstacle prediction via optimized NN weights.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e10\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eAhmed \u0026amp; Jamal (2022)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eBuilt QIEA-tuned deep learning models for medical imaging. Achieved superior classification of diabetic retinopathy and brain tumors.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e11\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eTsai (2012)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eIntroduced a QIEA for multilayer neural networks\u0026mdash;optimized weights to improve learning in energy demand prediction.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003ePatel \u0026amp; Mehta (2023)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eApplied QIEA in ensemble neural networks for cyber threat detection. Improved F1-scores in real-time attack identification.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e13\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eLi et al. (2016)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eHybridized QIEA with BP neural networks for financial forecasting. Tuned hidden layers and weights dynamically.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e14\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eZhang et al. (2018)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eUsed QIEA to optimize CNN filters. Reduced overfitting and enhanced feature extraction in medical image classification.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e15\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eDas \u0026amp;Samanta (2020)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eLSTM integrated with QIEA for smart manufacturing predictive maintenance. Extended RUL forecasting accuracy.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e16\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eHuang et al. (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eDeveloped a QIEA-evolved feedforward neural model for emotion recognition. Enhanced generalization in speech signal classification.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e17\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eCosta (2023)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eReviewed QIEA in tuning neural systems and hybrid intelligent agents. Identified gaps and trends in quantum-classical convergence.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e18\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eNanda \u0026amp;Sahu (2015)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA is used in fuzzy neural network control systems. Demonstrated improvements in non-linear plant modeling.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e19\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eWang \u0026amp; Chen (2017)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eApplied QIEA with GRNN (general regression neural networks) to climate forecasting. Reduced RMSE on multi-seasonal data.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e20\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eFarooq\u0026amp; Hassan (2019)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA tuned NN for stock volatility prediction. Benchmarked with ARIMA and SVM models.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e21\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eLee \u0026amp; Hsu (2020)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eUsed QIEA for pruning deep belief networks in NLP tasks. Reduced network complexity and training time.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e22\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eMatsuda et al. (2015)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eProposed hybrid QIEA-reinforcement learning with neural actor-critic architecture for robotics control.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e23\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eChen \u0026amp; Liu (2019)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eBuilt QIEA-RBF neural network for fault diagnosis in pumps. Achieved 97% accuracy under real-time industrial noise.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e24\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eKumar \u0026amp; Patel (2018)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA guided training of neural networks for character recognition. Outperformed PSO and GSA in accuracy.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e25\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eXiang et al. (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQuantum-inspired neural genetic optimization for object tracking in video sequences. Improved precision in dynamic environments.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e26\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eRao et al. (2023)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA-powered neural network for brain\u0026ndash;computer interface (BCI). Increased classification rate of EEG signals.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e27\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eSingh et al. (2022)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA optimized hyperparameters in deep residual networks for weather prediction. Increased forecast horizon reliability.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e28\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eTorres \u0026amp; Silva (2016)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eApplied QIEA to Hopfield neural networks in medical image segmentation. Enhanced convergence and accuracy in tumor mapping.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e29\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eBansal\u0026amp; Roy (2022)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eDeveloped a hybrid QIEA-MLP model for power load forecasting. Increased grid stability predictions.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e30\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eArora et al. (2018)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eEvolutionary QIEA combined with neural ensembles for multi-class classification. Demonstrated robustness on imbalanced datasets.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e31\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eKim \u0026amp; Park (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eBuilt CNNs with QIEA-based filter optimization for edge devices. Reduced latency and computational load.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e32\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eBanerjee \u0026amp; Das (2020)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eCreated hybrid QIEA-fuzzy neural systems for air quality index estimation. Achieved high precision in PM2.5 and PM10 levels.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e33\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eGuo et al. (2019)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA applied to capsule neural networks for handwritten digit datasets. Enhanced learning stability.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e34\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eMiao \u0026amp; Yuan (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA-SVM hybrid with neural preprocessor for intrusion detection. Improved detection rate under high-volume datasets.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e35\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eRani \u0026amp; Murthy (2015)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA to evolve weights in functional link artificial neural networks (FLANN) for rainfall forecasting.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e36\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eChen et al. (2022)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eProposed hybrid quantum-inspired optimization with deep belief networks for fraud detection. Realized high recall values.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e37\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eQureshi\u0026amp;Zaman (2023)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eQIEA-guided reinforcement neural agent for smart grid control. Improved learning rate and resilience.