Multi-solution tracking in shifting sphere function using gravitational particle swarm algorithm

Abstract

In this study, we propose a novel optimization method, which can track multiple optimal solutions for dynamic problems. In our previous study, we proposed a gravitational particle swarm algorithm (GPSA), which is able to search for multiple optimal solutions. In this paper, first, we apply the original GPSA to a multi-solution tracking problem and reveal its drawback. Second, we propose a modified GPSA, called 𝜏GPSA, by replacing original GPSA's update rule for personal bests with a tolerance update rule. Finally, we demonstrate that 𝜏GPSA can track multiple optimal solutions in an one-dimensional shifting sphere function.