Stochastic ranking for constrained evolutionary optimization

TLDR

Penalty functions are commonly used in constrained optimization, but balancing them with objective functions is challenging. The study proposes stochastic ranking to balance objective and penalty functions and reinterprets penalty methods through dominance. The authors discuss pitfalls of naive penalty methods and evaluate stochastic ranking with a μ/λ evolution strategy on 13 benchmark problems. Results demonstrate that stochastic ranking alone improves search performance without specialized variation operators.

Abstract

Penalty functions are often used in constrained optimization. However, it is very difficult to strike the right balance between objective and penalty functions. This paper introduces a novel approach to balance objective and penalty functions stochastically, i.e., stochastic ranking, and presents a new view on penalty function methods in terms of the dominance of penalty and objective functions. Some of the pitfalls of naive penalty methods are discussed in these terms. The new ranking method is tested using a (/spl mu/, /spl lambda/) evolution strategy on 13 benchmark problems. Our results show that suitable ranking alone (i.e., selection), without the introduction of complicated and specialized variation operators, is capable of improving the search performance significantly.