Differential Evolution Using Superior Infeasible Solutions for Constrained Optimization

Differential Evolution (DE) is one of the effective metaheuristics for solving unconstrained optimization problems. Constraint Handling Technique (CHT) is needed to extend DE to constrained optimization. Feasibility Rule (FR) is one of the typical CHT. FR addresses constraints by using a simple rule that considers the objective function and constraint violation when comparing search individuals. However, since the solutions with small constraint violation, i.e., feasible solutions, are preferentially selected, the set of search individuals may be biased toward feasible regions and the improvement of the objective function value may stagnate. This paper overcomes this challenge by proposing a DE that uses a superior infeasible solution in an external archive. The external archive in the proposed DE stores search individuals that are superior in both objective function value and constraint violation and utilize them to generate mutant individuals. Finally, we verify the effectiveness of the proposed method using a benchmark problem where the feasible region is a convex set.