Handling multimodal multi-objective problems through self-organizing quantum-inspired particle swarm optimization

Abstract Multimodal multi-objective optimization problems (MMOPs) involve locating equivalent Pareto optimal solutions in decision space with the same objective values. The key to handling MMOPs is finding all equivalent Pareto optimal solutions and maintaining a promising balance between the convergence and diversity of solutions in both decision space and objective space. To tackle this issue, a self-organizing quantum-inspired particle swarm optimization algorithm (MMO_SO_QPSO) is proposed in this paper for handling MMOPs. In the proposed MMO_SO_QPSO, a self-organizing map is used to find the best neighbor leader of particles. With the aid of neighbor leader particles, a special zone searching method is adopted to update the position of particles and locate equivalent Pareto optimal solutions in decision space. To maintain diversity and convergence of Pareto optimal solutions, a special archive mechanism that relies on the maximum-minimum distance among solutions is introduced into MMO_SO_QPSO. And some outstanding Pareto optimal solutions are maintained in the special archive. In addition, a new performance indicator is developed to estimate properly the similarity between obtained Pareto optimal solutions and true Pareto optimal solutions. The performance of the proposed MMO_SO_QPSO is compared with six state-of-the-art multimodal multi-objective evolutionary algorithms on two well-known benchmark problems. Experimental results demonstrate the superior performance of MMO_SO_QPSO for solving MMOPs. The effectiveness of several strategies is also discussed.