L-SHADE-MA: Enhancing L-SHADE with Momentum and Adaptive Decay Coefficient

AbstractL-SHADE represents a modified form of the Differential Evolution (DE) algorithm, blending Linear Population Size Reduction (LPSR) with SHADE, the Success-History-Based Adaptation of DE. While acknowledged for its effectiveness, L-SHADE occasionally tends toward local optima and may converge too soon, especially during complex optimization challenges. Addressing these challenges, we introduce L-SHADE-MA, an advanced L-SHADE iteration employing a momentum-based mutation strategy. This approach minimizes oscillatory tendencies during searches, promoting quicker convergence and enhanced solution accuracy. Additionally, an adaptive decay coefficient, rooted in success-history, is integrated. It dynamically adjusts the balance of historical data and momentum in mutations, optimizing exploration and exploitation for each generation. This accelerates convergence and fosters population diversity. For a holistic assessment, L-SHADE-M is also presented, which adopts the momentum approach but omits the adaptive coefficient. To ascertain L-SHADE-MA’s effectiveness, it was tested on CEC2014 benchmark functions in two distinct dimensions. Performance comparisons spanned L-SHADE-M and seven other algorithms across 30 numerical functions in 50 and 100 dimensions. Empirical results unequivocally validate L-SHADE-MA’s enhancements over L-SHADE, confirming its dominance in most tested scenarios.