Nonlinear constrained optimization by enhanced co-evolutionary PSO

Penalty function methods have been the most popular methods for nonlinear constrained optimization due to their simplicity and easy implementation. However, it is often not easy to set suitable penalty factors or to design adaptive mechanisms. By employing the notion of co-evolution to adapt penalty factors, we present a co-evolutionary particle swarm optimization approach (CPSO) for nonlinear constrained optimization problems, where PSO is applied with two kinds of swarms for evolutionary exploration and exploitation in spaces of both solutions and penalty factors. To enhance the performance of our proposed algorithm, three improvement strategies are proposed. The proposed algorithm is population-based and easy to implement in parallel, in which the penalty factors to evolve in a self-tuning way. Simulation results based on three famous engineering constrained optimization problems demonstrate the effectiveness, efficiency and robustness of the proposed enhanced CPSO (ECPSO).