Coevolutionary genetic algorithm for constraint satisfaction with a genetic repair operator for effective schemata formation

We discuss a coevolutionary genetic algorithm for constraint satisfaction. Our basic idea is to explore effective genetic information in the population, i.e., schemata, and to exploit the genetic information in order to guide the population to better solutions. Our coevolutionary genetic algorithm (CGA) consists of two GA populations; the first GA, called “H-GA”, searches for the solutions in a given environment (problem), and the second GA, called “P-GA”, searches for effective genetic information involved in the H-GA, namely, good schemata. Thus, each individual in P-GA consists of alleles in H-GA or “don´t care” symbol representing a schema in the H-GA. These GA populations separately evolve in each genetic space at different abstraction levels and affect with each other by two genetic operators: “superposition” and “transcription”. We then applied our CGA to constraint satisfaction problems (CSPs) incorporating a new stochastic “repair” operator for P-GA to raise the consistency of schemata with the (local) constraint conditions in CSPs. We carried out two experiments: First, we examined the performance of CGA on various “general” CSPs that are generated randomly for a wide variety of “density” and “tightness” of constraint conditions in the CSPs that are the basic measures of characterizing CSPs. Next, we examined “structured” CSPs involving latent “cluster” structures among the variables in the CSPs. For these experiments, computer simulations confirmed us the effectiveness of our CGA