Constrained optimization by ε constrained differential evolution with dynamic ε-level control

Abstract

In this chapter, the improved ε constrained differential evolution (ε DE) is proposed to solve constrained optimization problems with very small feasible region, such as problems with equality constraints, efficiently. The εDE is the combination of the ε constrained method and differential evolution. In general, it is very difficult to solve constrained problems with very small feasible region. To solve such problems, static control schema of allowable constraint violation is often used, where solutions are searched within enlarged region specified by the allowable violation and the region is reduced to the feasible region gradually. However, the proper control depends on the initial population and searching process. In this study, the dynamic control of allowable violation is proposed to solve problems with equality constraints efficiently. In the εDE, the amount of allowable violation can be specified by the ε-level. The effectiveness of the εDE with dynamic ε-level control is shown by comparing with the original εDE and well known optimization method on some nonlinear constrained problems with equality constraints. © 2008 Springer-Verlag Berlin Heidelberg.