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MCDA and Multiobjective Evolutionary Algorithms

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Multiple Criteria Decision Analysis

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 233))

Abstract

Evolutionary multiobjective optimization promises to efficiently generate a representative set of Pareto optimal solutions in a single optimization run. This allows the decision maker to select the most preferred solution from the generated set, rather than having to specify preferences a priori. In recent years, there has been a growing interest in combining the ideas of evolutionary multiobjective optimization and MCDA. MCDA can be used before optimization, to specify partial user preferences, after optimization, to help select the most preferred solution from the set generated by the evolutionary algorithm, or be tightly integrated with the evolutionary algorithm to guide the optimization towards the most preferred solution. This chapter surveys the state of the art of using preference information within evolutionary multiobjective optimization.

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References

  1. Auger, A., Bader, J., Brockhoff, D., Zitzler, E.: Articulating user preference in many-objective problems by sampling the weighted hypervolume. In: Raidl, G., et al. (eds.) Genetic and Evolutionary Computation Conference, pp. 555–562. ACM, New York (2009)

    Google Scholar 

  2. Auger, A., Bader, J., Brockhoff, D., Zitzler, E.: Investigating and exploiting the bias of weighter hypervolume to articulate user preferences. In: Raidl, G., et al. (eds.) Genetic and Evolutionary Computation Conference, pp. 563–570. ACM, New York (2009)

    Google Scholar 

  3. Barbosa, H.J.C., Barreto, A.M.S.: An interactive genetic algorithm with co-evolution of weights for multiobjective problems. In: Spector, L., et al. (eds.) Genetic and Evolutionary Computation Conference, pp. 203–210. Morgan Kaufmann, Los Altos, CA (2001)

    Google Scholar 

  4. Battiti, R., Passerini, A.: Brain-computer evolutionary multiobjective optimization: a genetic algorithm adapting to the decision maker. IEEE Trans. Evol. Comput. 14(5), 671–687 (2010)

    Article  Google Scholar 

  5. Branke, J.: Consideration of user preferences in evolutionary multi-objective optimization. In: Branke, J., Deb, K., Miettinen, K., Slowinski, R. (eds.) Multiobjective Optimization—Interactive and Evolutionary Approaches. Lecture Notes in Computer Science, vol. 5252, pp. 157–178. Springer, Berlin (2008)

    Google Scholar 

  6. Branke, J., Deb, K.: Integrating user preference into evolutionary multi-objective optimization. In: Jin, Y. (ed.) Knowledge Incorporation in Evolutionary Computation, pp. 461–478. Springer, Berlin (2005)

    Chapter  Google Scholar 

  7. Branke, J., Kaußler, T., Schmeck, H.: Guidance in evolutionary multi-objective optimization. Adv. Eng. Softw. 32, 499–507 (2001)

    Article  Google Scholar 

  8. Branke, J., Deb, K., Dierolf, H., Osswald, M.: Finding knees in multi-objective optimization. In: Parallel Problem Solving from Nature. Lecture Notes in Computer Science, vol. 3242, pp. 722–731. Springer, Berlin (2004)

    Google Scholar 

  9. Branke, J., Greco, S., Słowiński, R., Zielniewicz, P.: Interactive evolutionary multiobjective optimization using robust ordinal regression. In: Ehrgott, M., et al. (eds.) International Conference on Evolutionary Multi-Criterion Optimization. Lecture Notes in Computer Science, vol. 5467, pp. 554–568. Springer, Berlin (2009)

    Chapter  Google Scholar 

  10. Branke, J., Greco, S., Słowiński, R., Zielniewicz, P.: Interactive evolutionary multiobjective optimization driven by robust ordinal regression. Bull. Pol. Acad. Sci. Tech. Sci. 58(3), 347–358 (2010)