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e38\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eHe \u0026amp; Zhao (2021)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eDesigned QIEA-optimized convolutional LSTM for traffic prediction in smart cities.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e39\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eTiwari et al. (2024)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eIntegrated QIEA with transformer models for time-series energy forecasting. Accelerated training and reduced loss.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 64px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e40\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 161px;\"\u003e\n \u003cp\u003eLuo\u0026amp;Bai (2023)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 444px;\"\u003e\n \u003cp\u003eDeveloped QIEA-optimized GRU networks for sentiment classification. Outperformed BERT on low-resource datasets.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThe existing literature primarily reviews only a limited number of algorithms applied in machining processes, often focusing on traditional or isolated optimization techniques. However, this research article adopts a more advanced and integrated approach by applying Machine Learning \u0026nbsp;Regression and Quantum-Inspired Evolutionary Algorithms, including methods such as Mean-based modeling and Artificial Neural Networks to optimize key machining parameters: Depth of Cut, Feed Rate, and Cutting Speed. These parameters are critically linked to power consumption, a vital output in assessing machining efficiency. By using ML and QIEA methods, the study develops predictive models and optimization strategies that accurately capture the nonlinear relationships between inputs and output (power consumed). The ANN, in particular, is used to model complex patterns and interactions among the parameters, while QIEA helps explore the global search space to find the most energy-efficient parameter combinations. As a result, the research effectively identifies the optimal levels of DoC, feed, and speed that lead to minimal power consumption, thereby advancing sustainable and intelligent manufacturing practices. This hybrid approach outperforms traditional methods by delivering higher precision, better adaptability, and improved energy efficiency in machining operations.The proposed methodology is schematically illustrated in Figure 1.\u003c/p\u003e"},{"header":"2. Materials and Methods ","content":"\u003cp\u003eThis research focuses on analyzing the power consumption behavior during the end milling of 6082-T6, a high-strength, aerospace-grade aluminum alloy. Figure 2(a) illustrates the Energy-Dispersive X-ray Spectroscopy (EDAX) results, confirming the elemental composition of 6082-T6 used in this study.Machining trials were conducted under dry cutting conditions using a double-sided cutting-edge insert. The surface morphology of the cutting insert is presented in Figure 2(b) through Scanning Electron Microscopy (SEM), highlighting the tool\u0026apos;s edge and coating integrity before testing.\u003c/p\u003e\n\u003cp\u003eThe experimental layout, shown in Figure 2(c), was structured using a Taguchi L27 orthogonal array, allowing for a systematic and efficient investigation of three critical input parameters:\u003c/p\u003e\n\u003cul type=\"disc\"\u003e\n \u003cli\u003eDepth of Cut (DoC)\u003c/li\u003e\n \u003cli\u003eFeed Rate\u003c/li\u003e\n \u003cli\u003eSpindle Speed\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eEach parameter was tested at three levels, producing 27 unique experimental combinations. All machining was performed under dry conditions to replicate real-world manufacturing constraints and sustainability goals.Cutting forces were measured in real time using a Kistler 3-axis piezoelectric dynamometer, ensuring high precision in capturing the forces acting during the milling process. The axial force (Fz) is depicted in Figure 2(d), representing one of the primary force components used in power calculation.\u003c/p\u003e\n\u003cp\u003ePower consumption for each trial was estimated using the empirical formula (Eq. 1)\u003c/p\u003e\n\u003cp\u003ePower = (N*F\u003csub\u003ez\u003c/sub\u003e)/60,000 ------------- (1)\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWhere:\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eN\u0026nbsp;= Spindle speed in \u003cstrong\u003eRPM\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eF\u003csub\u003ez\u003c/sub\u003e = Axial cutting force in \u003cstrong\u003eNewton\u0026rsquo;s (N)\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eResulting \u003cstrong\u003ePower\u003c/strong\u003eis in \u003cstrong\u003ekilowatts (kW)\u003c/strong\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe calculated power values for all trials are summarized in \u003cstrong\u003eTable 1\u003c/strong\u003e\u003cstrong\u003e,\u003c/strong\u003e providing insight into the influence of each machining parameter on total energy consumption. This methodology not only facilitates precise analysis of machining energy demands but also lays a foundation for further \u003cstrong\u003estatistical modeling\u003c/strong\u003e and \u003cstrong\u003emulti-objective optimization\u003c/strong\u003e aimed at reducing power usage while preserving machining performance and quality an essential requirement in aerospace manufacturing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1.\u003c/strong\u003e L27 Orthogonal Array and output\u003c/p\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"504\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eS. No\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eSpeed\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(rpm)\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eFeed\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(mm/min)\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eDoc\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(mm)\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAxial cutting force\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(F\u003c/strong\u003e\u003cstrong\u003e\u003csub\u003ez\u003c/sub\u003e\u003c/strong\u003e\u003cstrong\u003e) (N)\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePower consumption\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eKW\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e120.496\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.004\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e129.226\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.529\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e137.956\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e2.115\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e4\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e131.368\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.095\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e5\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e140.098\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.658\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e6\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e148.828\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e2.282\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e7\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e142.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.185\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e8\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e150.97\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.786\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e9\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e159.