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Revista de Matemática Teoría y Aplicaciones
versión impresa ISSN 1409-2433
Rev. Mat vol.21 no.2 San José jul./dic. 2014
Interactive multiobjective tabu/scatter Search based on reference point
Búsqueda tabú/dispersa multiobjetivo Interactivas basadas en punto de Referencia
Búsqueda tabú/dispersa multiobjetivo Interactivas basadas en punto de Referencia
Abstract
This paper presentsmultiobjective tabu/scatter search architecture with preference information based on reference points for problems of continuous nature. Features of this new version are: its interactive behavior, its deterministic approximation to Pareto-optimality solutions near the reference point, and the possibility to change progressively the reference point to explore different preference regions. The approach does not impose any restrictionswith respect to the location of the reference points in the objective space. On 2-objective to 10-objective optimization test problems the modified approach shows its efficacy and efficiency to find an adequate non-dominated set of solutions in the preferred region.
Keywords: multiple objectives; metaheuristics; reference point; continuous optimization.
Resumen
Este artículo presenta una arquitectura Tabú/Búsqueda Dispersa multiobjetivo, con información de preferencia basada en punto de referencia para problemas de naturaleza continua. Los rasgos de esta nueva versión son los siguientes: funcionamiento interactivo, aproximación determinística a las soluciones Pareto cercanas al punto de referencia y la posibilidad de cambiar el punto de referencia para explorar deferentes regiones de preferencia. El enfoque no impone restricciones con relación a los puntos de referencia en el espacio de los objetivos, y muestra su habilidad en la solución de problemas desde 2 hasta más de 10 objetivos, hallando conjuntos de soluciones eficientes cercanas al punto de preferencia.
Palabras clave: múltiples objetivos; metaheurísticas; punto de referencia; optimización continua.
Mathematics Subject Classification: 90C27.
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References
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[11] Deb, K.; Sundar, J.; Bhaskara Rao, N.U.; Chaudhuri, S. (2006) “Reference point based multi-objective optimization using evolutionary algorithms”, International Journal of Computational Intelligence Research 2(3): 273–286. [ Links ]
[12] Fonseca, C.M.; Fleming, P.J. (1993) “Genetic algorithm for multiobjective optimization: formulation, discussion and generalization”, in: S. Forrest (Ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, Morgan Kaufman, SanMateo CA: 416–423. [ Links ]
[13] Li, H.; Zhang, Q. (2009) “Multiobjective optimization problems with complicated Pareto sets,MOEA/D and NSGA-II ”, IEEE Transactions on Evolutionary Computation 13(2): 284–302. [ Links ]
[14] Miettinen, D.K.; Lotov, A.V.; Kamenev, G.K.; Berezkin, V.E. (2003) “Integration of two multiobjective optimization methods for nonlinear problems”, OptimizationMethods and Software 18(1): 63–80. [ Links ]
[15] Molina, J.; Santana, L.V.; Hernández-Díaz, A.G.; Coello Coello, C.A.; Caballero, R. (2009) “g-dominance:reference point based dominance for multiobjective metaheuristics”, European Journal of Operational Research 197(2): 685–692. [ Links ]
[16] Shukla, P.K.; Deb, K.; Tiwari, S. (2005) “Comparing classical generating methods with an evolutionary multi-objective optimization method”, Lecture Notes in Computer Science 3410, Springer-Verlag: 311–325 [ Links ]
[17] Thiele, L.; Miettinen, K.; Korhonen, P.; Molina, J. (2007) “A preferencebased evolutionary algorithm for multiobjective optimization”, Evolutionary Computation 19(3): 411–436. [ Links ]
[18] Wierzbicki, A.P. (1982) “A mathematical basis for satisficing decisionmaking”, Mathematical Modelling 3(5): 391–405. [ Links ]
[19] Wierzbicki, A.P. (1980) “The use of reference objectives in multiobjective optimization”, in: G. Fandel & T. Gal (Eds.) Multiple Criteria Decision Making. Theory and Application , Springer-Verlag, Berlin: 469–486. [ Links ]
[20] Van Veldhuizen, D.A.; Lamont, G.B. (1998) “Evolutionary computation and convergence to a Pareto front”, in: J.R. Koza (Ed.) Late Breaking Papers at the Genetic Programming Conferece Stanford University, Stanford CA: 221–228. [ Links ]
[21] Zitzler, E.; Thiele, L.; Bader, J. (2008) “SPAM: Set preference algorithm optimization”, in: G. Rudolph et al. (Eds.) Parallel Problem Solving from Nature (PPSN X), Dortmund, Lecture Notes in Computer Science 5199, Springer-Verlag: 847–858. [ Links ]
