Particle Swarm Optimization Algorithm With Self-Organizing Mapping for Nash Equilibrium Strategy in Application of Multiobjective Optimization

In this article, the Nash equilibrium strategy is used to solve the multiobjective optimization problems (MOPs) with the aid of an integrated algorithm combining the particle swarm optimization (PSO) algorithm and the self-organizing mapping (SOM) neural network. The Nash equilibrium strategy addresses the MOPs by comparing decision variables one by one under different objectives. The randomness of the PSO algorithm gives full play to the advantages of parallel computing and improves the rate of comparison calculation. In order to avoid falling into local optimal solutions and increase the diversity of particles, a nonlinear recursive function is introduced to adjust the inertia weight, which is called the adaptive particle swarm optimization (APSO). In addition, the neighborhood relations of current particles are constructed by SOM, and the leading particles are selected from the neighborhood to guide the local and global search, so as to achieve convergence. Compared with several advanced algorithms based on the eight multiobjective standard test functions with different Pareto solution sets and Pareto front characteristics in examples, the proposed algorithm has a better performance.

Automated summary

This article presents an integrated algorithm that uses the Nash equilibrium strategy combined with the PSO algorithm and SOM neural network to solve multiobjective optimization problems. The algorithm effectively addresses MOPs by comparing decision variables one by one and adjusting inertia weight using a nonlinear recursive function. Additionally, it utilizes SOM to construct neighborhood relations and select leading particles for local and global search, achieving superior performance compared to other advanced algorithms.