Estimating the reproductive potential of offspring in evolutionary heuristics for combinatorial optimization problems

This paper proposes a metaheuristic selection technique for controlling the progress of an evolutionary algorithm (and possibly other heuristic search techniques) to manipulate and make use of the relationship between runtime and solution quality. The paper examines the idea that very rapid increases in initial fitness may lead to premature convergence and a reported solution that is less than optimal. We examine the advantages provided by this metaheuristic selection technique in solving two different combinatorial optimization problems: including a “toy” problem of finding magic squares and a more realistic vehicle routing problem (VRP) benchmark. The method is found to be useful for finding both higher quality solutions with a marginally longer algorithm run time and for obtaining lower quality solutions in a shorter time. Furthermore, the impact on the search results is similar for both the magic square and the VRP problem providing evidence the method is scalable to other problem domains, and therefore is potentially a relatively straight forward addition to many heuristic approaches that can add value by improving both runtime and solution quality.