More Effective Crossover Operators for the All-Pairs Shortest Path Problem

The all-pairs shortest path problem is the first nonartificial problem for which it was shown that adding crossover can significantly speed up a mutation-only evolutionary algorithm. Recently, the analysis of this algorithm was refined and it was shown to have an expected optimization time of Θ(n3.25(log n)0.25). In this work, we study two variants of the algorithm. These are based on two central concepts in recombination, repair mechanisms and parent selection. We show that repairing infeasible offspring leads to an improved expected optimization time of O(n3.2(log n)0.2). Furthermore, we prove that choosing parents that guarantee feasible offspring results in an optimization time of O(n3 log n).