Abstract
Recently, we have proposed a Multi-Objective Bayesian Artificial Immune System (MOBAIS) to deal effectively with building blocks (high-quality partial solutions coded in the solution vector) in combinatorial multi-objective problems. By replacing the mutation and cloning operators with a probabilistic model, more specifically a Bayesian network representing the joint distribution of promising solutions, MOBAIS takes into account the relationships among the variables of the problem, avoiding the disruption of already obtained high-quality partial solutions. The preliminary results have indicated that our proposal is able to properly build the Pareto front. Motivated by this scenario, this paper better formalizes the proposal and investigates its usefulness on more challenging problems. In addition, an important enhancement regarding the Bayesian network learning was incorporated into the algorithm in order to speed up its execution. To conclude, we compare MOBAIS with state-of-the-art algorithms taking into account quantitative aspects of the Pareto front found by the algorithms. MOBAIS outperforms the contenders in terms of the quality of the obtained solutions and requires an amount of computational resource inferior or compatible with the contenders.
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References
Ada, G.L., Nossal, G.J.V.: The clonal selection theory. Sci. Am. 257(2), 50–57 (1987)
Baluja, S.: Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning. Technical Report, Carnegie Mellon University, Pittsburgh (1994)
Baluja, S., Davies, S.: Using optimal dependency-trees for combinational optimization. In: Proc. of the 14th Int. Conf. on Machine Learning, pp. 30–38. San Francisco (1997)
De Bonet, J.S., Isbell, C.L.: MIMIC: finding optima by estimating probability densities. Adv. Neural Inf. Process. Syst. 9, 424 (1997)
Castro, P.A.D., Von Zuben, F.J.: Bayesian learning of neural networks by means of artificial immune systems. In: Proc. of the 5th Int. Joint Conf. on Neural Networks, pp. 9885–9892 (2006)
Castro, P.A.D., Von Zuben, F.J.: BAIS: A Bayesian artificial immune system for the effective handling of building blocks. Inf. Sci. (2009, in press)
Castro, P.A.D., Von Zuben, F.J.: Feature subset selection by means of a Bayesian artificial immune system. In: Proc. of the 8th Int. Conf. on Hybrid Intelligent Systems, pp. 561–56 (2008)
Castro, P.A.D., Von Zuben, F.J.: MOBAIS: a Bayesian artificial immune system for multi-objective optimization. In: Proc. of the 7th Int. Conf. on Artificial Immune Systems, pp. 48–59 (2008)
Chen, J., Mahfouf, M.: A population adaptive based immune algorithm for solving multi-objective optimization problems. In: Bersini, H., Carneiro, J. (eds.) Lecture Notes in Computer Sciences - Artificial Immune Systems, vol. 4163, pp. 280–293. Springer, New York (2006)
Chickering, D.M.: Learning Bayesian networks is NP-complete. In: Learning from Data: Artificial Intelligence and Statistics V, pp. 121–130. Springer, New York (1996)
Coelho, G.P., Von Zuben, F.J.: Omni-aiNet: an immune-inspired approach for omni optimization. In: Bersini, H., Carneiro, J. (eds.) Lecture Notes in Computer Sciences—Artificial Immune Systems, vol. 4163, pp. 294–308. Springer, New York (2006)
Coello Coello, C., Cortés, N.C.: An approach to solve multiobjective optimization problems based on an artificial immune system. In: Proc. of the 1st Int. Conf. on Artificial Immune System, pp. 212–221 (2002)
Coello Coello, C., Cortés, N.C.: Solving multiobjective optimization problems using an artificial immune system. Genet. Program. Evolv. Mach. 6(2), 163–190 (2005)
Cooper, G., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Mach. Learn. 9, 309–347 (1992)
Dasgupta, D.: Advances in artificial immune systems. IEEE Comput. Intell. Mag. 1, 40–49 (2006)
de Castro, L.N., Timmis, J.: Artificial Immune Systems: A New Computational Intelligence Approach. Springer, New York (2002)
de Castro, L.N., Von Zuben, F.J.: Learning and optimization using the clonal selection principle. IEEE Trans. Evol. Comput. 6(3), 239–251 (2002)