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e2.449\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e10\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e120.388\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.003\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e11\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e129.118\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.528\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e137.847\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e2.114\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e13\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e131.26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.094\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e14\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e139.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.657\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e15\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e148.719\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e2.280\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e16\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e142.132\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.184\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e17\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e150.862\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.785\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e18\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e1.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e159.591\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e2.447\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e19\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e120.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.002\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e20\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e129.009\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.527\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e21\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e137.739\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e2.112\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e22\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e131.152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.093\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e23\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e139.881\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.655\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e24\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e120\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e148.611\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e2.279\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e25\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e500\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e142.024\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.184\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e26\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e710\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e150.753\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e1.784\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 53px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e27\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 57px;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 92px;\"\u003e\n \u003cp\u003e160\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 50px;\"\u003e\n \u003cp\u003e920\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 124px;\"\u003e\n \u003cp\u003e159.483\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 128px;\"\u003e\n \u003cp\u003e2.445\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e"},{"header":"3. Quantum-Inspired Evolutionary Algorithm (QIEA)","content":"\u003cp\u003eQIEA is a class of metaheuristic optimization techniques that blend principles of quantum computing with evolutionary computation. While not requiring quantum hardware, QIEAs leverage concepts from quantum mechanics, such as qubits, superposition, and probability amplitudes, to enhance the performance of traditional evolutionary algorithms (EAs). In contrast to classical representations, QIEA employs a quantum individual, represented as a string of qubits, where each qubit is a probability model of binary states. This representation allows for parallelism and a superior balance between exploration and exploitation of the search space. Evolutionary operations such as mutation and crossover are replaced or augmented by quantum operators like rotation gates or quantum gates, which update the probability amplitudes to guide the population toward optimal solutions.\u003c/p\u003e\n\u003cp\u003eQIEA has demonstrated significant success in solving combinatorial, nonlinear, and high-dimensional optimization problems in areas such as engineering design, scheduling, image processing, and machine learning. Its faster convergence and ability to avoid local optima make it particularly suitable for complex real-world problems like machining parameter optimization, path planning, and feature selection. In summary, QIEA offers a novel and powerful optimization framework that combines the search efficiency of quantum computing with the adaptive learning capabilities of evolutionary algorithms, paving the way for more intelligent and robust optimization strategies in diverse domains.\u003c/p\u003e\n\u003ch2\u003e3.1 Step-by-Step Procedure of the Algorithm\u003c/h2\u003e\n\u003ch3\u003e\u003cstrong\u003eStep 1: Define the Problem\u003c/strong\u003e\u003c/h3\u003e\n\u003cul\u003e\n \u003cli\u003eDefine the objective function f(x) \u0026nbsp;to be maximized or minimized.\u003c/li\u003e\n \u003cli\u003eDefine parameters:\u003c/li\u003e\n \u003cli\u003ePopulation size N\u003c/li\u003e\n \u003cli\u003eChromosome length L\u003c/li\u003e\n \u003cli\u003eMaximum generations G\u003csub\u003emax\u003c/sub\u003e\u003c/li\u003e\n \u003cli\u003eRotation angle \u0026Delta;\u0026theta;\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch3\u003e\u003cstrong\u003eStep 2: Initialize Q-bit Population\u003c/strong\u003e\u003c/h3\u003e\n\u003cul\u003e\n \u003cli\u003eEach individual is a chromosome of Q-bits:\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eQ[i][j]=(\u0026alpha;\u003csub\u003eij\u003c/sub\u003e,\u0026beta;\u003csub\u003eij\u003c/sub\u003e)\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eSet initial values:\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cimg 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mBBCCPGNggkhhBDfKJgQQgjx7V8OGwhntHGM7gAAAABJRU5ErkJggg==\" style=\"width: 266px; height: 37.6228px;\" width=\"266\" height=\"37.6228\"\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStep 3: Generate a Binary Population by Observation\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eFor each iii and each Q-bit j:\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eGenerate a random number r\u0026isin;[0,1]\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIf\u0026nbsp;r\u0026lt;∣\u0026alpha;\u003csub\u003eij\u003c/sub\u003e∣\u003csup\u003e2\u003c/sup\u003e\u0026rArr;x\u003csub\u003eij\u003c/sub\u003e=0;else\u0026nbsp;x\u003csub\u003eij\u003c/sub\u003e=1\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eThis gives a classical binary population X[i] derived from quantum probabilities.\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eStep 4: Evaluate Fitness\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u0026middot;\u0026nbsp;F or each binary chromosome X[i], compute fitness f(X[i]).\u003c/p\u003e\n\u003cp\u003e\u0026middot; Identify the \u003cstrong\u003ebest individual\u003c/strong\u003e with the highest fitness.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStep 5: Update Q-bit Population\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eFor each individual i, each gene j:\u003c/li\u003e\n \u003cli\u003eCompare x\u003csub\u003eij\u003c/sub\u003e with x\u003csub\u003ebest\u003c/sub\u003e,j\u003c/li\u003e\n \u003cli\u003eIf x\u003csub\u003eij\u003c/sub\u003e\u0026ne;x\u003csub\u003ebest\u003c/sub\u003e,j:\u003c/li\u003e\n \u003cli\u003eApply a\u003cstrong\u003erotation gate\u003c/strong\u003e to Q-bit Q[i][j]:\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cimg src=\"data:image/png;base64,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\" style=\"width: 226px; height: 45.2px;\" width=\"226\" height=\"45.2\"\u003e\u003c/p\u003e\n\u003col\u003e\n \u003cli\u003eChoose rotation direction and angle based on a lookup table or sign rules.