    Google Scholar 

  11. Brans, J.P., Mareschal, B.: PROMETHEE methods. In: Figueira, J., et al. (eds.) Multiple Criteria Decision Analysis, pp. 163–196. Springer, Berlin (2005)

    Google Scholar 

  12. Braun, M.A., Shukla, P.K., Schmeck, H.: Preference ranking schemes in multi-objective evolutionary algorithms. In: Takahashi, R.H.C., et al. (eds.) Evolutionary Multi-Criterion Optimization. Lecture Notes in Computer Science, vol. 6576, pp. 226–240. Springer, Berlin (2011)

    Chapter  Google Scholar 

  13. Bringmann, K., Friedrich, T.: An efficient algorithm for computing hypervolume contributions. Evol. Comput. J. 18(3), 383–402 (2010)

    Article  Google Scholar 

  14. Campigotto, P., Passerini, A.: Adapting to a realistic decision maker: experiments towards a reactive multi-objective optimizer. In: International Conference on Learning and Intelligent Optimization. Lecture Notes in Computer Science, vol. 6073, pp. 338–341. Springer, Berlin (2010)

    Google Scholar 

  15. Coello, C.A.C.: Handling preferences in evolutionary multiobjective optimization: a survey. In: Congress on Evolutionary Computation, vol. 1, pp. 30–37. IEEE (2000)

    Google Scholar 

  16. Coello, C.A.C.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191(11–12), 1245–1287 (2002)

    Article  Google Scholar 

  17. Coello, C.A.C., Veldhuizen, D.A.V., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer, Dordrecht (2002)

    Book  Google Scholar 

  18. Coelho, R.F., Bersini, H., Bouillard, P.: Parametrical mechanical design with constraints and preferences: application to a purge valve. Comput. Methods Appl. Mech. Eng. 192, 4355–4378 (2003)

    Article  Google Scholar 

  19. Cvetkovic, D., Parmee, I.C.: Preferences and their application in evolutionary multiobjective optimisation. IEEE Trans. Evol. Comput. 6(1), 42–57 (2002)

    Article  Google Scholar 

  20. Das, I.: On characterizing the ‘knee’ of the pareto curve based on normal-boundary intersection. Struct. Optim. 18(2/3), 107–115 (1999)

    Article  Google Scholar 

  21. Deb, K.: Solving goal programming problems using multi-objective genetic algorithms. In: Proceedings of Congress on Evolutionary Computation, pp. 77–84 (1999)

    Google Scholar 

  22. Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186(2–4), 311–338 (2000)

    Article  Google Scholar 

  23. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, New York (2001)

    Google Scholar 

  24. Deb, K.: Multi-objective evolutionary algorithms: introducing bias among Pareto-optimal solutions. In: Ghosh, A., Tsutsui, S. (eds.) Advances in Evolutionary Computing: Theory and Applications, pp. 263–292. Springer, London (2003)

    Chapter  Google Scholar 

  25. Deb, K., Chaudhuri, S.: I-MODE: an interactive multi-objective optimization and decision-making using evolutionary methods. Technical Report KanGAL Report No. 2007003, Indian Institute of Technology Kanpur (2007)

    Google Scholar 

  26. Deb, K., Kumar, A.: Interactive evolutionary multi-objective optimization and decision-making using reference direction method. In: Genetic and Evolutionary Computation Conference, pp. 781–788. ACM, New York (2007)

    Google Scholar 

  27. Deb, K., Kumar, A.: Light beam search based multi-objective optimization using evolutionary algorithms. In: Congress on Evolutionary Computation, pp. 2125–2132. IEEE, Los Alamitos (2007)

    Google Scholar 

  28. Deb, K., Sundar, J.: Reference point based multi-objective optimization using evolutionary algorithms. In: Genetic and Evolutionary Computation Conference, pp. 635–642. ACM, New York (2006)

