Efficient Constrained Optimization by the ε Constrained Rank-Based 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 rank-based DE (εRDE), which adopts a new and simple scheme of controlling algorithm parameters in DE. In the scheme, different parameter values are selected for each individual. Small scaling factor and large crossover rate are selected for good individuals to improve the efficiency of search. Large scaling factor and small crossover rate are selected for bad individuals to improve the stability of search. The goodness is given by the ranking information. The εRDE is a very efficient constrained optimization algorithm that can find high-quality solutions in very small number of function evaluations. It is shown that the εRDE 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. Keywords-constrained optimization; ε constrained method; differential evolution; parameter control