APPROXIMATE MODELS FOR CONSTRAINT FUNCTIONS IN EVOLUTIONARY CONSTRAINED OPTIMIZATION

Abstract

Many real-world scientific and engineering problems are constrained optimization problems (COPs). To solve those COPs, a variety of evolutionary algorithms have been proposed by incorporating various constraint handling techniques. However, many of them are not able to achieve the global optimum due to the presence of highly constrained, isolated feasible regions in the search space. To effectively address the low ratio of feasible regions in the search space, this paper presents a genetic programming based approximation approach in combination with a multi-membered evolution strategy. In the proposed constraint-handling method, we generate an approximate model for each constraint function with an increasing accuracy, from a linear-type approximation to a model that has a complexity similar to the original constraint functions, thereby manipulating the complexity of the feasible region. Thanks to this feature, our constrained evolutionary optimization algorithm can achieve the optimal solution, effectively. Simulations are carried out to compare the proposed algorithm with the state-of-the-art algorithms for handling COPs on 13 benchmark problems and three engineering optimization problems. Our simulation results demonstrate that the proposed algorithm is comparable to or better than the state-of-the-art on most test problems, and clearly outperforms many algorithms in solving the engineering design optimization problems.