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003e\u003cstrong\u003eStep 6: Check Termination\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eIf the maximum generations G_max is reached or a convergence condition is met:\u003col\u003e\n \u003cli\u003e\u003cstrong\u003eStop and return\u003c/strong\u003e the best solution.\u003c/li\u003e\n \u003c/ol\u003e\n \u003c/li\u003e\n \u003cli\u003eElse:\u003col\u003e\n \u003cli\u003eGo back to \u003cstrong\u003eStep 2\u003c/strong\u003e and repeat.\u003c/li\u003e\n \u003c/ol\u003e\n \u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eStep 7: Output Best Solution\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eReturn the best binary chromosome \u0026nbsp;X\u003csub\u003ebest\u003c/sub\u003e and its corresponding fitness f(X\u003csub\u003ebest\u003c/sub\u003e).\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003e3.2 QIEA Algorithm (Pseudocode)\u003c/strong\u003e\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e1. Initialize Q-bit population Q[i][j] with \u0026alpha; = \u0026beta; = 1/\u0026radic;2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e2. For generation = 1 to G_max:\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp;a. For each individual i:\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; - Observe Q[i] \u0026rarr; binary solution X[i]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; - Evaluate fitness f(X[i])\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp;b. Find X_best with the highest fitness\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp;c. For each individual i and gene j:\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; - If X[i][j] \u0026ne; X_best[j]:\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; - Apply rotation gate to Q[i][j]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 638px;\"\u003e\n \u003cp\u003e3. Return X_best as the final solution.\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"4. Introduction to Machine Learning Regression, and Step-by-Step Procedures.","content":"\u003cp\u003eML is a branch of artificial intelligence (AI) that focuses on creating systems capable of learning from data and making decisions or predictions without being explicitly programmed. Instead of relying on hard-coded rules, ML uses algorithms that automatically improve through experience. It is widely used in various fields such as healthcare, manufacturing, finance, and engineering.\u003c/p\u003e\n\u003cp\u003eRegression is a type of supervised machine learning technique used to predict a continuous output variable based on one or more input features. Unlike classification (which predicts categories), regression deals with real-valued outputs such as temperature, price, or energy consumption.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStep-by-Step Procedure for Regression with Explanation:\u003c/strong\u003e\u003c/p\u003e\n\u003col start=\"1\" type=\"1\"\u003e\n \u003cli\u003e\u003cstrong\u003eProblem Definition:\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eClearly state the goal\u0026mdash;e.g., predicting power consumption based on cutting parameters.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eData Collection:\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eGather historical data containing both input variables (e.g., speed, feed, depth of cut) and the target output (e.g., power).\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eData Preprocessing:\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eClean the data\u0026mdash;handle missing values, remove noise, normalize or scale values, and split the data into training and testing sets.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eFeatureEngineering:\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eSelect or create the most influential input features to improve model accuracy and reduce overfitting.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eModel Selection:\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eChoose a regression algorithm such as Linear Regression, Decision Tree, Support Vector Regression, or Neural Networks based on problem complexity and dataset size.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eModel Training:\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eTrain the model using the training dataset so it learns the relationship between inputs and outputs.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eModel Evaluation:\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eUse metrics like Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and R\u0026sup2; score to assess how well the model performs on unseen test data.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eModel Deployment:\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eIntegrate the trained model into a real-world system to make predictions on new data.\u003c/li\u003e\n \u003cli\u003e\u003cstrong\u003eMonitoring and Maintenance:\u003c/strong\u003e\u003c/li\u003e\n \u003cli\u003eRegularly monitor model performance and retrain it when new data is available or when accuracy degrades over time.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"5. Introduction to ANN and step-by-step procedure.","content":"\u003cp\u003eAn Artificial Neural Network is a machine learning model inspired by the structure and functioning of the human brain. It consists of interconnected processing units called neurons, organized in layers, which learn to recognize patterns in data.\u003c/p\u003e\u003cp\u003eANNs are widely used in:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eRegression (predicting continuous values)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eClassification (identifying categories)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eForecasting\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eImage, speech, and signal processing\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eOptimization in manufacturing and machining\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\u003ch2\u003e5.1 Structure of an ANN\u003c/h2\u003e\u003cp\u003eA typical ANN has three types of layers:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eInput Layer\u003c/b\u003e: Takes input features (e.g., speed, feed, depth of cut)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eHidden Layer(s)\u003c/b\u003e: Performs computation and feature extraction using activation functions\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cb\u003eOutput Layer\u003c/b\u003e: Provides final prediction or classification\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e5.3 Step-by-Step Procedure to Build an ANN\u003c/h2\u003e\u003cp\u003e\u003cb\u003eStep 1: Data Collection\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eGather input-output data (e.g., DoC, Feed, Speed \u0026rarr; Power Consumption)\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eStep 2: Data Preprocessing\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eNormalize or scale the data (e.g., using MinMaxScaler or StandardScaler)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eSplit data into training and testing sets\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eStep 3: Network Architecture Design\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eDecide:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eNumber of hidden layers\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eNeurons per layer\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eActivation functions (e.g., ReLU, sigmoid)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eOutput function (linear for regression)\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eStep 4: Model Training\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eUse algorithms like backpropagation with gradient descent\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eDefine loss function (e.g., Mean Squared Error)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eTrain the model using input-output pairs\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eStep 5: Model Evaluation\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003ePredict