Permutation distance measures for memetic algorithms with population management
Résumé
Several new metaheuristic optimization approaches use a distance measure in the solution space to control diversity. Memetic algorithms with population management (MA|PM) are relatively new metaheuristics, that actively control the diversity of a small population of high-quality solutions. The distance measure used should reflect the difference between a given pair of solutions in the solution space. Although difficult to prove, it seems natural to conjecture that a distance measure that more accurately reflects the distance between two solutions is preferable to one that does not. For permutation problems, a myriad of distance measures has been developed, originating in different domains (statistics, computer science, molecular biology,...). In this paper, we look at nine of them. We determine the effort required to calculate them and develop a normalized version of each distance measure, that produces a value between 0 and 1. We then compare their performance by implementing them in a simple MA|PM for the single-machine total weighted tardiness scheduling problem.