PSO and CMA-ES based on Optima Tracking for Dynamic Function Optimization

Abstract

This paper proposes Tracking Swarm Optimization based on PSO and CMA-ES (TSOPC), which aims to continuously track optima in dynamic optimization problems with frequent environmental changes. The proposed algorithm tracks optima by roughly estimating the direction of optima movement by Tracking CMA-ES (TCMA-ES) and locally searching optima by Tracking PSO (TPSO), each of which is improved from CMA-ES and PSO. In TSCPC, TPSO and TCMA-ES cooperate with each other by exchanging their own superior solutions to find better solutions and by relocating their solutions when losing to track optima. Through the intensive experiments on four evaluation functions in two and ten dimensions based on the Moving Peaks Benchmark (MPB), the following implications have revealed: (1) the offline-error (which value becomes small when tracking solutions are close to optima) of TSOPC is smaller than that of TPSO and TCMA-ES; (2) the offline-error of TSOPC is affected by the ratio of TPSO and TCMA-ES, and an increase of the ratio of TCMA-ES contributes to decreasing the offline-error in the case of difficulty in tracking optima.