Particle Swarm Optimization with Random Forest Surrogates Modelling for Rational Design of Antimicrobial Fluoride Toothpaste Formulations against Clinically Significant Oral Pathogens

Abstract To make effective antimicrobial toothpastes, you need to optimize many parts that work together. Creating new formulations the old-fashioned way takes a lot of time and money. This research formulates and substantiates a methodological framework that combines systematic antimicrobial susceptibility testing with Particle Swarm Optimization (PSO) to enhance toothpaste formulations against clinically significant oral pathogens. Using a D-optimal mixture design, we made 24 different toothpaste formulations by changing the type of fluoride (NaF, MFP, SnF₂), the concentration of fluoride (1000–1500 ppm), the concentration of SLS (0.5–2.5%), the type of abrasive (silica, calcium carbonate, dicalcium phosphate), and the concentration of abrasive (10–30%). We used agar well diffusion and minimum inhibitory concentration (MIC) tests to see how well the drugs worked against Streptococcus mutans ATCC 25175, Porphyromonas gingivalis ATCC 33277, and Lactobacillus acidophilus ATCC 4356. A Random Forest surrogate model was trained on 120 experimental data points (24 formulations × 5 concentrations) and validated through 10-fold cross-validation. Multi-objective PSO was used to improve the effectiveness of antimicrobials, the availability of fluoride, and the cost of the formulation. Chosen PSO-predicted formulations underwent experimental validation. The antimicrobial activity changed a lot (p < 0.001) depending on the formulation parameters. The optimized formulation (sodium fluoride 1120 ppm, SLS 2.3%, hydrated silica 18%, pH 7.2) showed 28.4 ± 1.2 mm of inhibition against S. mutans, 26.8 ± 1.4 mm against P. gingivalis, and 24.2 ± 1.1 mm against L. acidophilus. These were improvements of 18.5%, 22.3%, and 19.8%, respectively, over the best commercial comparator. Experimental validation corroborated PSO predictions with a mean absolute error of 5.2%. Multi-objective Optimization found Pareto-optimal formulations that let you choose based on trade-offs between effectiveness, safety, and cost. Combining systematic experimental design with PSO gives a tested framework for making rational toothpaste formulations. This method significantly lowers the amount of work needed for experiments while also allowing for the Optimization of multiple competing formulation goals. Competing Interest Statement The authors have declared no competing interest.