Comparison of Constraint-Handling Mechanisms for the (1,λ)-ES on a Simple Constrained Problem

This paper investigates constraint-handling techniques used in nonelitist single-parent evolution strategies for the problem of maximizing a linear function with a single linear constraint. Two repair mechanisms are considered, and the analytical results are compared to those of earlier repair approaches in the same fitness environment. The first algorithm variant applies reflection to initially infeasible candidate solutions, and the second repair method uses truncation to generate feasible solutions from infeasible ones. The distributions describing the strategies' one-generation behavior are calculated and used in a zeroth-order model for the steady state attained when operating with fixed step size. Considering cumulative step size adaptation, the qualitative differences in the behavior of the algorithm variants can be explained. The approach extends the theoretical knowledge of constraint-handling methods in the field of evolutionary computation and has implications for the design of constraint-handling techniques in connection with cumulative step size adaptation.