Abstract
The introduction of learning to the search mechanisms of optimization algorithms has been nominated as one of the viable approaches when dealing with complex optimization problems, in particular with multi-objective ones. One of the forms of carrying out this hybridization process is by using multi-objective optimization estimation of distribution algorithms (MOEDAs). However, it has been pointed out that current MOEDAs have a intrinsic shortcoming in their model-building algorithms that hamper their performance.
In this work we argue that error-based learning, the class of learning most commonly used in MOEDAs is responsible for current MOEDA underachievement. We present adaptive resonance theory (ART) as a suitable learning paradigm alternative and present a novel algorithm called multi-objective ART-based EDA (MARTEDA) that uses a Gaussian ART neural network for model-building and an hypervolume-based selector as described for the HypE algorithm. In order to assert the improvement obtained by combining two cutting-edge approaches to optimization an extensive set of experiments are carried out. These experiments also test the scalability of MARTEDA as the number of objective functions increases.
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References
Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems. In: Genetic and Evolutionary Computation, 2nd edn. Springer, New York (2007)
Miettinen, K.: Nonlinear Multiobjective Optimization. International Series in Operations Research & Management Science, vol. 12. Kluwer, Norwell (1999)
Pareto, V.: Cours D’Économie Politique. F. Rouge, Lausanne (1896)
Purshouse, R.C., Fleming, P.J.: On the evolutionary optimization of many conflicting objectives. IEEE Transactions on Evolutionary Computation 11(6), 770–784 (2007)
Stewart, T., Bandte, O., Braun, H., Chakraborti, N., Ehrgott, M., Göbelt, M., Jin, Y., Nakayama, H., Poles, S., Di Stefano, D.: Real-world applications of multiobjective optimization. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization. LNCS, vol. 5252, pp. 285–327. Springer, Heidelberg (2008)
Wagner, T., Beume, N., Naujoks, B.: Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 742–756. Springer, Heidelberg (2007)
Bader, J., Deb, K., Zitzler, E.: Faster hypervolume-based search using Monte Carlo sampling. In: Beckmann, M., Künzi, H.P., Fandel, G., Trockel, W., Basile, A., Drexl, A., Dawid, H., Inderfurth, K., Kürsten, W., Schittko, U., Ehrgott, M., Naujoks, B., Stewart, T.J., Wallenius, J. (eds.) Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems. LNEMS, vol. 634, pp. 313–326. Springer, Berlin (2010)
Bader, J., Zitzler, E.: HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization. TIK Report 286, Computer Engineering and Networks Laboratory (TIK), ETH Zurich (2008)
Deb, K., Saxena, D.K.: Searching for Pareto–optimal solutions through dimensionality reduction for certain large–dimensional multi–objective optimization problems. In: 2006 IEEE Conference on Evolutionary Computation (CEC 2006), pp. 3352–3360. IEEE Press, Piscataway (2006)
Brockhoff, D., Zitzler, E.: Dimensionality reduction in multiobjective optimization: The minimum objective subset problem. In: Waldmann, K.H., Stocker, U.M. (eds.) Operations Research Proceedings 2006, pp. 423–429. Springer, Heidelberg (2007)
Brockhoff, D., Saxena, D.K., Deb, K., Zitzler, E.: On handling a large number of objectives a posteriori and during optimization. In: Knowles, J., Corne, D., Deb, K. (eds.) Multi–Objective Problem Solving from Nature: From Concepts to Applications. Natural Computing Series, pp. 377–403. Springer, Heidelberg (2008)
Corne, D.W.: Single objective = past, multiobjective = present,??? = future. In: Michalewicz, Z. (ed.) 2008 IEEE Conference on Evolutionary Computation (CEC), Part of 2008 IEEE World Congress on Computational Intelligence (WCCI 2008). IEEE Press, Piscataway (2008)
Michalski, R.S.: Learnable evolution model: Evolutionary processes guided by machine learning. Machine Learning 38, 9–40 (2000)
Sheri, G., Corne, D.W.: The simplest evolution/learning hybrid: LEM with KNN. In: IEEE World Congress on Computational Intelligence, pp. 3244–3251. IEEE Press, Hong Kong (2008)
Sheri, G., Corne, D.W.: Learning-assisted evolutionary search for scalable function optimization: LEM(ID3). In: IEEE World Congress on Computational Intelligence. IEEE Press, Barcelona (2010)
Lozano, J.A., Larrañaga, P., Inza, I., Bengoetxea, E. (eds.): Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms. Springer, Heidelberg (2006)
Pelikan, M., Sastry, K., Goldberg, D.E.: Multiobjective estimation of distribution algorithms. In: Pelikan, M., Sastry, K., Cantú-Paz, E. (eds.) Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications. SCI, pp. 223–248. Springer, Heidelberg (2006)
Martí, L., García, J., Berlanga, A., Coello Coello, C.A., Molina, J.M.: On current model-building methods for multi-objective estimation of distribution algorithms: Shortcommings and directions for improvement. Technical Report GIAA2010E001, Grupo de Inteligencia Artificial Aplicada, Universidad Carlos III de Madrid, Colmenarejo, Spain (2010)
Grossberg, S.: Studies of Mind and Brain: Neural Principles of Learning, Perception, Development, Cognition, and Motor Control. Reidel, Boston (1982)
