An Analysis on Linear Crossover for Real Number Chromosomes in an Infinite Population Size

In this paper, as one approach for mathematical analysis of genetic algorithms with real number chromosomes, we focus our attention on crossovers using a linear combination of the elements on the locus and verify the property in the change of the distribution of the chromosomes. This framework includes the average crossover and the Unfair Average Crossover we have proposed. We apply this result to these crossover methods. I. Introduction A lot of experimental and theoretical researches on Genetic Algorithms (GA) or Evolutionary Algorithms (EA) have been recently reported. GAs basically use bit strings as chromosomes and EAs use real value vectors as chromosomes. In fact, the difference between them has not been strictly perceived and some algorithms by the name of "GA" use real value vectors. In the theoretical results, most of them are ones for the Simple GA (SGA). These are based on the theory of Finite Markov Chain because the SGA uses bit strings with a constant length. However, t..