Constrained Multimodal Function Optimization using a Simple Evolutionary Algorithm

Practical function optimization problems often contain several constraints. Although evolutionary algorithms (EAs) have been successfully applied to unconstrained real-parameter optimization problems, it is sometimes difficult for these methods even to find feasible solutions in constrained ones. In this study, we thus propose a technique that makes EAs possible to solve function optimization problems with several inequality and a single equality constraints. The proposed technique simply forces individuals newly generated to satisfy the equality constraint. In order to generate these individuals, this study utilizes a Markov chain Monte Carlo (MCMC) method and crossover kernels. While the proposed technique can be applied to any EA, this study applies it to a relatively simple one, UNDX/MGG. Experimental results show that UNDX/MGG with the proposed technique has an ability to solve unimodal and multimodal function optimization problems with constraints. Finally, we show that, although our approach cannot solve function optimization problems with multiple equality constraints, we can convert some of them into those with a single equality constraint.