Particle Swarm Optimization with Rotational Invariance Using Correlativity
Wataru Kumagai, Keiichiro Yasuda · 2018
Metaheuristics are required in invariance when transforming the solution space or objective function (transformation invariance) for the robustness of the optimization algorithm because they are used in various environments. In this study, we first construct an analysis framework based on transformation invariance using a proof. Second, we point out that particle swarm optimization (PSO) lacks invariance under rotation of the solution space (rotational invariance) using the analysis framework. Third, we develop PSO with rotational invariance using correlativity (CRIPSO), which has a coordinate transformation function based on a covariance matrix. Fourth, we confirm that CRIPSO shows rotational invariance using the analysis framework. Finally, the performance of CRIPSO is verified through numerical experiments for typical separable benchmark functions with and without rotation of the solution space by comparing PSO values.