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Australasian Conference on Artificial Life and Computational Intelligence

ACALCI 2017: Artificial Life and Computational Intelligence pp 241–253Cite as

Multi-objective Optimisation with Multiple Preferred Regions

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10142))

Abstract

The typical goal in multi-objective optimization is to find a set of good and well-distributed solutions. It has become popular to focus on specific regions of the objective space, e.g., due to market demands or personal preferences.

In the past, a range of different approaches has been proposed to consider preferences for regions, including reference points and weights. While the former technique requires knowledge over the true set of trade-offs (and a notion of “closeness”) in order to perform well, it is not trivial to encode a non-standard preference for the latter.

With this article, we contribute to the set of algorithms that consider preferences. In particular, we propose the easy-to-use concept of “preferred regions” that can be used by laypeople, we explain algorithmic modifications of NSGAII and AGE, and we validate their effectiveness on benchmark problems and on a real-world problem.

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Notes

  1. 1.

    Consequently, our pNSGAII is somewhat equivalent to an island model approach for multi-objective optimization, with islands being responsible for preferred regions. In contrast to existing island model-MOO approaches (e.g. [2]), we are focussing on user-defined parts of the search space that are defined in an easy-to-use way.

  2. 2.

    The ZDT functions are used as provided by the jMetal framework. The number of decision variables is 30 for ZDT1/2/3 and 10 for ZDT4/6.

  3. 3.

    Number of decision variables is 12 for DTLZ2/3, as set in the jMetal framework.

  4. 4.

    If we use \(\mu =30\) for typical MOEA (please see Table 1) then it is less probable to find adequate number of solutions in preferred regions, that makes it difficult to compare with pMOEA. In addition, compared in terms of FE, MOEA uses 50 less function evaluations than pMOEA only because the number is compatible with \(\mu \) (no extra function evaluations after completing last generation).

  5. 5.

    We do not report other indicator values, such as inverted generational distance (IGD) [20] or the Hausdorff distance [19] due to space constraints.

  6. 6.

    We uploaded all code and results to https://github.com/shaikatcse/pMOEAs. This includes pSPEA2 as an algorithm and also IGD indicator values.

References

  1. Branke, J.: Consideration of partial user preferences in evolutionary multiobjective optimization. In: Branke, J., Deb, K., Miettinen, K., Słowiński, R. (eds.) Multiobjective Optimization: Interactive and Evolutionary Approaches. LNCS, vol. 5252, pp. 157–178. Springer, Heidelberg (2008). doi:10.1007/978-3-540-88908-3_6

    Chapter  Google Scholar 

  2. Branke, J., Schmeck, H., Deb, K.: Parallelizing multi-objective evolutionary algorithms: cone separation. In: Congress on Evolutionary Computation (CEC), vol. 2, pp. 1952–1957 (2004)

    Google Scholar 

  3. Bringmann, K., Friedrich, T., Neumann, F., Wagner, M.: Approximation-guided evolutionary multi-objective optimization. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 1198–1203. AAAI (2011)

    Google Scholar 

  4. Chand, S., Wagner, M.: Evolutionary many-objective optimization: a quick-start guide. Surv. Oper. Res. Manag. Sci. 20(2), 35–42 (2015)

    MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. Trans. Evol. Comp. 6(2), 182–197 (2002)

    Article  Google Scholar 

  7. Deb, K., Sundar, J., Udaya Bhaskara, R.N., Chaudhuri, S.: Reference point based multi-objective optimization using evolutionary algorithms. Int. J. Comput. Intell. Res. 2, 635–642 (2006)

    Article  MathSciNet  Google Scholar 

  8. Durillo, J.J., Nebro, A.J.: jMetal: a Java framework for multi-objective optimization. Adv. Eng. Softw. 42, 760–771 (2011)

    Article  Google Scholar 

  9. Friedrich, T., Kroeger, T., Neumann, F.: Weighted preferences in evolutionary multi-objective optimization. In: Wang, D., Reynolds, M. (eds.) AI 2011. LNCS (LNAI), vol. 7106, pp. 291–300. Springer, Heidelberg (2011). doi:10.1007/978-3-642-25832-9_30

    Chapter  Google Scholar 

  10. Guo, Y., Zheng, J., Li, X.: An improved performance metric for multiobjective evolutionary algorithms with user preferences. In: Congress on Evolutionary Computation (CEC), pp. 908–915 (2015)

    Google Scholar 

  11. Huband, S., Hingston, P., Barone, L., While, L.: A review of multiobjective test problems and a scalable test problem toolkit. Trans. Evol. Comput. 10(5), 477–506 (2006)

    Article  MATH  Google Scholar 

  12. Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: a short review. In: Congress on Evolutionary Computation (CEC), pp. 2419–2426 (2008)

