PID-Controlled Particle Swarm Optimization

Premature convergence is a major challenge for particle swarm optimization algorithm (PSO) when dealing with multi-modal problems. The reason is partly due to the insufficient exploration capability because of the fast convergent speed especially in the final stage. In this paper, the PSO is regarded as a two-inputs one-output feedback system, and two PID controllers are incorporated into the methodology of PSO to improve the population diversity. Different from the integral controller, PID controller has three independent parameters and adjusts them dynamically. Theoretical results with support set theory and stability analysis both demonstrate that PID controller provides more chances to escaping from a local optimum. To validate the efficiency of this new variant, four other famous variants are used to compare including the comprehensive leaning PSO, modified time-varying accelerator coefficients PSO, integral-controlled PSO and the standard version, the test suit consists five unconstrained numerical benchmarks with dimensionality 30 and 100, respectively. Simulation results show PID-controlled PSO is suitable for highdimensional multi-modal problems due to the large exploration capability in the final stage.