A Knee-Based EMO Algorithm with an Efficient Method to Update Mobile Reference Points

  • Yu SetoguchiEmail author
  • Kaname Narukawa
  • Hisao Ishibuchi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9018)


A number of evolutionary multi-objective optimization (EMO) algorithms have been proposed to search for non-dominated solutions around reference points that are usually assumed to be given by a decision maker (DM) based on his/her preference. However, setting the reference point needs a priori knowledge that the DM sometimes does not have. In order to obtain favorable solutions without a priori knowledge, “knee points” can be used. Some algorithms have already been proposed to obtain solutions around the knee points. TKR-NSGA-II is one of them. In this algorithm, the DM is supposed to specify the number of knee points as a parameter whereas such information is usually unknown. In this paper, we propose an EMO algorithm that does not require the DM to specify the number of knee points in advance. We demonstrate that the proposed method can efficiently find solutions around knee points.


Knee point Preference Reference point Decision maker 


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  1. 1.
    Bechikh, S., Said, L.B., Ghedira, K.: Searching for knee regions in multi-objecitve optimization using mobile reference points. In: Proc. of the 2010 ACM Symposium on Applied Computing, pp. 1118–1125. ACM (2010)Google Scholar
  2. 2.
    Bechikh, S., Said, L.B., Ghedira, K.: Searching for knee regions of the pareto front using mobile reference points. Soft Computing 15(9), 1807–1823 (2011)CrossRefGoogle Scholar
  3. 3.
    Branke, J., Deb, K., Dierolf, H., Osswald, M.: Finding knees in multi-objective optimization. In: Yao, X., et al. (eds.) PPSN VIII. LNCS, vol. 3242, pp. 722–731. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  4. 4.
    Das, I.: On characterizing the “knee” of the pareto curve based on normal-boundary intersection. Structural Optimization 18(2–3), 107–115 (1999)CrossRefGoogle Scholar
  5. 5.
    Deb, K., Gupta, S.: Understanding knee points in bicriteria problems and their implications as preferred solution principles. Engineering Optimization 43(11), 1175–1204 (2011)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Deb, K., Sundar, J., Udaya Bhaskara Rao, N., Chaudhuri, S.: Reference point based multi-objective optimization using evolutionary algorithms. International Journal of Computational Intelligence Research 2(3), 273–286 (2006)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Mattson, C.A., Mullur, A.A., Messac, A.: Smart pareto filter: Obtaining a minimal representation of multiobjective design space. Engineering Optimization 36(6), 721–740 (2004)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Narukawa, K., Tanigaki, Y., Ishibuchi, H.: Evolutionary many-objective optimization using preference on hyperplane. In: Proc. of 2014 Conference Companion on Genetic and Evolutionary Computation Conference, pp. 91–92. ACM (2014)Google Scholar
  9. 9.
    Rachmawati, L., Srinivasan, D.: Multiobjective evolutionary algorithm with controllable focus on the knees of the pareto front. IEEE Trans. on Evolutionary Computation 13(4), 810–824 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Yu Setoguchi
    • 1
    Email author
  • Kaname Narukawa
    • 2
  • Hisao Ishibuchi
    • 1
  1. 1.Department of Computer Science and Intelligent Systems, Graduate School of EngineeringOsaka Prefecture UniversitySakaiJapan
  2. 2.Honda Research Institute Europe GmbHOffenbach am MainGermany

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