Multimodal Particle Swarm Optimization: Enhancements and Applications

Optimization problems with multiple optima (local or global) are called multimodal problems. Many real world problems are multimodal and challenging to solve as compared to unimodal problems due to the possibility of premature convergence to a local optimum solution and possibly requiring a higher number of function evaluations. A multimodal optimization algorithm provides multiple solutions, thus a better understanding of the design space at minimal additional computational cost. The goal of multimodal particle swarm optimizer (MPSO) is to converge to multiple local and global optima with a reasonable number of function evaluations. The modifications to PSO include reduction in the personal best weight and an additional step to replace the global best with a group best in the PSO procedure. The modifications only allow a user defined number of particles (m ) to converge to a solution and relocate the particles if more than m particles converge to a solution. The relocation is active or inactive based on a predefined set of rules. MPSO is demonstrated on several optimization problems such as benchmark problems from the literature, spring design, and sequential sampling.