Analysis of a repair mechanism for the (1,λ)-ES applied to a simple constrained problem
Dirk V. Arnold · 2011
We study the behaviour of a (1,λ)-ES that applies a simple repair mechanism to infeasible candidate solutions for the problem of maximising a linear function with a single linear constraint. Integral expressions that describe the strategy's one-generation behaviour are derived and used in a simple zeroth order model for the steady state of the strategy. Applied to the analysis of cumulative step size adaptation, the approach provides an intuitive explanation for the algorithm's behaviour as well as a condition on the setting of its parameters. A comparison with the strategy that resamples infeasible candidate solutions rather than repairing them is drawn, and the qualitatively different behaviour is explained.