de Castro, L.N., Timmis, J.: An artificial immune network for multimodal optimisation. In: Proc. of the IEEE World Congress on Evolutionary Computation, pp. 669–674 (2002)
Deb, K.: Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol. Comput. 7, 205–230 (1999)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Deb, K., Tiwari, S.: Omni-optimizer: a procedure for single and multi-objective optimization. In: Proc. of the of EMO, pp. 47–61 (2005)
Freschi, F., Repetto, M.: VIS: an artificial immune network for multi-objective optimization. Engin. Optim. 38, 975–996 (2006)
Goldberg, D.E., Deb, K., Kargupta, H., Harik, G.: Rapid accurate optimization of difficult problems using fast messy genetic algorithms. In: Proc. of the Fifth Int. Conf. on Genetic Algorithms, pp. 56–64. Morgan Kaufmann, San Francisco (1993)
Goldberg, D.E., Korb, G., Deb, K.: Messy genetic algorithms: motivation, analysis, and first results. Complex Syst. 3, 493–530 (1989)
Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)
Henrion, M.: Propagating uncertainty in Bayesian networks by probabilistic logic sampling. Uncertainty Artif. Intell. 2, 149–163 (1998)
Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. MIT, Cambridge (1992)
Jerne, N.K.: Towards a network theory of the immune system. Ann. Immunol. (Inst. Pasteur) 125C, 373–389 (1974)
Khan, N., Goldberg, D.E., Pelikan, M.: Multi-Objective Bayesian Optimization Algorithm. Technical report, University of Illinois, Illigal Report 2002009 (2002)
Luh, G.-C., Chueh, C.-H., Liu, W.-M.: MOIA: multi-objective immune algorithm. Eng. Optim. 35(2), 143–164 (2003)
Mühlenbein, H., Paass, G.: From recombination of genes to the estimation of distributions I. Binary parameters. In: Proc. of the 4th Int. Conf. on Parallel Problem Solving from Nature, pp. 178–187 (1996)
Mühlenbein, H., Mahnig, T.: FDA—a scalable evolutionary algorithm for the optimization of additively decomposed functions. Evol. Comput. 7, 353–376 (1999)
Osyczka, A.: Multicriteria optimization for engineering design. In: Gero, J.S. (ed.) Design Optimization, pp. 193–227. Academic, London (1985)
Pelikan, M., Goldberg, D., Lobo, F.: A Survey of Optimization by Building and Using Probabilistic Models. Technical report, University of Illinois, ILLIGAL Report n 99018 (1999)
Pelikan, M., Mühlenbein, H.: The bivariate marginal distribution algorithm. In: Roy, R., Furuhashi, T., Chawdhry, P.K. (eds.) Advances in Soft Computing—Engineering Design and Manufacturing, pp. 521–535. Springer, London (1999)
Pelikan, M., Goldberg, D.E., Cantú-Paz, E.: BOA: the Bayesian optimization algorithm. In: Proc. of the Genetic and Evol. Comput. Conference, vol. I., pp. 525–532 (1999)
Pelikan, M., Goldberg, D., Lobo, F.: A survey of optimization by building and using probabilistic models. Comput. Optim. Appl. 21(1), 5–20 (2002)
Pelikan, M., Sastry, K., Cantú-Paz, E.: Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications. Springer, New York (2005)
Peña, J.M., Lozano, J.A., Larrañaga, P.: Globally multimodal problem optimization via an estimation of distribution algorithm based on unsupervised learning of Bayesian networks. Evol. Comput. 13, 43–66 (2005)
Schott, J.R.: Fault tolerant design using single and multicriteria genetic algorithm optimization. Master’s thesis, Dept. of Aeronautics and Astronautics, Massachusetts Institute of Technology (1995)
Van Veldhuizen, D.A.: Multiobjective Evolutionary Algorithms: Classifications, Analysis, and New Innovations. Ph.D. thesis, Graduate School of Engineering of the Air Force Inst. of Tech., Wright-Patterson AFB (1999)
Yoo, J., Hajela, P.: Immune network simulations in multicriterion design. Struct. Optim. 18, 85–94 (1999)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)
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Castro, P.A.D., Von Zuben, F.J. Multi-objective Bayesian Artificial Immune System: Empirical Evaluation and Comparative Analyses. J Math Model Algor 8, 151–173 (2009). https://doi.org/10.1007/s10852-009-9108-2
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DOI: https://doi.org/10.1007/s10852-009-9108-2