    Google Scholar 

  29. Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  30. Deb, K., Sundar, J., Udaya Bhaskara Rao, N., Chaudhuri, S.: Reference point based multi-objective optimization using evolutionary algorithms. Int. J. Comput. Intell. Res. 2(3), 273–286 (2006)

    Google Scholar 

  31. Deb, K., Sinha, A., Korhonen, P., Wallenius, J.: An interactive evolutionary multiobjective optimization method based on progressively approximated value functions. IEEE Trans. Evol. Comput. 14(5), 723–739 (2010)

    Article  Google Scholar 

  32. Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer, Berlin (2003)

    Book  Google Scholar 

  33. Emmerich, M., Beume, N., Naujoks, B.: An EMO algorithm using the hypervolume measure as selection criterion. In: Evolutionary Multi-Criterion Optimization. Lecture Notes in Computer Science, vol. 3410. Springer, Berlin (2005)

    Google Scholar 

  34. Fernandez, E., Lopez, E., Bernal, S., Coello, C.A.C., Navarro, J.: Evolutionary multiobjective optimization using an outranking-based dominance generalization. Comput. Oper. Res. 37(2), 390–395 (2010)

    Article  Google Scholar 

  35. Fernandez, E., Lopez, E., Lopez, F., Coello, C.A.C.: Increasing selective pressure towards the best compromise in evolutionary multiobjective optimization: the extended NOSGA method. Inf. Sci. 181, 44–56 (2011)

    Article  Google Scholar 

  36. Figueira, J., Mousseau, V., Roy, B.: ELECTRE methods. In: Figueia, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys, pp. 134–162. Springer, Berlin (2005)

    Chapter  Google Scholar 

  37. Figueira, J., Greco, S., Słowiński, R.: Building a set of additive value functions representing a reference preorder and intensities of preference: Grip method. Eur. J. Oper. Res. 195(2), 460–486 (2009)

    Article  Google Scholar 

  38. Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: formulation, discussion, and generalization. In: Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 416–423 (1993)

    Google Scholar 

  39. Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms—part I: a unified formulation. IEEE Trans. Syst. Man Cybern. Part A 28(1), 26–37 (1998)

    Article  Google Scholar 

  40. Fowler, J.W., Gel, E.S., Köksalan, M.M., Korhonen, P., Marquis, J.L., Wallenius, J.: Interactive evolutionary multi-objective optimization for quasi-concave preference functions. Eur. J. Oper. Res. 206, 417–425 (2010)

    Article  Google Scholar 

  41. Friedrich, T., Kroeger, T., Neumann, F.: Weighted preferences in evolutionary multi-objective optimization. Int. J. Mach. Learn. Cybern. (to appear) 4(2), 139–148, Springer (2013)

    Google Scholar 

  42. Gong, M., Liu, F., Zhang, W., Jiao, L., Zhang, Q.: Interactive MOEA/D for multi-objective decision making. In: Genetic and Evolutionary Computation Conference, pp. 721–728. ACM, New York (2011)

    Google Scholar 

  43. Greco, S., Słowiński, R., Figueira, J., Mousseau, V.: Robust ordinal regression. In: Ehrgott, M., et al. (eds.) New Advances in Multiple Criteria Decision Analysis, pp. 273–320. Springer, Berlin (2010)

    Google Scholar 

  44. Greenwood, G.W., Hu, X.S., D’Ambrosio, J.G.: Fitness functions for multiple objective optimization problems: combining preferences with Pareto rankings. In: Belew, R.K., Vose, M.D. (eds.) Foundations of Genetic Algorithms, pp. 437–455. Morgan Kaufmann, Los Altos, CA (1997)

    Google Scholar 

  45. Hapke, M., Jaszkiewicz, A., Słowiński, R.: Interactive analysis of multiple-criteria project scheduling problems. Eur. J. Oper. Res. 107, 315–324 (1998)

    Article  Google Scholar 

  46. Hughes, E.J.: Constraint handling with uncertain and noisy multi-objective evolution. In: Congress on Evolutionary Computation, pp. 963–970. IEEE, Los Alamitos (2001)

