Constraint Handling Heuristics for Evolution Strategies

Abstract

Whenever the search space is restricted due to constraints of the underlying problem, the EA has to make use of heuristic extensions which are called constraint handling methods. Constraint handling is very relevant to practical applications. A constraint is a restriction on possible value combinations of variables. EAs and in particular ES are used for constrained numerical parameter optimization. The optimum quite often lies on the constraint boundary or even in a vertex of the feasible search space. In such cases the EA frequently suffers from premature convergence because of a low success probability near the constraint boundaries. We prove premature step size reduction for a (1+1)-EA under simplified conditions, analyzing the success rates at the constraint boundary and the expected changes of the step sizes.