An improved predator-prey particle swarm optimization algorithm for Nash equilibrium solution.

Yufeng Meng,Jianhua He,Shichu Luo,Jiancheng Xu,Siqi Tao,Seyedali Mirjalili

doi:10.1371/journal.pone.0260231

Yufeng Meng, Jianhua He + Show 4 more

Open Access

https://doi.org/10.1371/journal.pone.0260231

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Journal: PloS one	Publication Date: Nov 24, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: Northwestern Polytechnical University

Abstract

Focusing on the problem incurred during particle swarm optimization (PSO) that tends to fall into local optimization when solving Nash equilibrium solutions of games, as well as the problem of slow convergence when solving higher order game pay off matrices, this paper proposes an improved Predator-Prey particle swarm optimization (IPP-PSO) algorithm based on a Predator-Prey particle swarm optimization (PP-PSO) algorithm. First, the convergence of the algorithm is advanced by improving the distribution of the initial predator and prey. By improving the inertia weight of both predator and prey, the problem of “precocity” of the algorithm is improved. By improving the formula used to represent particle velocity, the problems of local optimizations and slowed convergence rates are solved. By increasing pathfinder weight, the diversity of the population is increased, and the global search ability of the algorithm is improved. Then, by solving the Nash equilibrium solution of both a zero-sum game and a non-zero-sum game, the convergence speed and global optimal performance of the original PSO, the PP-PSO and the IPP-PSO are compared. Simulation results demonstrated that the improved Predator-Prey algorithm is convergent and effective. The convergence speed of the IPP-PSO is significantly higher than that of the other two algorithms. In the simulation, the PSO does not converge to the global optimal solution, and PP-PSO approximately converges to the global optimal solution after about 40 iterations, while IPP-PSO approximately converges to the global optimal solution after about 20 iterations. Furthermore, the IPP-PSO is superior to the other two algorithms in terms of global optimization and accuracy.

Highlights

During the strategy selection for a swarm of Unmanned Aerial Vehicles (UAVs), the state of UAV itself and the strategy of the enemy should be considered
This paper mainly studies a generally improved Predator-Prey Particle Swarm Optimization(IPP-particle swarm optimization (PSO)) algorithm to solve the Nash equilibrium of the game
When we study the game model of attack and defense confrontation of swarm UAVs, we encounter the problem of choosing the best algorithm to solve the game model

Summary

Introduction

During the strategy selection for a swarm of Unmanned Aerial Vehicles (UAVs), the state of UAV itself and the strategy of the enemy should be considered. An improved predator-prey particle swarm optimization algorithm for Nash equilibrium solution decision-making [1,2,3,4,5]. Due to the large number of swarming UAVs and the many available alternative countermeasures, each strategy needs to be evaluated, resulting in the amount of digital storage space needed for the evaluation values exploding exponentially as the number of countermeasures increases Problems such as slow algorithm convergence or convergence to the local optimal solution will be encountered when solving the Nash equilibrium solution of such a game. The main methods for solving the Nash equilibrium solution include the game solution based on an evolutionary algorithm, an ant colony algorithm, application of graph theory and use of particle swarm optimization (PSO). This paper mainly studies a generally improved Predator-Prey Particle Swarm Optimization(IPP-PSO) algorithm to solve the Nash equilibrium of the game.

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