    Google Scholar 

  47. Jaimes, A.L., Montano, A.A., Coello, C.A.C.: Preference incorporation to solve many-ojective airfoil design problems. In: Congress on Evolutionary Computation, pp. 1605–1612. IEEE, New Orleans (2011)

    Google Scholar 

  48. Jaszkiewicz, A., Slowinski, R.: The light beam search over a non-dominated surface of a multiple-objective programming problem. Eur. J. Oper. Res. 113(2), 300–314 (1999)

    Article  Google Scholar 

  49. Jaszkiewicz, A.: A comparative study of multiple-objective metaheuristics on the bi-objective set covering problem and the pareto memetic algorithm. Ann. Oper. Res. 131(1–4), 135–158 (2004)

    Article  Google Scholar 

  50. Jaszkiewicz, A.: Interactive multiobjective optimization with the Pareto memetic algorithm. Found. Comput. Decis. Sci. 32(1), 15–32 (2007)

    Google Scholar 

  51. Jiménez, F., Verdegay, J.L.: Evolutionary techniques for constrained optimization problems. In: Zimmermann, H.J. (ed.) European Congress on Intelligent Techniques and Soft Computing. Verlag Mainz, Germany (1999)

    Google Scholar 

  52. Jin, Y., Sendhoff, B.: Incorporation of fuzzy preferences into evolutionary multiobjective optimization. In: Wang, L., et al. (eds.) Asia-Pacific Conference on Simulated Evolution and Learning, pp. 26–30. Nanyang Technical University, Singapore (2002)

    Google Scholar 

  53. Kamalian, R., Takagi, H., Agogino, A.M.: Optimized design of mems by evolutionary multi-objective optimization with interactive evolutionary computation. In: Genetic and Evolutionary Computation Conference, pp. 1030–1041 (2004)

    Google Scholar 

  54. Karahan, I., Köksalan, M.: A territory defining multiobjective evolutionary algorithmsw and preference incorporation. IEEE Trans. Evol. Comput. 14(4), 636–664 (2010)

    Article  Google Scholar 

  55. Köksalan, M., Karahan, I.: An interactive territory defining evolutionary algorithm: iTDEA. IEEE Trans. Evol. Comput. 14(5), 702–722 (2010)

    Article  Google Scholar 

  56. Korhonen, P., Laakso, J.: A visual interactive method for solving the multiple criteria problem. Eur. J. Oper. Res. 24, 277–287 (1986)

    Article  Google Scholar 

  57. Korhonen, P., Wallenius, J., Zionts, S.: Solving the discrete multiple criteria problem using convex cones. Manage. Sci. 30, 1336–1345 (1984)

    Article  Google Scholar 

  58. Luque, J.M., Santana-Quintero, L.V., Hernandez-Diaz, A.G., Coello, C.A.C., Caballero, R.: g-dominance: reference point based dominance for multiobjective metaheuristics. Eur. J. Oper. Res. 197(2), 685–692 (2009)

    Google Scholar 

  59. Parreiras, R.O., Vasconcelos, J.A.: Decision making in multiobjective optimization problems. In: Nedjah, N., de Macedo Mourelle, L. (eds.) Real-World Multi-Objective System Engineering, pp. 29–52. Nova Science Publishers, New York (2005)

    Google Scholar 

  60. Phelps, S., Köksalan, M.: An interactive evolutionary metaheuristic for multiobjective combinatorial optimization. Manage. Sci. 49(12), 1726–1738 (2003)

    Article  Google Scholar 

  61. Rachmawati, L., Srinivasan, D.: Preference incorporation in multi-objective evolutionary algorithms: a survey. In: Congress on Evolutionary Computation, pp. 3385–3391. IEEE, Los Alamitos (2006)

