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 (w. r. t. the number of fitness evaluations) of Θ(n3.25(log n)0.25). In contrast to this simple algorithm, evolutionary algorithms used in practice usually employ refined recombination strategies in order to avoid the creation of infeasible offspring. We study extensions of the basic algorithm by two such concepts which are central in recombination, namely 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). As a second part of our study we prove that choosing parents that guarantee feasible offspring results in an even better optimization time of O(n3 log n). Both results show that already simple adjustments of the recombination operator can asymptotically improve the runtime of evolutionary algorithms. This work greatly benefited from various discussions at the Dagstuhl seminar 08051 on Theory of Evolutionary Algorithms. Department 1: Algorithms and Complexity, Max-Planck-Institut für Informatik, 66123 Saarbrücken, Germany School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel Part of this work was done while Daniel Johannsen was with the Max-Planck-Institut für Informatik, Saarbrücken. He is now supported by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD). Timo Kötzing was supported by the Deutsche Forschungsgemeinschaft (DFG) under grant no. NE 1182/5-1. School of Computer Science, The University of Adelaide, Adelaide, SA 5005, Australia This work was partially done while Frank Neumann was affiliated with the Max-Planck-Institut für Informatik, Saarbrücken. Institut für Mathematik, Technische Universität Berlin 10623 Berlin, Germany