A Multi-Strategy Co-Evolutionary Particle Swarm Optimization Algorithm with Its Convergence Analysis

Compared to the single-strategy particle swarm optimization (PSO) algorithm, the multi-strategy PSO shows potential advantages in solving complex optimization problems. In this study, a novel framework of the multi-strategy co-evolutionary PSO (M-PSO) is first proposed in which a matrix parameter pool scheme is introduced. In the scheme, multiple strategies are taken into account in the matrix parameter pool and new hybrid strategies can be generated. Then, the convergence analysis is made and the convergence conditions are provided for the co-evolutionary PSO framework when some operators are specified. Subsequently, based on the PSO framework, a novel multi-strategy co-evolutionary PSO is developed using Q-learning which is a classical reinforcement learning technique. In the proposed M-PSO, both the parameter optimization by the orthogonal method and the convergence conditions are embedded to improve the performance of the algorithm. Finally, the experiments are conducted on two test suites, CEC2017 and CEC2019, and the results indicate that M-PSO outperforms several meta-heuristic algorithms on most of the test problems.