Multi-objective Cooperative Coevolutionary Evolutionary Algorithms for Continuous and Combinatorial Optimization

This chapter introduces three new multi-objective cooperative coevolutionary variants of three state-of-the-art multi-objective evolutionary algorithms, namely, Nondominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Multi-objective Cellular Genetic Algorithm (MOCell). In such a coevolutionary architecture, the population is split into several subpopulations, each of them being in charge of optimizing a subset of the global solution by using the original multi-objective algorithm. Evaluation of complete solutions is achieved through cooperation, i.e., all subpopulations share a subset of their current partial solutions. Our purpose is to study the performance of the coevolutionary multi-objective approaches in two different contexts: continuous and combinatorial optimization. In the first case we deal with a set of well-known benchmark problems, while in the the second one we conduct a study about a real-world problem related to grid computing, the bi-objective robust scheduling problem of independent tasks. The goal in this problem is to minimize makespan (i.e., the time when the latest machine finishes its assigned tasks) and to maximize the robustness of the schedule (i.e., its tolerance to unexpected changes on the estimated time to complete the tasks). We have made a parallel, multithreaded implementation of the coevolutionary algorithms and we have analyzed the results obtained in terms of both the quality of the Pareto front approximations yielded by the techniques as well as the resulting speedups when running them on a multicore machine. Bernabé Dorronsoro Interdisciplinary Centre for Security, Reliability, and Trust, University of Luxembourg, e-mail: [email protected] Grégoire Danoy and Pascal Bouvry Faculty of Sciences, Technology and Communication, University of Luxembourg e-mail: {gregoire.danoy, pascal.bouvry}@uni.lu Antonio J. Nebro E.T.S.I. Informática, University of Málaga, Spain e-mail: [email protected]