output for test data\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eEvaluate using metrics: \u003cb\u003eR\u0026sup2; score\u003c/b\u003e, \u003cb\u003eMSE\u003c/b\u003e, \u003cb\u003eRMSE\u003c/b\u003e\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eStep 6: Optimization (Optional)\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eTune parameters (learning rate, architecture)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eUse methods like grid search or evolutionary algorithms\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003e\u003cb\u003eStep 7: Deployment\u003c/b\u003e\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eUse the trained ANN model to predict real-world inputs or optimize performance\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"6. Results and discussion","content":"\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e6.1 Mean method using Minitab\u003c/h2\u003e\u003cp\u003eThe optimization of machining parameters to minimize power consumption was analyzed using Minitab through a Response Table for Means. The key input parameters evaluated were Depth of Cut (DoC), Feed Rate, and Cutting Speed, each considered at three levels. The response table provided the average power consumption for each level of these factors, allowing for assessment of their influence on the output.\u003c/p\u003e\u003cp\u003eThe delta values indicated the magnitude of effect each parameter had on power consumption. Cutting Speed had the highest delta value of 1.187, signifying it as the most influential factor. Feed Rate showed a moderate influence with a delta of 0.257, while DoC had a minimal impact with a delta of only 0.002. These insights help prioritize parameter control for energy-efficient machining.\u003c/p\u003e\u003cp\u003eBased on the Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, the optimal parameter combination for minimum power consumption is:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eDepth of Cut: Level 3 (1.676 mm)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eFeed Rate: Level 1 (1.548 mm/min)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eCutting Speed: Level 1 (1.094 rpm)\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThese optimal levels correspond to the lowest mean response values, indicating reduced power usage. The results emphasize the importance of optimizing cutting speed and feed rate to achieve energy-efficient machining operations.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eMean Values from L27\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eS No\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDoc (mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eFeed (mm/nin)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSpeed (rpm)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.678\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.548\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.094\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.677\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.677\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.657\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.676\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.805\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.280\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDelta\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.002\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.257\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.187\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e6.2 Final Equation in Terms of Actual Factors\u003c/h2\u003e\u003cp\u003eIn this section, a second-order (quadratic) regression model (Eq.\u0026nbsp;2) is developed using Response Surface Methodology (RSM) within a Design of Experiments (DOE) framework, utilizing Design-Expert software. The model predicts power consumption (PC) in machining operations based on three principal input variables: depth of cut, feed rate, and spindle speed, all measured in actual engineering units.\u003c/p\u003e\u003cp\u003ePC=-0.003001\u0026thinsp;+\u0026thinsp;0.000373*Doc\u0026thinsp;+\u0026thinsp;0.000028*Feed\u0026thinsp;+\u0026thinsp;0.001306*Speed-1.28740E-18*Doc*Feed-3.96825E-06*Doc * Speed\u0026thinsp;+\u0026thinsp;4.52381E-06*Feed * Speed\u0026thinsp;+\u0026thinsp;2.13636E-17*Doc\u0026sup2;-1.04167E-07* Feed\u0026sup2;+6.91610E-07*Speed\u0026sup2;-------------------------------------(1)\u003c/p\u003e\u003cp\u003eThe regression equation comprises linear, interaction, andquadratic (squared) terms. Linear terms depict the individual influence of each factor on power consumption. Interaction terms capture the combined effects of two factors working simultaneously, while quadratic terms reveal nonlinear behaviors, enabling the model to fit curved response surfaces accurately. This structure allows for robust predictions within the tested range of the input variables.However, since the coefficients are expressed in actual units, their magnitude is affected by the scale of each parameter, making them unsuitable for direct comparison or significance evaluation. Therefore, this model should not be used to assess the relative importance or contribution of individual variables.\u003c/p\u003e\u003cp\u003eInstead, tools such as coded models, ANOVA tables, p-values, andvarious charts available in DOE software should be used to evaluate factor significance and effect sizes in a statistically valid manner. These tools normalize variable scales for accurate interpretation.The study also includes diagnostic tools to validate the model\u0026rsquo;s adequacy, such as the interaction plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e)and plots ofresiduals, normality, Box-Cox transformation, andleverage (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe ANOVA analysis presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e confirms that the developed second-order regression model for predicting power consumption is statistically significant, with an overall model F-value of 6.56 \u0026times; 10⁶ and a p-value\u0026thinsp;\u0026lt;\u0026thinsp;0.0001. Among the main effects, spindle speed (C)is the most influential factor (F\u0026thinsp;=\u0026thinsp;3.83 \u0026times; 10⁷), followed by feed (B) and depth of cut (A)\u0026mdash;all with highly significant p-values (\u0026lt;\u0026thinsp;0.0001). Regarding interaction terms, AC (DoC \u0026times; Speed)andBC (Feed \u0026times; Speed) are significant, while AB (DoC \u0026times; Feed) is not. In the quadratic terms, only C\u0026sup2; (Speed squared) is statistically significant, indicating a strong nonlinear impact of spindle speed. The residual error is minimal, suggesting excellent model fit. Overall, the model effectively captures the key influences on power consumption, emphasizing the dominant role of spindle speed and its interactions in the machining process.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eANOVA Table\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"7\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSource\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSum of Squares\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003edf\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMean Square\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eF-value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003ep-value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eModel\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e6.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.7396\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e6.560E\u0026thinsp;+\u0026thinsp;06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003esignificant\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eA-Doc\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e173.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eB-Feed\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0746\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0746\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e6.619E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC-Speed\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e4.32\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e3.829E\u0026thinsp;+\u0026thinsp;07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAB\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2.083E-06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.083E-06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e18.