Adaptive Ranking Mutation Operator Based Differential Evolution for Constrained Optimization

Differential evolution (DE) is a powerful evolutionary algorithm (EA) for numerical optimization. Combining with the constraint-handling techniques, recently, DE has been successfully used for the constrained optimization problems (COPs). In this paper, we propose the adaptive ranking mutation operator (ARMOR) for DE when solving the COPs. The ARMOR is expected to make DE converge faster and achieve feasible solutions faster. In ARMOR, the solutions are adaptively ranked according to the situation of the current population. More specifically, the population is classified into three situations, i.e., infeasible situation, semi-feasible situation, and feasible situation. In the infeasible situation, the solutions are ranked only based on their constraint violations; in the semi-feasible situation, they are ranked according to the transformed fitness; while in the feasible situation, the objective function value is used to assign ranks to different solutions. In addition, the selection probability of each solution is calculated differently in different situations. The ARMOR is simple, and it can be easily combined with most of constrained DE (CDE) variants. As illustrations, we integrate our approach into three representative CDE variants to evaluate its performance. The 24 benchmark functions presented in CEC 2006 and 18 benchmark functions presented in CEC 2010 are chosen as the test suite. Experimental results verify our expectation that the ARMOR is able to accelerate the original CDE variants in the majority of test cases. Additionally, ARMOR-based CDE is able to provide highly competitive results compared with other state-of-the-art EAs.