Expected Running Time of Parallel Evolutionary Algorithms on Unimodal Pseudo-Boolean Functions over Small-World Networks

This paper proposes a theoretical and experimental analysis of the expected running time for an elitist parallel Evolutionary Algorithm (pEA) based on an island model executed over small-world networks. Our study assumes the resolution of optimization problems based on unimodal pseudo-boolean funtions. In particular, for such function with d values, we improve the previous asymptotic upper bound for the expected parallel running time from O(d√n) to O(d log n). This study is a first step towards the analysis of influence of more complex network topologies (like random graphs created by P2P networks) on the runtime of pEAs. A concrete implementation of the analysed algorithm have been performed on top of the ParadisEO framework and run on the HPC platform of the University of Luxembourg (UL). Our experiments confirm the expected speed- up demonstrated in this article and prove the benefit that pEA can gain from a small-world network topology.