Sarle, W.S.: Why statisticians should not FART. Technical report, SAS Institute, Cary, NC (1995)
Williamson, J.R.: Gaussian ARTMAP: A neural network for fast incremental learning of noisy multidimensional maps. Neural Networks 9, 881–897 (1996)
Martí, L., García, J., Berlanga, A., Molina, J.M.: Moving away from error-based learning in multi-objective estimation of distribution algorithms. In: Branke, J., Alba, E., Arnold, D., Bongard, J., Brabazon, A., Butz, M.V., Clune, J., Cohen, M., Deb, K., Engelbrecht, A., Krasnogor, N., Miller, J., O’Neill, M., Sastry, K., Thierens, D., Vanneschi, L., van Hemert, J., Witt, C. (eds.) GECCO 2010: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, pp. 545–546. ACM Press, New York (2010)
Ahn, C.W., Ramakrishna, R.S.: Multiobjective real-coded Bayesian optimization algorithm revisited: Diversity preservation. In: GECCO 2007: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, pp. 593–600. ACM Press, New York (2007)
Shapiro, J.: Diversity loss in general estimation of distribution algorithms. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 92–101. Springer, Heidelberg (2006)
Yuan, B., Gallagher, M.: On the importance of diversity maintenance in estimation of distribution algorithms. In: GECCO 2005: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, pp. 719–726. ACM Press, New York (2005)
Peña, J.M., Robles, V., Larrañaga, P., Herves, V., Rosales, F., Pérez, M.S.: GA-EDA: Hybrid evolutionary algorithm using genetic and estimation of distribution algorithms. In: Orchard, B., Yang, C., Ali, M. (eds.) IEA/AIE 2004. LNCS (LNAI), vol. 3029, pp. 361–371. Springer, Heidelberg (2004)
Zhang, Q., Sun, J., Tsang, E.: An evolutionary algorithm with guided mutation for the maximum clique problem. IEEE Transactions on Evolutionary Computation 9(2), 192–200 (2005)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
While, L., Hingston, P., Barone, L., Huband, S.: A faster algorithm for calculating hypervolume. IEEE Transactions on Evolutionary Computation 10(1), 29–38 (2006)
Fonseca, C.M., Paquete, L., López-Ibánez, M.: An improved dimension–sweep algorithm for the hypervolume indicator. In: 2006 IEEE Congress on Evolutionary Computation (CEC 2006), pp. 1157–1163 (2006)
Beume, N., Rudolph, G.: Faster S–metric calculation by considering dominated hypervolume as Klee’s measure problem. In: Kovalerchuk, B. (ed.) Proceedings of the Second IASTED International Conference on Computational Intelligence, pp. 233–238. IASTED/ACTA Press (2006)
Beume, N.: S–metric calculation by considering dominated hypervolume as Klee’s measure problem. Evolutionary Computation 17(4), 477–492 (2009); PMID: 19916778
Bringmann, K., Friedrich, T.: Approximating the volume of unions and intersections of high–dimensional geometric objects. Computational Geometry 43(6-7), 601–610 (2010)
Papadimitriou, C.M.: Computational Complexity. Addison-Wesley, Reading (1994)
Deolalikar, V.: P≠NP. Technical report, Hewlett Packard Research Labs, Palo Alto, CA, USA (2010)
Box, G.E.P., Muller, M.E.: A note on the generation of random normal deviates. Annals of Mathematical Statistics 29, 610–611 (1958)
Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. IEEE Transactions on Evolutionary Computation 10(5), 477–506 (2006)
Martí, L., García, J., Berlanga, A., Molina, J.M.: Introducing MONEDA: Scalable multiobjective optimization with a neural estimation of distribution algorithm. In: Keizer, M., Antoniol, G., Congdon, C., Deb, K., Doerr, B., Hansen, N., Holmes, J., Hornby, G., Howard, D., Kennedy, J., Kumar, S., Lobo, F., Miller, J., Moore, J., Neumann, F., Pelikan, M., Pollack, J., Sastry, K., Stanley, K., Stoica, A., Talbi, E.G., Wegener, I. (eds.) GECCO 2008: 10th Annual Conference on Genetic and Evolutionary Computation, pp. 689–696. ACM Press, New York (2008); EMO Track “Best Paper” Nominee
Bosman, P.A.N., Thierens, D.: The naive MIDEA: A baseline multi–objective EA. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 428–442. Springer, Heidelberg (2005)
Ahn, C.W.: Advances in Evolutionary Algorithms. In: Theory, Design and Practice. Springer, Heidelberg (2006) ISBN 3-540-31758-9
Beume, N., Naujoks, B., Emmerich, M.: SMS–EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181(3), 1653–1669 (2007)
Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. TIK Report 214, Computer Engineering and Networks Laboratory (TIK), ETH Zurich (2006)
Chambers, J., Cleveland, W., Kleiner, B., Tukey, P.: Graphical Methods for Data Analysis. Wadsworth, Belmont (1983)
Mann, H.B., Whitney, D.R.: On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics 18, 50–60 (1947)
Bader, J.: Hypervolume-Based Search for Multiobjective Optimization: Theory and Methods. PhD thesis, ETH Zurich, Switzerland (2010)
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Martí, L., García, J., Berlanga, A., Molina, J.M. (2011). Multi-Objective Optimization with an Adaptive Resonance Theory-Based Estimation of Distribution Algorithm: A Comparative Study. In: Coello, C.A.C. (eds) Learning and Intelligent Optimization. LION 2011. Lecture Notes in Computer Science, vol 6683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25566-3_36
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