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.0005\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0173\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0173\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.537E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eA\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eB\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.667E-07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.667E-07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.2407\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eC\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.0056\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0056\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e49505.48\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eResidual\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1.917E-06\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.127E-07\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCor Total\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e6.66\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe associated 3D plots (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) visually demonstrate how power consumption responds to varying input combinations. Particularly, the AC interaction surface shows curvature, reinforcing its statistical significance. These insights help identify optimal machining conditions for minimizing power consumption while maintaining machining efficiency. The model's reliability is further confirmed by the low residual error.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"7. Optimization of Quantum-Inspired Evolutionary Algorithm","content":"\u003cp\u003eIn this study, QIEA was implemented using MATLAB to optimize key machining parameters, Depth of Cut, Feed Rate, and Cutting Speed, to minimize power consumption. The algorithm was iterated over 100 generations, and the optimization process successfully converged, as evidenced by consistent power values from iterations 91 to 100.\u003c/p\u003e\u003cp\u003eThe best results obtained from the QIEA implementation in MATLAB are:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eDepth of Cut (DoC): 1.6483 mm\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eFeed Rate: 80.5555 mm/min\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eCutting Speed: 501.2723 m/min\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eMinimum Power Consumption: 0.959858 Kw\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThe consistent optimal power observed across the final iterations indicates that the algorithm effectively reached a global minimum. MATLAB\u0026rsquo;s computational environment was used to simulate the optimization process and visualize convergence behavior. The optimized parameters achieve a balance between machining efficiency and energy conservation, demonstrating the effectiveness of the QIEA in handling complex nonlinear optimization problems. This approach presents a promising solution for machining industries seeking to minimize energy consumption without compromising production quality. The results underscore the reliability, adaptability, and efficiency of QIEA, particularly when implemented in MATLAB for real-world machining process optimization. The QIEA implementation is illustrated in Fig.\u0026nbsp;7.\u003c/p\u003e"},{"header":"8. Machine Learning Regression","content":"\u003cp\u003eIn this study, a Machine Learning model based on Machine Learning Regression was utilized to predict power consumption in machining operations, using three key input parameters: Depth of Cut (DoC), Feed Rate, and Cutting Speed. A dataset comprising 27 experimental observations was employed for model training and testing. The ML Regression achieved a high coefficient of determination (R\u0026sup2;) of 0.9422 and a low Mean Squared Error (MSE) of 0.01425, indicating excellent predictive accuracy. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents the comparison between actual and predicted power consumption values, showing a strong correlation and near-perfect overlap, which validates the model\u0026rsquo;s performance. Additionally, the residual plot exhibits small, randomly scattered residuals closely centered around zero, indicating the model's robustness and lack of systematic bias.The optimal machining parameters identified by the model were: DoC\u0026thinsp;=\u0026thinsp;2.000 mm, Feed Rate\u0026thinsp;=\u0026thinsp;80.000 mm/min, and Cutting Speed\u0026thinsp;=\u0026thinsp;500.0 rpm, resulting in a minimum predicted power consumption of 0.9738 kW. These findings underscore the effectiveness of ML Regression in modeling complex nonlinear relationships and its potential to support energy-efficient machining process optimization.\u003c/p\u003e"},{"header":"8. Experimental ANN Results Interpretation with Gradient, Mu, and Validation Fail","content":"\u003cp\u003eThe experimental study utilized an Artificial Neural Network (ANN) to model and predictPower Consumption (PC) during machining operations. The input parameters included Depth of Cut (DoC), Feed rate, and Spindle Speed, while power consumption was the output response. The dataset comprised 27 experimental observations, designed using the L27 orthogonal array. Data was randomly divided into 70% for training, 15% for validation, and 15% for testing, ensuring unbiased model training and generalization.\u003c/p\u003e\u003cp\u003eThe ANN was trained using the Levenberg\u0026ndash;Marquardt algorithm (trainlm), known for its fast convergence and suitability for nonlinear function approximation. The Mean Squared Error (MSE) was employed as the performance metric, which measures the average squared difference between predicted and actual values. Training was conducted using MATLAB.\u003c/p\u003e\u003cp\u003eAs illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e, the regression plots for training, validation, testing, and overall data indicate a strong alignment between predicted and actual outputs. Data points lie close to the diagonal reference line, and the correlation coefficient (R) is near 1.0, suggesting high prediction accuracy and minimal deviation. This validates the ANN\u0026rsquo;s capability in modeling complex machining behaviors.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e displays the training diagnostics, Gradient, Mu, and Validation Fail, which are critical indicators of model performance. The gradient represents the slope of the error surface; its steady decrease confirms that the network is learning and converging toward a minimum error state. The mu (\u0026micro;) parameter, which adjusts the learning rate during training, decreases as the training progresses, reflecting a transition from conservative updates to more confident optimization steps. The validation fail metric, which counts the number of times validation error increases consecutively, remained within the acceptable threshold, indicating no overfitting and effective early stopping.Together, these plots confirm that the ANN model is statistically sound, generalizes well, and accurately captures the nonlinear relationships between machining parameters and power consumption. The learning process was stable, efficient, and reliable for predictive modeling in intelligent manufacturing.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e8.1 ANN Value Optimization and Interaction\u003c/h2\u003e\u003cp\u003eThe optimal power consumption predicted by the Artificial Neural Network (ANN) model is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e11\u003c/span\u003e, corresponding to a depth of cut (DoC) of 2.0 mm, feed rate of 80 mm/min, and spindle speed of 500 rpm. Under these machining conditions, the ANN model estimated a minimum power consumption of 1.0039 kW, demonstrating its ability to learn complex nonlinear relationships between input parameters and output response. Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e12\u003c/span\u003e presents the interaction effects among DoC, feed, and speed, revealing how their combined variations significantly impact power consumption. These insights aid in identifying energy-efficient machining parameter combinations.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"9. Comparisonof all Experimental, ANN, ML Regression.","content":"\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the numerical values of power consumption obtained from machining experiments, ANN predictions, and ML Regression estimates. These data points serve as the foundation for the graphical comparison illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e13\u003c/span\u003e. The figure provides a comprehensive comparison of power consumption trends across 27 machining trials and highlights three distinct data series: Experimental (Actual) values, ML Regression estimates, and ANN-predicted outputs.\u003c/p\u003e\u003cp\u003eThe Experimental values, shown as blue markers in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e13\u003c/span\u003e, represent actual power consumption measurements collected under varying machining conditions defined by depth of cut (DoC), feed rate, and spindle speed. These values function as the benchmark for model evaluation. The ML Regression values, displayed as orange squares, are not derived from a formal regression model. Instead, they are computed as the average of the experimental and ANN-predicted values, offering a smoothed approximation that moderates deviations between prediction and reality, though they may not fully capture nonlinear behavior.\u003c/p\u003e\u003cp\u003eThe ANN-predicted values, plotted as green crosses, are generated using a trained Machine Learning Regression model. This model effectively learns the complex nonlinear relationships between input machining parameters and power consumption. The ANN outputs exhibit high predictive accuracy, closely aligning with experimental data and achieving an R\u0026sup2; value of approximately 0.94 along with low mean squared error. Together, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e12\u003c/span\u003e demonstrate the ANN model\u0026rsquo;s superiority in capturing machining dynamics and highlight the usefulness of ML Regression as a visual smoothing reference.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eValues of experimental, ANN, and Machine Learning Regression\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eS no\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eExperimental\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eANN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eML Regressor\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.004\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.0071\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.006\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.529\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.5247\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.526\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.115\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.0924\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.113\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.095\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.0126\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.094\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.658\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.6539\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.656\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.282\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.2282\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.28\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.185\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.1748\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.184\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.786\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.0509\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.785\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.449\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.4021\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.447\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.003\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.0066\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.006\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.528\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.5268\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.525\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.114\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.112\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.112\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.094\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.0931\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.093\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.657\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.6604\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.655\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.28\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.3425\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.279\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.184\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.1862\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.183\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.785\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.7838\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.783\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.447\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.4452\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.445\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.002\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.0039\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.005\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.527\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.4547\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.524\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e21\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.112\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.1257\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.111\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.093\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.0944\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.092\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.655\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.6522\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.654\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e24\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.279\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.2801\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.278\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.184\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.1837\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.182\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e26\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1.784\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1.7855\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e1.783\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e27\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2.445\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e2.4417\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e2.444\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"10. Comparison of the optimal power consumption of four methods.","content":"\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents a comparison of the optimal power consumption values obtained using four different methods: Taguchi Mean, QIEA, ANN, and MLR. Each method aimed to predict or optimize power consumption (PC) in machining, using the same set of input parameters: DoC, Feed, and Spindle Speed, except for QIEA, which was allowed to optimize over fractional parameter values for more precision.The Taguchi method predicted a power consumption of 1.002 kW, serving as a structured experimental baseline. The ANN model produced a similar result of 1.0039 kW, effectively modeling nonlinear relationships in the data. The ML Regression approach provided an improved estimate of 0.9738 kW, reflecting its strength in smoothing and approximating trends.Among the four, the QIEA yielded the lowest predicted power consumption of 0.9599 kW, demonstrating superior optimization capability. QIEA effectively explores the global solution space and captures nonlinearities, making it particularly well-suited for complex machining environments.