Encoding graphs for genetic algorithms: An investigation using the minimum spanning tree problem

Abstract

We present a comparison of modified and unmodified GAs for the MST problem. A GA assembles successful gene substrings into improved solutions, but it does not have a mechanism to enforce global constraints. Graph theory contains many problems that are suitable for GAs because polynomial-time algorithms do not exist, but they often have global constraints. Special encodings and modifications of GA operators have been developed to deal with this difficulty. We use the MST as an example problem because it is representative of the encoding difficulty, while the existence of polynomial-time algorithms makes the evaluation of performance relatively simple. We modify the GA crossover operator to preserve the property that an MST has 1 fewer edges than the number of vertices. Although this restricts the search space substantially, our results show that the expected benefits are not obtained. The GA demonstrates its power by successfully restricting the search without help.