Constraint-activated differential evolution for constrained min–max optimization problems: Theory and methodology

A constraint-activated differential evolution is proposed to solve constrained min–max optimization problems in this paper. To provide theoretical understanding for these problems, their global optima are specified in the proposed definitions. Based on the definition, we propose theorems to prove that a min–max algorithm can be used to solve a max–min problem without any algorithmic changes. Based on the theorems, we propose a constraint-activated differential evolution to solve constrained min–max problems. The proposed method consists of three components, propagation, constraint activation, and inner level evolution. The propagation provides exploitation power of evolution. The constraint activation directly finds a solution which can best activate constraints. The inner level evolution provides continuous evolutionary behavior to prevent convergence premature. The simulation results show that the proposed method attains 100% success rates for all of the numerical benchmarks with an exploitative mutation strategy.