Engineering Optimization Using an Improved Epsilon Differential Evolution with Directional Mutation and Nearest Neighbor Comparison

Abstract

In this paper, an efficient differential evolution (DE) algorithm is presented to solve constrained optimization problem. To skip unnecessary function evaluations, a simple mechanism called nearest neighbor comparison (NNC) is applied. The NNC is a method to prejudge a solution by its nearest point in the search population, so that unpromising solution will be skipped without evaluation. The NNC has been proposed to reduce the number of function evaluations effectively in unconstrained optimization. In this study, the NNC method is proposed for constrained optimization by combining with the ε constrained method. Moreover, a simple directional mutation rule is introduced to increase the possibility of creating improved solutions. Both the NNC method and the directional mutation rule do not require additional control parameter for DE, as often found in several modified DE variants. The effectiveness of the proposed constrained DE algorithm, named as εDEdn, is illustrated by solving five benchmark engineering design problems. The results show that the NNC combined with the ε constrained method can omit up to fifty percents function evaluations. It is also shown that the direction mutation can increase the convergence rate of the optimization. Comparing with other state-of-the-art DE variants reported in the literature, the proposed DE often gives equal or better results with considerably smaller number of function calls.