On Weight-Biased Mutation for Graph Problems

Many graph problems seek subgraphs of minimum weight that satisfy the problems’ constraints. Examples include the degreeconstrained minimum spanning tree and traveling salesman problems. Low-weight edges predominate in optimal solutions to these problems, and the performance of evolutionary algorithms for them is often improved by biasing their operators to favor these edges. From the distributions of edges’ ranks in optimal solutions to these two problems, we identify probabilities for edges that minimize the average expected time until mutation chooses them for inclusion in a solution. On instances of the degree-constrained minimum spanning tree problem, an evolutionary algorithm performs better with this operator than with alternative mutations. These results are not replicated on instances of the traveling salesman problem, where the inclusion of one edge in a tour requires the inclusion of another dependant edge.