[2] Barbosa H.J.; Barreto A.M. (2001) “An interactive genetic algorithm with co-evolution of weights for multiobjective problems”, in: L. Spector, E.D. Goodman, A. Wu, W. Langdom, H.M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M.H. Garzon & E. Burke, (Eds.) Proceedings of the Genetic and EvolutionaryComputationConference (GECCO’2001), MorganKaufmann Publishers, San Francisco CA: 203–210 [ Links ]
[3] Beausoleil, R.P. (2006) “MOSS multiobjective scatter search applied to non-linear multiple criteria optimization”, European Journal of Operational Research 169(2): 426–449. [ Links ]
[4] Beausoleil, R.P. (2008) “MOSS-II tabu/scatter search for nonlinear multiobjective optimization”, in: P. Siarry & Z. Michalewicz (Eds.) Advances in Metaheuristics for Hard Optimization, Natural Computing Series, Springer: 39–67. [ Links ]
[5] Branke, J.; Kauler, T.; Schmeck, H. (2001) “Guidance in evolutionary multi-objective optimization”, Advances in Engineering Software 32: 499– 507. [ Links ]
[6] Cvetkovic, D.; Parmee, I. (1998) “Evolutionary design and multiobjective optimization”, Proceedings of the Sixth European Congress on Intelligent Techniques and Soft Computing (EUFIT), Aachen,Germany: 397–401. [ Links ]
[7] Deb, K. (1999) “Solving goal programming problems using multi-objective genetic algorithms”, Proceedings of Congress on Evolutionary Computation: 77–84. [ Links ]
[8] Deb, K. (2001) Multi-Objective Optimization using Evolutionary Algorithms. JohnWiley &Sons, Chichester UK. [ Links ]
[9] Deb, K.; Pratap, A.; Mayaravian, T.; (2001) “Constrained test problems for multi-objective evolutionary optimization”, in: E. Zitzler, K. Deb, L. Thiele, C. Coello & D. Corne (Eds.) First International Conference On EvolutionaryMulti-criterion Optimization, Lecture Notes in Computer Science 1993, Springer-Verlag, London: 284–298. [ Links ]
[10] Deb, K.; Thiele, L.; Laumanns, M.; Zitzler, E. (2002) “Scalable multiobjective optimization test problems”, in: Proceedings of the Congress on Evolutionary Computation (CEC-2002) Honolulu HW, Vol. 1. IEEE Service Center, Piscataway, NJ: 825–830. [ Links ]
[11] Deb, K.; Sundar, J.; Bhaskara Rao, N.U.; Chaudhuri, S. (2006) “Reference point based multi-objective optimization using evolutionary algorithms”, International Journal of Computational Intelligence Research 2(3): 273–286. [ Links ]
[12] Fonseca, C.M.; Fleming, P.J. (1993) “Genetic algorithm for multiobjective optimization: formulation, discussion and generalization”, in: S. Forrest (Ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, Morgan Kaufman, SanMateo CA: 416–423. [ Links ]
[13] Li, H.; Zhang, Q. (2009) “Multiobjective optimization problems with complicated Pareto sets,MOEA/D and NSGA-II ”, IEEE Transactions on Evolutionary Computation 13(2): 284–302. [ Links ]
[14] Miettinen, D.K.; Lotov, A.V.; Kamenev, G.K.; Berezkin, V.E. (2003) “Integration of two multiobjective optimization methods for nonlinear problems”, OptimizationMethods and Software 18(1): 63–80. [ Links ]
[15] Molina, J.; Santana, L.V.; Hernández-Díaz, A.G.; Coello Coello, C.A.; Caballero, R. (2009) “g-dominance:reference point based dominance for multiobjective metaheuristics”, European Journal of Operational Research 197(2): 685–692. [ Links ]
[16] Shukla, P.K.; Deb, K.; Tiwari, S. (2005) “Comparing classical generating methods with an evolutionary multi-objective optimization method”, Lecture Notes in Computer Science 3410, Springer-Verlag: 311–325 [ Links ]
[17] Thiele, L.; Miettinen, K.; Korhonen, P.; Molina, J. (2007) “A preferencebased evolutionary algorithm for multiobjective optimization”, Evolutionary Computation 19(3): 411–436. [ Links ]
[18] Wierzbicki, A.P. (1982) “A mathematical basis for satisficing decisionmaking”, Mathematical Modelling 3(5): 391–405. [ Links ]
[19] Wierzbicki, A.P. (1980) “The use of reference objectives in multiobjective optimization”, in: G. Fandel & T. Gal (Eds.) Multiple Criteria Decision Making. Theory and Application , Springer-Verlag, Berlin: 469–486. [ Links ]
[20] Van Veldhuizen, D.A.; Lamont, G.B. (1998) “Evolutionary computation and convergence to a Pareto front”, in: J.R. Koza (Ed.) Late Breaking Papers at the Genetic Programming Conferece Stanford University, Stanford CA: 221–228. [ Links ]
[21] Zitzler, E.; Thiele, L.; Bader, J. (2008) “SPAM: Set preference algorithm optimization”, in: G. Rudolph et al. (Eds.) Parallel Problem Solving from Nature (PPSN X), Dortmund, Lecture Notes in Computer Science 5199, Springer-Verlag: 847–858. [ Links ]
*Departmento de Matemática Interdisciplinaria, Instituto de Cibernética Matemática y Física. La Habana, Cuba. E-Mail: rbeausol@icimaf.cu
Received: 17/Apr/2012; Revised: 7/Feb/2014; Accepted: 29/May/2014