    Google Scholar 

  13. Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multiobjective optimization. Evol. Comput. 10(3), 263–282 (2002)

    Article  Google Scholar 

  14. Mahbub, M.S., Cozzini, M., Østergaard, P.A., Alberti, F.: Combining multi-objective evolutionary algorithms and descriptive analytical modelling in energy scenario design. Appl. Energ. 164, 140–151 (2016)

    Article  Google Scholar 

  15. Mohammadi, A., Omidvar, M., Li, X.: A new performance metric for user-preference based multi-objective evolutionary algorithms. In: Congress on Evolutionary Computation (CEC), pp. 2825–2832 (2013)

    Google Scholar 

  16. Nguyen, A.Q., Wagner, M., Neumann, F.: User preferences for approximation-guided multi-objective evolution. In: Dick, G., Browne, W.N., Whigham, P., Zhang, M., Bui, L.T., Ishibuchi, H., Jin, Y., Li, X., Shi, Y., Singh, P., Tan, K.C., Tang, K. (eds.) SEAL 2014. LNCS, vol. 8886, pp. 251–262. Springer, Heidelberg (2014). doi:10.1007/978-3-319-13563-2_22

    Google Scholar 

  17. Østergaard, P.A., Mathiesen, B.V., Möller, B.: A renewable energy scenario for Aalborg municipality based on low-temperature geothermal heat, wind power and biomass. Energy 35(12), 4892–4901 (2010)

    Article  Google Scholar 

  18. Purshouse, R.C., Deb, K., Mansor, M.M., Mostaghim, S., Wang, R.: A review of hybrid evolutionary multiple criteria decision making methods. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp. 1147–1154. IEEE (2014)

    Google Scholar 

  19. Rudolph, G., Schütze, O., Grimme, C., Trautmann, H.: A multiobjective evolutionary algorithm guided by averaged Hausdorff distance to aspiration sets. In: Tantar, A.-A., et al. (eds.) EVOLVE - A Bridge between Probability, Set Oriented Numerics, and Evolutionary Computation V. AISC, vol. 288, pp. 261–273. Springer, Heidelberg (2014). doi:10.1007/978-3-319-07494-8_18

    Google Scholar 

  20. Sato, H., Aguirre, H., Tanaka, K.: Local dominance using polar coordinates to enhance multiobjective evolutionary algorithms. In: Congress on Evolutionary Computation (CEC), pp. 188–195 (2004)

    Google Scholar 

  21. Wagner, M., Bringmann, K., Friedrich, T., Neumann, F.: Efficient optimization of many objectives by approximation-guided evolution. Eur. J. Oper. Res. 243(2), 465–479 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  22. Wagner, M., Friedrich, T.: Efficient parent selection for approximation-guided evolutionary multi-objective optimization. In: Congress on Evolutionary Computation (CEC), pp. 1846–1853 (2013)

    Google Scholar 

  23. Wagner, M., Neumann, F.: A fast approximation-guided evolutionary multi-objective algorithm. In: Genetic and Evolutionary Computation Conference (GECCO), pp. 687–694. ACM (2013)

    Google Scholar 

  24. 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). doi:10.1007/978-3-540-70928-2_56

    Chapter  Google Scholar 

  25. Wierzbicki, A.P.: Reference point approaches. In: Gal, T., Stewart, T.J., Hanne, T. (eds.) Multicriteria Decision Making, vol. 21, pp. 237–275. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

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Acknowledgements

This work has been supported by the ARC Discovery Early Career Researcher Award DE160100850.

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Authors and Affiliations

  1. Fondazione Bruno Kessler, Via Sommarive 18, 38123, Povo, Trento, Italy

    Md. Shahriar Mahbub & Luigi Crema

  2. University of Trento, Via Sommarive 9, 38123, Povo, Trento, Italy

    Md. Shahriar Mahbub

  3. University of Adelaide, Adelaide, South Australia, 5005, Australia

    Markus Wagner

Authors
  1. Md. Shahriar Mahbub
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  2. Markus Wagner
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  3. Luigi Crema
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Correspondence to Markus Wagner .

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Editors and Affiliations

  1. The University of Adelaide, Adelaide, South Australia, Australia

    Markus Wagner

  2. RMIT University, Melbourne, Victoria, Australia

    Xiaodong Li

  3. Swinburne University, Melbourne, Victoria, Australia

    Tim Hendtlass

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Mahbub, M.S., Wagner, M., Crema, L. (2017). Multi-objective Optimisation with Multiple Preferred Regions. In: Wagner, M., Li, X., Hendtlass, T. (eds) Artificial Life and Computational Intelligence. ACALCI 2017. Lecture Notes in Computer Science(), vol 10142. Springer, Cham. https://doi.org/10.1007/978-3-319-51691-2_21

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  • DOI: https://doi.org/10.1007/978-3-319-51691-2_21

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