An adaptive mutation scheme for a penalty-based graph-colouring GA

Abstract

The folklore of evolutionary algorithms still seems to contain some gross over-generalistions, such as that direct encodings are inferior to indirect ones, that penalty-function methods are often poor, and that observed performance on a few instances can be extrapolated to a whole class. In the interests of exploring the status of such folklore we have continued to investigate in depth the use of a simple representation for graph-colouring problems. In this paper we demonstrate that good performance on a variety of medium-sized problems can be obtained with a simple adaptive mutation scheme. The scheme was originally motivated by considering an artificial counter-example to an earlier approach that had seemed very successful, because it had been used to solve some large real-world exam timetabling problems for certain universities. Those solutions were used in practice, and it would have been tempting to assert that the method was a practical success. This paper represents part of a continuing effort to map out the strengths and weaknesses of using a simple direct encoding and penalty functions for graph colouring.