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Towards a Better Balance of Diversity and Convergence in NSGA-III: First Results

  • Haitham Seada
  • Mohamed Abouhawwash
  • Kalyanmoy Deb
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10173)

Abstract

Over the last few decades we have experienced a plethora of successful optimization concepts, algorithms, techniques and softwares. Each trying to excel in its own niche. Logically, combining a carefully selected subset of them may deliver a novel approach that brings together the best of some those previously independent worlds. The span of applicability of the new approach and the magnitude of improvement are completely dependent on the selected techniques and the level of perfection in weaving them together. In this study, we combine NSGA-III with local search and use the recently proposed Karush-Kuhn-Tucker Proximity Measure (KKTPM) to guide the whole process. These three carefully selected building blocks are intended to perform well on several levels. Here, we focus on Diversity and Convergence (DC-NSGA-III), hence we use Local Search and KKTPM respectively, in the course of a multi/many objective algorithm (NSGA-III). The results show how DC-NSGA-III can significantly improve performance on several standard multi- and many-objective optimization problems.

Keywords

NSGA-III Diversity Convergence Local Search KKTPM 

References

  1. 1.
    Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms, vol. 16. John Wiley Sons, Hoboken (2001)zbMATHGoogle Scholar
  2. 2.
    DeJong, K.A.: An analysis of the behavior of a class of genetic adaptive systems. Ph.D. thesis, Ann Arbor, MI: University of Michigan, Dissertation Abstracts International 36(10), 5140B (University Microlms No. 76–9381) (1975)Google Scholar
  3. 3.
    Zitzler, E., Laumanns, M., Thiele, L., Zitzler, E., Zitzler, E., Thiele, L., Thiele, L.: SPEA2: improving the strength pareto evolutionary algorithm (2001)Google Scholar
  4. 4.
    Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J.J., Schwefel, H.-P. (eds.) PPSN 2000. LNCS, vol. 1917. Springer, Heidelberg (2000)Google Scholar
  5. 5.
    Khare, V., Yao, X., Deb, K.: Performance scaling of multi-objective evolutionary algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds.) EMO 2003. LNCS, vol. 2632, pp. 376–390. Springer, Heidelberg (2003). doi: 10.1007/3-540-36970-8_27 CrossRefGoogle Scholar
  6. 6.
    Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 6, 712–731 (2007)CrossRefGoogle Scholar
  7. 7.
    Deb, K., Jain, H.: An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans. Evol. Comput. 18(4), 577–601 (2014)CrossRefGoogle Scholar
  8. 8.
    Ishibuchi, H., Murata, T.: A multi-objective genetic local search algorithm and its application to owshop scheduling. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 28(3), 392–403 (1998)CrossRefGoogle Scholar
  9. 9.
    Knowles, J.D., Corne, D.W.: M-PAES: a memetic algorithm for multiobjective optimization. In: Proceedings of the Congress on Evolutionary Computation, vol. 1, pp. 325–332. IEEE (2000)Google Scholar
  10. 10.
    Bosman, P.A.: On gradients and hybrid evolutionary algorithms for real-valued multiobjective optimization. IEEE Trans. Evol. Comput. 1, 51–69 (2012)CrossRefGoogle Scholar
  11. 11.
    Sindhya, K., Deb, K., Miettinen, K.: A local search based evolutionary multi-objective optimization approach for fast and accurate convergence. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 815–824. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-87700-4_81 CrossRefGoogle Scholar
  12. 12.
    Dutta, J., Deb, K., Tulshyan, R., Arora, R.: Approximate KKT points and a proximity measure for termination. J. Global Optim. 4, 1463–1499 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Deb, K., Abouhawwash, M.: An optimality theory based proximity measure for set based multi-objective optimization. IEEE Trans. Evol. Comput. (in press)Google Scholar
  14. 14.
    Deb, K., Abouhawwash, M.: A computationally fast and approximate method for Karush-Kuhn-Tucker proximity measure. Technical report, COIN Report No. 015, Department of Electrical and Computer Engineering, Michigan State University, East Lansing, USA (2015)Google Scholar
  15. 15.
    Abouhawwash, M., Seada, H., Deb, K.: Karush-Kuhn-Tucker optimality based local search for enhanced convergence of evolutionary multi-criterion optimization methods. Comput. Oper. Res. (in press)Google Scholar
  16. 16.
    Seada, H., Abouhawwash, M., Deb, K.: Towards a better diversity of evolutionary multi-criterion optimization algorithms using local searches. In: Proceedings of the on Genetic and Evolutionary Computation Conference Companion, pp. 77–78. ACM (2016)Google Scholar
  17. 17.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000)CrossRefGoogle Scholar
  18. 18.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multiobjective optimization. In: Abraham, A., Jain, L., Goldberg, R. (eds.) Evolutionary Multiobjective Optimization. Springer, Heidelberg (2005)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Haitham Seada
    • 1
  • Mohamed Abouhawwash
    • 2
  • Kalyanmoy Deb
    • 3
  1. 1.Department of Computer Science and EngineeringMichigan State UniversityEast LansingUSA
  2. 2.Department of Mathematics, Faculty of ScienceMansoura UniversityMansouraEgypt
  3. 3.Department of Electrical and Computer EngineeringMichigan State UniversityEast LansingUSA

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