    Google Scholar 

  62. Rekiek, B., Lit, P.D., Fabrice, P., L’Eglise, T., Emanuel, F., Delchambre, A.: Dealing with users’s preferences in hybrid assembly lines design. In: Binder, Z., et al. (eds.) Management and Control of Production and Logistics Conference, pp. 989–994. Pergamon, New York (2000)

    Google Scholar 

  63. Said, L.B., Bechikh, S., Ghedira, K.: The r-dominance: a new dominance relation for interactive evolutionary multicriteria decision making. IEEE Trans. Evol. Comput. 14(5), 801–818 (2010)

    Article  Google Scholar 

  64. Takagi, H.: Interactive evolutionary computation: fusion of the capabilities of ec optimization and human evaluation. In: Proceedings of the IEEE, vol. 89, pp. 1275–1296 (2001)

    Google Scholar 

  65. Tan, K.C., Lee, T.H., Khor, E.F.: Evolutionary algorithms with goal and priority information for multi-objective optimization. In: Congress on Evolutionary Computation, pp. 106–113. IEEE, Los Alamitos (1999)

    Google Scholar 

  66. Thiele, L., Miettinen, K., Korhonen, P.J., Molina, J.: A preference-based interactive evolutionary algorithm for multiobjective optimization. Evol. Comput. J. 17(3), 411–436 (2009)

    Article  Google Scholar 

  67. Todd, D.S., Sen, P.: Directed multiple objective search of design spaces using genetic algorithms and neural networks. In: Banzhaf, W., et al. (eds.) Genetic and Evolutionary Computation Conference, pp. 1738–1743. Morgan Kaufmann, San Francisco, CA (1999)

    Google Scholar 

  68. Trautmann, H., Mehnen, J.: A method for including a-priori-preference in multicriteria optimization. Technical Report 49/2005, SFG 475, University of Dortmund, Germany (2005)

    Google Scholar 

  69. Wagner, T., Trautmann, H.: Integration of preferences in hypervolume-based multiobjective evolutionary algorithms by means of desirability functions. IEEE Trans. Evol. Comput. 14(5), 688–701 (2010)

    Article  Google Scholar 

  70. White, C., Sage, A., Dozono, S.: A model of multiattribute decision-making and tradeoff weight determination under uncertainty. IEEE Trans. Syst. Man Cybern. 14, 223–229 (1984)

    Article  Google Scholar 

  71. Wierzbicki, A.P.: Basic properties of scalarizing functions for multiobjective optimization. Optimization 8(1), 55–60 (1977)

    Google Scholar 

  72. Wierzbicki, A.P.: On the completeness and constructiveness of parametric characterizations to vector optimization problems. OR Spektrum 8(2), 73–87 (1986)

    Article  Google Scholar 

  73. Zhang, Q., Li, H.: MOEA/D: a multi-objective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. Evol. Comput. 11(6), 712–731 (2007)

    Article  Google Scholar 

  74. Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Parallel Problem Solving from Nature. Lecture Notes in Computer Science, vol. 3242, pp. 832–842. Springer, Berlin (2004)

    Google Scholar 

  75. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K., et al. (eds.) Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems (EUROGEN 2001), pp. 95–100. International Center for Numerical Methods in Engineering, Spain (2002)

    Google Scholar 

  76. Zitzler, E., Brockhoff, D., Thiele, L.: The hypervolume indicator revisited: on the design of Pareto-compliant indicators via weighted integration. In: Obayashi, S., et al. (eds.) Evolutionary Multi-Criterion Optimization. Lecture Notes in Computer Science, vol. 4403, pp. 862–876. Springer, Berlin (2007)

    Chapter  Google Scholar 

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Branke, J. (2016). MCDA and Multiobjective Evolutionary Algorithms. In: Greco, S., Ehrgott, M., Figueira, J. (eds) Multiple Criteria Decision Analysis. International Series in Operations Research & Management Science, vol 233. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3094-4_23

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