Stopping criteria for genetic algorithms with application to multiobjective optimization

Abstract

For a general Markov chain model of genetic algorithm, we establish an upper bound for the number of iterations which must be executed in order to generate, with a prescribed probability, a population consisting entirely of minimal solutions to a multiobjective optimization problem. However, since populations may contain multiple copies of the same element, we can only guarantee that at least one minimal solution is found. Using this upper bound, we then derive a stopping criterion which ensures that at least one minimal element is a member of the last population generated. © 2010 Springer-Verlag.