Constrained real parameter optimization with a gradient repair based Differential Evolution algorithm

Abstract

Till now several constraint handling techniques have been proposed to be used in conjunction with Evolutionary Algorithms (EAs). Optimizing the constrained objective functions are computationally difficult, especially if the constraints are non-linear and nonconvex. Differential Evolution (DE) is a simple, fast, and robust population-based global optimizer that can efficiently search multi-modal fitness landscapes. We proposed a constrained optimizer based on DE by incorporating the idea of gradient-based repair with a DE/rand/1/bin scheme. If the individual candidate solutions generated by DE are infeasible we apply gradient-based repair to convert those into feasible solutions. Thus as the generations progress, the ratio between feasible search space and the whole search space is enhanced. This in turn accelerates the search process and leads to an efficient search for very high quality solutions within the feasible region. To handle the equality constraints we have used a small tolerance parameter. The 18 problems given in special session and competition on “Single Objective Constrained Real Parameter Optimization” under Congress on Evolutionary Computation (CEC 2010) are solved by gradient repair based DE and have been compared with the results obtained with two other recent and best-known constrained optimizers published.