Toward More Powerful Recombinations

This paper suggests a exible framework for n-dimensional crossover, consisting of cutting, classi cation, and copying of genes. We prove that under this framework, any cutting strategy generates two equivalence classes of genes, making the framework appropriate as a crossover scheme. Three notable features of this framework are: (i) it enables more e ective use of genes' geographical linkage, (ii) it enables more diverse ways of cutting than traditional multi-point crossover on linear strings or existing 2-dimensional crossover schemes, and (iii) it can be readily used within most existing genetic algorithm implementations, i.e., the underlying problem need not be inherently multidimensional. We provide guidelines for designing a crossover strategy under this framework, along with two example crossovers. Experimental results show that one can design new crossovers under this framework which outperform traditional crossover on linear strings, uniform crossover, and existing two-dimensional crossovers.