Efficient Constrained Optimization by the ε Constrained Differential Evolution Using an Approximation Model with Low Accuracy

Abstract

Researches on constrained optimization using evolutionary algorithms have been actively studied. However, evolutionary algorithms often need a large number of function evaluations before a well acceptable solution can be found. Thus, in order to solve expensive or costly problems, it needs to reduce the number of function evaluations. There are many studies on reducing function evaluations by constructing an approximation model and optimizing problems using approximate values. In general, it is difficult to learn proper approximation model which has enough generalization ability, and it needs much time to learn the model. We have proposed Estimated Comparison Method, where function evaluations are efficiently reduced even when an approximation model with low accuracy is used. In the method, a comparison which compares approximate or estimated values is introduced. The potential model, which is an approximation model with low accuracy and does not need to learn model parameters, is used for approximation. Also, we have proposed the ε constrained method that can convert algorithms for unconstrained problems to algorithms for constrained problems using the ε-level comparison, which compares the search points based on the constraint violation of them. In this study, we propose an effective method to combine the ε constrained method and the estimated comparison method. We define the εDE^pm by applying the method to Differential Evolution. The εDE^pm realizes stable and very efficient search to solve constrained optimization problems. The advantage of the εDE^pm is shown by applying it to various type of well-known 13 constrained problems and comparing the results with the results by other methods.