A merit function approach for evolution strategies

• A globally convergent evolution strategy to solve general constrained optimization problems. • Quantifiable relaxable constraints are handled using a merit function approach combined with a specific restoration procedure. • The proposed approach is very competitive compared to existing derivative-free optimization solvers on a large set of problems. In this paper, we extend a class of globally convergent evolution strategies to handle general constrained optimization problems. The proposed framework handles quantifiable relaxable constraints using a merit function approach combined with a specific restoration procedure. The unrelaxable constraints, when present, can be treated either by using the extreme barrier function or through a projection approach. Under reasonable assumptions, the introduced extension guarantees to the regarded class of evolution strategies global convergence properties for first order stationary constraints. Numerical experiments are carried out on a set of problems from the CUTEst collection as well as on known global optimization problems.