Solving Difficult Constrained Optimization Problems by the ε Constrained Differential Evolution with Gradient-Based Mutation

While research on constrained optimization using evolutionary algorithms has been actively pursued, it has had to face the problem that the ability to solve multi-modal problems is insufficient, that the ability to solve problems with equality constraints is inadequate, and that the stability and efficiency of searches is low. We have proposed the

ε

DE, defined by applying the

ε

constrained method to differential evolution (DE). It is shown that the

ε

DE is a fast and stable algorithm that is robust to multi-modal problems and it can solve problems with many equality constraints by introducing a gradient-based mutation which finds a feasible point using the gradient of constraints. In this chapter, an improved

ε

DE is proposed, in which faster reduction of the relaxation of equality constraints in the

ε

constrained method and higher gradient-based mutation rate are adopted in order to solve problems with many equality constraints and to find feasible solutions faster and very stably. Also, cutting off and reflecting back solutions outside of search space are adopted to improve the efficiency in finding optimal solutions. The improved

ε

DE realizes stable and efficient searches, and can solve difficult constrained optimization problems with equality constraints. The advantage of the improved

ε

DE is shown by applying it to twenty four constrained problems of various types.