Self-adaptivity for constraint satisfaction: learning penalty functions

Treating constrained problems with EAs is a very challenging problem. Whether one considers constrained optimization problems or constraint satisfaction problems, the presence of a fitness function (penalty function) reflecting constraint violation is essential. The definition of such a penalty function has a great impact on the GA performance, and it is therefore very important to choose it properly. We show that ad hoc setting of penalties for constraint violations can be circumvented by using self-adaptivity. We illustrate the matter on a discrete CSP, the Zebra problem, and show that the penalties learned by the GA are to a large extent independent of the applied genetic operators as well as the initial constraint weights.