Replicators, Majorization and Genetic Algorithms: New Models and Analytical tools.
Anil Menon, Kishan G. Mehrotra, Chilukuri K. Mohan, Sanjay Ranka · 1996
This paper advocates the use of replicator selection models and quadratic crossover models for the analysis of evolutionary algorithms. We establish two sets of results. The first is a global optimization theorem for replicator systems that allows replicator fitnesses to vary, depending on the replicator proportions. The second set of results establishes a strong connection between evolutionary algorithms and majorization theory, using replicator models as a bridge. Specifically, we establish sufficient conditions for replicator selection and crossover models to implement the majorization ordering. The connection with majorization theory suggests new selection and crossover operators, new convergence results and significant theoretical gains such as generalization of previous results on quadratic dynamical systems. Quantities such as relative entropy are known to increase in quadratic crossover models; majorization results are used to derive bounds on the increase. 1 Introduction It h...