Heuristics To Avoid Redundant Solutions On Population-based Multimodal Continuous Optimization

In population-based meta-heuristics, the generation and maintenance of diversity seem to be crucial to deal with multimodal continuous optimization. However, usually this crucial aspect is not an inherent feature of generally adopted meta-heuristics. In this paper, we propose to associate diversity maintenance with the detection and elimination of redundant candidate solutions in the search space, more specifically candidate solutions located at the same attraction basin of a local optimum. Two low computational cost heuristics are proposed to detect redundancy, in a pairwise comparison of candidate solutions and by extracting local features of the fitness landscape at runtime. Those heuristics are not tied to a specific class of algorithms, and are thus able to be incorporated into a broad range of population-based meta-heuristics, and even into multiple executions of non-population-based algorithms. In a set of experimental results, the two heuristics were implemented as an attached module of an already existing multipopulation meta-heuristics, and the results indicate that they operate properly, no matter the number and conformation of the attraction basins in multimodal optimization problems. © 2011 IEEE.23212328Czogala, E., Zimmermann, H., Hans-Jurgen, Decision making in uncertain environments (1986) European Journal of Operational Research, 23 (2), pp. 202-212. , Elsevier, FebruaryDeb, K., (2001) Multi-objective Optimization Using Evolutionary Algorithms, , WileyJin, Y.J., Branke, Evolutionary optimization in uncertain environments - A survey (2005) IEEE Trans. on Evolutionary Computation, 9 (3)Pasti, R., De Castro, L.N., Bio-inspired and gradient-based algorithms to train MLPs: The influence of diversity (2009) Information Sciences, 179, pp. 1441-1453Alba, E., (2005) Parallel Metaheuristics: A New Class of Algorithms, , WileyGlover, F., Kochenberger, G.A., (2003) Handbook of Metaheuristics, , SpringerBazaraa, M.M., Sherali, H.D.H.D., Shetty, C.M.C.M., (1993) Nonlinear Programming - Theory and Algorithms, , 2° edição, John Wiley & Sons IncBäck, T.T., Fogel, D.B., Michalewicz, Z., Evolutionary computation 1 basic algorithms and operators (2000) Institute of Physiscs Publishing (IOP), Bristol and PhiladelphiaBäck, T.T., Fogel, D.B., Michalewicz, Z., (2000) Evolutionary Computation 2 Advanced Algorithms and Operators, , Institute of Physiscs Publishing IOP, Bristol and PhiladelphiaKennedy, J., Eberhart, R.R., Shi, Y., (2001) Swarm Intelligence, , Morgan Kauffman PublishersDe Castro, L.N., Timmis, J., (2002) Artificial Immune Systems: A New Computational Intelligence Approach, , Springer-VerlagAlba, E., Dorronsoro, B., The exploration/exploitation tradeoff in dynamic cellular genetic algorithms (2005) IEEE Transactions on Evolutionary Computation, 9 (2), pp. 126-142. , DOI 10.1109/TEVC.2005.843751Reyes-Sierra, M., Coello Coello, C.A., Multi-objective particle swarm optimizers: A survey of the state-of-the-art (2006) International Journal of Computational Intelligence Research, 2 (3), pp. 287-308Maia, R.D., Pasti, R.R., De Castro, L.N., A bio-inspired strategy to generate diversity in the particle swarm optimization algorithm (2009) First Workshop on Emergent Computing, , Santiago. Jornadas Chilenas de Computación, 2009De Castro, L.N., Von Zuben, F.J., Learning and optimization using the clonal selection principle (2002) IEEE Transactions on Evolutionary Computation, 6 (3), pp. 239-251. , DOI 10.1109/TEVC.2002.1011539, PII S1089778X02060654De Franca, F.O., Von Zuben, F.J., De Castro, L.N., An artificial immune network for multimodal function optimization on dynamic environments (2005) GECCO 2005 - Genetic and Evolutionary Computation Conference, pp. 289-296. , GECCO 2005 - Genetic and Evolutionary Computation Conferenc