Constrained min–max optimization via the improved constraint-activated differential evolution with escape vectors

• A new scheme to solve the issue of premature convergence of differential evolution.
• New test functions to evaluate constrained min–max optimization algorithms (CMMOA).
• An improved CMMOA to achieve a quite satisfied success rate.

In system design, the best system designed under a simple experimental environment may not be suitable for application in real world if dramatic changes caused by uncertainties contained in the real world are considered. To deal with the problem caused by uncertainties, designers should try their best to get the most robust solution. The most robust solution can be obtained by constrained min–max optimization algorithms. In this paper, the scheme of generating escape vectors has been proposed to solve the problem of premature convergence of differential evolution. After applying the proposed scheme to the constrained min–max optimization algorithm, the performance of the algorithm could be greatly improved. To evaluate the performance of constrained min–max optimization algorithms, more complex test problems have also been proposed in this paper. Experimental results show that the improved constrained min–max optimization algorithm is able to achieve a quite satisfied success rate on all considered test problems under limited accuracy.