Efficient Constrained Optimization by the ε Constrained Adaptive Differential Evolution

The epsilon constrained method is an algorithm transformation method, which can convert algorithms for unconstrained problems to algorithms for constrained problems using the epsilon level comparison, which compares search points based on the pair of objective value and constraint violation of them. We have proposed the epsilon constrained differential evolution epsilon DE, which is the combination of the epsilon constrained method and differential evolution ( DE), and have shown that the eDE can run very fast and can find very high quality solutions. In this study, we propose the epsilon constrained adaptive DE (epsilon ADE), which adopts a new and stable way of controlling the epsilon level and adaptive control of algorithm parameters in DE. The epsilon ADE is very efficient constrained optimization algorithm that can find high-quality solutions in very small number of function evaluations. It is shown that the epsilon ADE 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.