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

The All-Pairs Shortest Path problem is the first non-artificial 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 $\Theta(n^{3.25}(\log n)^{0.25})$. In this work, we study two variants of the algorithm. These are based on two central concepts in recombination, \emph{repair mechanisms} and \emph{parent selection}. We show that repairing infeasible offspring leads to an improved expected optimization time of $\mathord{O}(n^{3.2}(\log n)^{0.2})$. Furthermore, we prove that choosing parents that guarantee feasible offspring results in an optimization time of $\mathord{O}(n^{3}\log n)$