Feasibility preserving constraint-handling strategies for real parameter evolutionary optimization

Abstract

Evolutionary algorithms (EAs) are being routinely applied for a variety of optimization tasks, and real-parameter optimization in the presence of constraints is one such important area. During constrained optimization EAs often create solutions that fall outside the feasible region; hence a viable constraint-handling strategy is needed. This paper focuses on the class of constraint-handling strategies that repair infeasible solutions by bringing them back into the search space and explicitly preserve feasibility of the solutions. Several existing constraint-handling strategies are studied, and two new single parameter constraint-handling methodologies based on parent-centric and inverse parabolic probability (IP) distribution are proposed. The existing and newly proposed constraint-handling methods are first studied with PSO, DE, GAs, and simulation results on four scalable test-problems under different location settings of the optimum are presented. The newly proposed constraint-handling methods exhibit robustness in terms of performance and also succeed on search spaces comprising up-to $$500$$500 variables while locating the optimum within an error of $$10^{-10}$$10-10. The working principle of the IP based methods is also demonstrated on (i) some generic constrained optimization problems, and (ii) a classic `Weld' problem from structural design and mechanics. The successful performance of the proposed methods clearly exhibits their efficacy as a generic constrained-handling strategy for a wide range of applications.