A self-organizing multimodal multi-objective pigeon-inspired optimization algorithm

Multi-objective optimization algorithms have recently attracted much attention as they can solve problems involving two or more conflicting objectives effectively and efficiently. However, most existing studies focus on improving the performance of the solutions in the objective spaces. This paper proposes a novel multimodal multi-objective pigeon-inspired optimization (MMOPIO) algorithm where some mechanisms are designed for the distribution of the solutions in the decision spaces. First, MMOPIO employs an improved pigeon-inspired optimization (PIO) based on consolidation parameters for simplifying the structure of the standard PIO. Second, the self-organizing map (SOM) is combined with the improved PIO for better control of the decision spaces, and thus, contributes to building a good neighborhood relation for the improved PIO. Finally, the elite learning strategy and the special crowding distance calculation mechanisms are used to prevent premature convergence and obtain solutions with uniform distribution, respectively. We evaluate the performance of the proposed MMOPIO in comparison to five state-of-the-art multi-objective optimization algorithms on some test instances, and demonstrate the superiority of MMOPIO in solving multimodal multi-objective optimization problems.