Incremental approximation of nonlinear constraint functions for evolutionary constrained optimization

Abstract

This paper proposes an alternative approach to efficient solving of nonlinear constrained optimization problems using evolutionary algorithms. It is assumed that the separate-ness of the feasible regions, which imposes big difficulties for evolutionary search, is partially resulted from the complexity of the nonlinear constraint functions. Based on this hypothesis, an approximate model is built for each constraint function with an increasing accuracy, starting from a simple linear approximation. As a result, the feasible region based on the approximate constraint functions will be much simpler, and the isolated feasible regions will become more likely connected. As the evolutionary search goes on, the approximated feasible regions should gradually change back to the original one by increasing the accuracy of the approximate models to ensure that the optimum found by the evolutionary algorithm does not violate any of the original constraints. Empirical studies have been performed on 13 test problems and four engineering design optimization problems. Simulation results suggest that the proposed method is competitive compared to the state-of-the-art techniques for solving nonlinear constrained optimization problems