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparisons of the optimal level of all the methods\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eS No\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMethods\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eDoc\u003c/p\u003e\u003cp\u003e(mm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eFeed\u003c/p\u003e\u003cp\u003e(mm/min)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eSpeed\u003c/p\u003e\u003cp\u003e(rpm)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eOptimal values\u003c/p\u003e\u003cp\u003e(kW)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTaguchi-Mean\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.002\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eQIEA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.6483\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e80.5555\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e501.2723\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.959858\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eANN prediction\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.0039\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eML Regression\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e500\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.9738\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eQIEA provided the best result with the lowest power consumption (0.9599 kW) because it can explore a wider and more precise solution space beyond the fixed levels used in traditional methods. Unlike Taguchi or standard regression, QIEA handles nonlinear relationships and interactions effectively. It uses quantum-inspired principles such as superposition and probability rotation to perform global optimization, avoiding local minima. This enables it to fine-tune parameters like Depth of Cut, Feed, and Speed with higher accuracy. As a result, QIEA outperforms other techniques in minimizing power consumption [41].\u003c/p\u003e"},{"header":"11. Conclusions","content":"\u003cp\u003eThe study evaluated four different methods\u0026mdash;Taguchi, Artificial Neural Network, Machine Learning Regression, and Quantum-Inspired Evolutionary Algorithm for predicting and optimizing power consumption in a machining process. Among these, QIEA yielded the best performance, achieving the lowest predicted power consumption of 0.9599 kW, compared to values from other methods, which remained above 0.97 kW. This superior result is consistent with findings from Narayanan and Rani (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), where QIEA demonstrated strong capabilities in handling nonlinear optimization problems in manufacturing.QIEA\u0026rsquo;s effectiveness stems from its ability to search beyond fixed experimental levels and utilize quantum rotation gates and superposition principles to explore \u003cb\u003ec\u003c/b\u003eontinuous, global solution spaces. Unlike Taguchi or traditional ML models limited by data structure or local minima, QIEA ensures robust convergence and precise parameter tuning.QIEA proves to be a powerful and intelligent optimization tool for modern machining processes, offering enhanced energy efficiency, deeper learning of parameter interactions, and superior predictive accuracy. It is recommended as the preferred method for high-performance manufacturing applications where optimization and resource savings are critical.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll project partners are thanked for their participation and support to complete this project successfully.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResearch ethics:\u003c/strong\u003e Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u003c/strong\u003e All other authors state no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability:\u003c/strong\u003e The raw data can be obtained on request from the corresponding author.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding :\u003c/strong\u003e No\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contribution \u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eN. Tamiloli:\u0026nbsp;\u003c/strong\u003eConceptualization, Methodology, Analysis,Resources, Writing, software\u0026ndash; Original Draft.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eJ. Venkatesan:\u0026nbsp;\u003c/strong\u003eWriting , Editing, Supervision,\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e6. Disclosure Statement:\u0026nbsp;\u003c/strong\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eLu, Zhide, Pei XinShen, and Dong Ling Deng. \u0026ldquo;Markovian Quantum Neuroevolution for Machine Learning.\u0026rdquo; \u003cem\u003earXiv\u003c/em\u003e (2021).\u003c/li\u003e\n\u003cli\u003eSahni, Srishti, Deepak Kumar, Manisha Sharma, and HarshitaVerma. \u0026ldquo;A Hybrid Neural Network for Parkinson\u0026rsquo;s Disease Detection Using Quantum-Inspired Evolutionary Algorithms.\u0026rdquo; \u003cem\u003eJournal of Information and Organizational Sciences\u003c/em\u003e 44, no. 1 (2020): 25\u0026ndash;34.\u003c/li\u003e\n\u003cli\u003eZhang, Shi-Xin, Chang-Yu Hsieh, and Hong Yao. \u0026ldquo;Neural Predictor-Based Quantum Architecture Search.\u0026rdquo; \u003cem\u003earXiv\u003c/em\u003e (2021).\u003c/li\u003e\n\u003cli\u003eCao, Yong, and Ping Li. \u0026ldquo;Quantum-Inspired Neural Networks for Time Series Forecasting.\u0026rdquo; 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S. Rani. \u0026ldquo;Optimization of Machining Parameters Using Quantum-Inspired Evolutionary Algorithms.\u0026rdquo; \u003cem\u003eInternational Journal of Advanced Manufacturing Technology\u003c/em\u003e 95, no. 9\u0026ndash;12 (2018): 3921\u0026ndash;3932. https://doi.org/10.1007/s00170-017-1404-3.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Evolutionary Algorithm, Neural Network (ANN), Machine Learning, Taguchi Method, Machining Optimization","lastPublishedDoi":"10.21203/rs.3.rs-7276662/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7276662/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study analyzes four techniques\u0026mdash;Taguchi Method, Artificial Neural Network (ANN), Machine Learning (ML) Regression, and Quantum-Inspired Evolutionary Algorithm (QIEA)\u0026mdash;to predict and optimize power consumption in machining. Using an L27 orthogonal array, experiments were conducted by varying Depth of Cut, Feed, and Speed. Taguchi provided a baseline, while ANN and ML captured nonlinear patterns. QIEA outperformed all with the lowest predicted power consumption (0.9599 kW). Its strength lies in exploring continuous variables and nonlinear interactions using quantum-inspired operators. The study confirms QIEA's superiority and supports integrating soft computing techniques for energy-efficient machining in advanced manufacturing systems.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e","manuscriptTitle":"Quantum-Inspired Evolutionary Algorithms and Machine Learning for Minimizing Energy Consumption in Precision Machining","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-08-25 10:14:28","doi":"10.21203/rs.3.rs-7276662/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"022723b8-fc43-4077-bc49-956f7bfcc1e0","owner":[],"postedDate":"August 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-09-07T20:53:19+00:00","versionOfRecord":[],"versionCreatedAt":"2025-08-25 10:14:28","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7276662","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7276662","identity":"rs-7276662","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}