Multi-modal Multi-objective Particle Swarm Optimization Algorithm with Bi-topological Structures and Rebirth Mechanism

The multi-modal multi-objective particle swarm optimization algorithm (MMOPSO) suffers from issues such as easily falling into local optima and uneven distribution of solutions. To solve these problems, this paper presents a combinatorial topology with a fast search on the global scale using fully connected topologies in the early stage and an dynamic index-based ring topology in the later stage to avoid falling into the local optima, find the optimal solution and maintain the optimal solution. A new crowding distance (NCD) calculation method is employed in the Pareto ordering of the particle population, enabling the solutions to be more evenly distributed in the decision space. Finally, a rebirth mechanism is introduced, which gives the sorted inferior particles the opportunity to rebirth, increasing the randomness of the particle search, and thus increasing the uniformity of the solutions distribution. Testing of 14 benchmark functions fully demonstrates the effectiveness of the multi-modal multi-objective particle swarm optimization algorithm with bi-topological structures and rebirth mechanism (MMOPSO-BSRM) for the distribution of particle populations in the decision space.