Penalty Function Methods for Constrained Optimization with Genetic Algorithms: A Statistical Analysis

Genetic algorithms (GAs) have been successfully applied to numerical optimization problems. Since GAs are usually designed for unconstrained optimization, they have to be adapted to tackle the constrained cases, i.e. those in which not all representable solutions are valid. In this work we experimentally compare 5 ways to attain such adaptation. Our analysis relies on the usual method of selecting an arbitrary suite of test functions (25 of these) albeit applying a methodology which allows us to determine which method is better within statistical certainty limits. In order to do this we have selected 5 penalty function strategies; for each of these we have further selected 3 particular GAs. The behavior of each strategy and the associated GAs is then established by extensively sampling the function suite and finding the worst case best values from Chebyshev's theorem. We have found some counterintuitive results which we discuss and try to explain.