Parameterless penalty function for solving constrained evolutionary optimization

A criticism of evolutionary algorithms might be the lack of efficient and robust generic methods to handle constraints. The most widespread approach for constrained search problems is to use penalty methods, because of their simplicity and ease of implementation. The penalty function approach is generic and applicable to any type of constraint (linear or nonlinear). Nonetheless, the most difficult aspect of the penalty function approach is to find an appropriate penalty parameters needed to guide the search towards the constrained optimum. In this paper, GA's population-based approach and Ranks are exploited to devise a penalty function approach that does not require any penalty parameter called Adaptive GA-RRWS. Adaptive penalty parameters assignment among feasible and infeasible solutions are made with a view to provide a search direction towards the feasible region. rank-based roulette wheel selection operator (RRWS) is used. The new adaptive penalty and rank-based roulette wheel selection operator allow GA's to continuously find better feasible solutions, gradually leading the search near the true optimum solution. GAs with this constraint handling approach have been tested on five problems commonly used in the literature. In all cases, the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier.