13. P. Korhonen and J. Laakso, “A visual interactive method for solving the multiple criteria problem,” European Journal of Operational Reseaech, vol. 24, pp. 277–287, 1986. 14. P. Korhonen and G. Y. Yu, “A reference direction approach to multiple objective quadraticlinear programming,” European Journal of Operational Reseaech, vol. 102, pp. 601–610, 1997. 15. J. Branke, S. Greco, R. Slowinski, and P. Zielniewicz, “<strong>Interactive</strong> evolutionary multiobjective optimization using robust ordinal regression,” in Proceedings of the Fifth International Conference on <strong>Evolutionary</strong> <strong>Multi</strong>-Criterion <strong>Optimization</strong> (EMO-09). Berlin: Springer- Verlag, 2009, pp. 554–568. 16. P. Korhonen, H. Moskowitz, and J. Wallenius, “A progressive algorithm for modeling and solving multiple-criteria decision problems,” Operations Research, vol. 34, no. 5, pp. 726– 731, 1986. 17. P. Korhonen, H. Moskowitz, P. Salminen, and J. Wallenius, “Further developments and tests of a progressive algorithm for multiple criteria decision making,” Operations Research, vol. 41, no. 6, pp. 1033–1045, 1993. 18. K. Deb, S. Agrawal, A. Pratap, and T. Meyarivan, “A fast and elitist multi-objective genetic algorithm: NSGA-II,” IEEE Transactions on <strong>Evolutionary</strong> Computation, vol. 6, no. 2, pp. 182–197, 2002. 19. G. W. Greenwood, X. Hu, and J. G. D’Ambrosio, “Fitness functions for multiple objective optimization problems: Combining preferences with pareto rankings,” in Foundations of Genetic Algorithms (FOGA). San Mateo: Morgan Kauffman, 1996, pp. 437–455. 20. S. Phelps and M. Koksalan, “An interactive evolutionary metaheuristic for multiobjective combinatorial optimization,” Management Science, vol. 49, no. 12, pp. 1726–1738, December 2003. 21. A. Jaszkiewicz, “<strong>Interactive</strong> multiobjective optimization with the pareto memetic algorithm,” Foundations of Computing and Decision Sciences, vol. 32, no. 1, pp. 15–32, 2007. 22. E. Zitzler, M. Laumanns, and L. Thiele, “SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization,” in <strong>Evolutionary</strong> Methods for Design <strong>Optimization</strong> and Control with Applications to Industrial Problems, K. C. Giannakoglou, D. T. Tsahalis, J. Périaux, K. D. Papailiou, and T. Fogarty, Eds. Athens, Greece: International Center for Numerical Methods in Engineering (CIMNE), 2001, pp. 95–100. 23. K. Miettinen, Nonlinear <strong>Multi</strong>objective <strong>Optimization</strong>. Boston: Kluwer, 1999. 24. A. P. Wierzbicki, “The use of reference objectives in multiobjective optimization,” in <strong>Multi</strong>ple Criteria Decision Making Theory and Applications, G. Fandel and T. Gal, Eds. Berlin: Springer-Verlag, 1980, pp. 468–486. 25. K. Deb and R. B. Agrawal, “Simulated binary crossover for continuous search space,” Complex Systems, vol. 9, no. 2, pp. 115–148, 1995. 26. K. V. Price, R. Storn, and J. Lampinen, Differential Evolution: A Practical Approach to Global <strong>Optimization</strong>. Berlin: Springer-Verlag, 2005. 27. R. H. Byrd, J. Nocedal, and R. A. Waltz, KNITRO: An integrated package for nonlinear optimization. Springer-Verlag, 2006, pp. 35–59. 28. K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, “Scalable test problems for evolutionary multi-objective optimization,” in <strong>Evolutionary</strong> <strong>Multi</strong>objective <strong>Optimization</strong>, A. Abraham, L. Jain, and R. Goldberg, Eds. London: Springer-Verlag, 2005, pp. 105–145. 29. J. W. Fowler, E. S. Gel, M. Koksalan, P. Korhonen, J. L. Marquis and J. Wallenius “<strong>Interactive</strong> <strong>Evolutionary</strong> <strong>Multi</strong>-<strong>Objective</strong> <strong>Optimization</strong> for Quasi-Concave Preference Functions,” Submitted to European Journal of Operational Research, 2009. 30. P. Korhonen and J. Karaivanova “An Algorithm for Projecting a Reference Direction onto the Nondominated Set of Given Points,” IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, vol. 29, pp. 429–435, 1999. 72
4 An efficient and accurate solution methodology for bilevel multi-objective programming problems using a hybrid evolutionary-local-search algorithm K. Deb and A. Sinha <strong>Evolutionary</strong> Computation Journal, 18(3), 403-449. MIT Press, 2010. 73
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Department of Business Technology P
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Aalto University publication series
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Progressively Interactive Evolution
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Acknowledgements The dissertation h
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II List of Papers 27 1 An interacti
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1 Introduction Many real-world appl
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• f(x (1) ) ≥ f(x (2) ) fi(x (1
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for a maximization problem. Mathema
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• x (1) ∼ x (2) ⇔ x (1) and x
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Start Initialise Population Assign
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ithm can approximate the Pareto-opt
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Minimize/Maximize F(x) = (f1(x), f2
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the search is chosen. A scalarizing
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of the papers is provided in this s
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to get close to the most preferred
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F2 0.4 0.2 0 −0.2 Lower level P
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F2 2 1.5 1 0.5 Most Preferred Point
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provement in terms of function eval
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9HSTFMG*aeafcd+ ISBN: 978-952-60-40