Hybridization of the Snake Optimizer and Particle Swarm Optimization for continuous optimization problems

The Snake Optimizer (SO), despite its reasonable performance in a variety of continuous optimization problems, struggles by inefficient exploration, stagnation in local optima, and a slow convergence. To improve exploration, accelerate convergence, and avoid local optima, the velocity vector of Particle Swarm Optimization (PSO) was integrated into the Snake Optimizer (SO), resulting in the proposal of the Snake Optimizer Particle Swarm Optimization (SO-PSO) metaheuristic method. To evaluate the applicability of the proposed SO-PSO method, it was evaluated on continuous numerical problems (CEC-2017) and seven real-world engineering problems, benchmarking its performance against contemporary metaheuristic algorithms, including WOA, PSO, GWO, EO, LSHADE, and SO. A comparative analysis of six metaheuristics and SO-PSO was conducted on 30 shifted and rotated benchmark problems across dimensions and population sizes of 30, 50, and 100, as well as seven engineering challenges with population sizes of 30, 50, and 100, each evaluated over 30 independent runs. According to the Friedman ranking results from 270 experimental tests on CEC17 functions, SO-PSO, WOA, PSO, GWO, EO, LSHADE, and SO achieved rankings of 1.62 , 6.5, 5.91, 4.18, 1.98, 4.53, and 3.28, respectively. Regarding the results of the engineering functions, SO-PSO, WOA, PSO, GWO, EO, LSHADE, and SO achieved rankings of 1.82 , 6.19, 3.95, 4, 3.38, 4.34, and 4.33, respectively. Besides, the proposed SO-PSO shows statistically significant difference from other methods in 96.42 % and 93.65 % of experimental tests obtained from Wilcoxon’s signed-rank test in CEC17 functions and engineering problems, respectively. Consequently, SO-PSO demonstrated superior performance over other metaheuristics based on experimental and statistical test results.