A Self-adaptive Differential Evolution Algorithm with Constraint Sequencing

Abstract

Constrained optimization is an active area of research where attempts are being regularly made to improve the efficiency of the underlying optimization algorithms. While population based stochastic algorithms such as evolutionary algorithms, differential evolution (DE), particle swarm optimization etc. have been the popular choice as the underlying optimization scheme, adaptive strategies are usually employed to deal with constraints. Most of such approaches adopt a complete evaluation policy, i.e., all constraints and objectives corresponding to a solution is always evaluated for every solution under consideration. However, in a typical constrained optimization problem, one or more constraints are often difficult to satisfy and it might be beneficial to evaluate the constraints in a sequence. Evaluation of subsequent constraints and objective function can be skipped whenever a constraint is violated. In this paper, a self adaptive differential evolution algorithm is introduced which maintains multiple subpopulations, each of which is assigned a prescribed constraint sequence based on a ring topology. Solutions are ranked in each subpopulation and a migration scheme is employed to transfer feasible solutions to a subpopulation of feasible individuals. The performance of the proposed scheme is compared with a single sequence approach and other state of the art DE forms using the standard g-series test functions having inequality constraints. The results clearly indicate the potential savings in the computational cost. Apart from savings in computational cost, the paper also makes an important contribution as it provides useful physical insights on the search trajectories and their effect in various forms of constrained optimization problems.