Efficient constrained optimization by the ε constrained adaptive differential evolution

The ε constrained method is an algorithm transformation method, which can convert algorithms for unconstrained problems to algorithms for constrained problems using the ε level comparison, which compares search points based on the pair of objective value and constraint violation of them. We have proposed the ε constrained differential evolution εDE, which is the combination of the ε constrained method and differential evolution (DE), and have shown that the εDE can run very fast and can find very high quality solutions. In this study, we propose the ε constrained adaptive DE (εADE), which adopts a new and stable way of controlling the ε level and adaptive control of algorithm parameters in DE. The εADE is very efficient constrained optimization algorithm that can find high-quality solutions in very small number of function evaluations. It is shown that the εADE can find near optimal solutions stably in about half the number of function evaluations compared with various other methods on well known nonlinear constrained problems.