Modification of the PSO Algorithm: Variable Population Size and Hybridization with the Nelder-Mead Method

This paper presents a modified Particle Swarm Optimization (PSO) algorithm designed to enhance computational efficiency without compromising solution quality. Two approaches are proposed: the first emphasizes the advantages of incorporating a variable population size to optimize both computational efficiency and solution quality. The second integrates this adaptive population strategy with the Nelder-Mead method to refine local search capabilities. By combining these techniques, the hybrid algorithm achieves a balance between global exploration and local exploitation, while also improving the algorithm’s speed without sacrificing solution quality. The performance of both approaches is evaluated through numerical experiments, demonstrating their ability to deliver high-quality solutions with reduced computational resources.