A Novel Hybrid Multi-objective Optimization Framework: Rotating the Objective Space

  • Xin Qiu
  • Ye Huang
  • Jian-Xin Xu
  • Kay Chen Tan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8886)


Multi-objective Evolutionary Algorithms (MOEAs) are popular approaches for solving multi-objective problems (MOPs). One representative method is Non-dominated Sorting Genetic Algorithm II (NSGA-II), which has achieved great success in the field by introducing non-dominated sorting into survival selection. However, as a common issue for dominance-based algorithms, the performance of NSGA-II will decline in solving problems with 3 or more objectives. This paper aims to circumvent this issue by incorporating the concept of decomposition into NSGA-II. A grouping-based hybrid multi-objective optimization framework is proposed for tackling 3-objective problems. Original MOP is decomposed into several scalar subproblems, and each group of population is assigned with two scalar subproblems as new objectives. In order to better cover the whole objective space, new objective spaces are formulated via rotating the original objective space. Simulation results show that the performance of the proposed algorithm is competitive when dealing with 3-objective problems.


Multi-objective evolutionary algorithm hybrid decomposition 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zhang, Q., Li, H.: MOEA/D: A multiobjective evolutionary algorithm based on decomposition. IEEE Transactions on Evolutionary Computation 11(6), 712–731 (2007)CrossRefGoogle Scholar
  2. 2.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjec-tive genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  3. 3.
    Antonin, P., Antonio, L.J., Carlos, A.C.C.: A Survey on Multiobjective Evolutionary Algorithms for the Solution of the Portfolio Optimization Problem and Other Finance and Economics Applications. IEEE Transactions on Evolutionary Computation 17(3), 321–344 (2013)CrossRefGoogle Scholar
  4. 4.
    Anirban, M., Ujjwal, M., Sanghamitra, B., Carlos, A.C.C.: A Survey of Multiobjective Evolutionary Algorithms for Data Mining: Part I. IEEE Transactions on Evolutionary Computation 18(1), 4–19 (2014)CrossRefGoogle Scholar
  5. 5.
    Pindoriya, N.M., Singh, S.N., Kwang, Y.L.: A Comprehensive Survey on Multi-objective Evolutionary Optimization in Power System Applications. In: 2010 IEEE Power and Energy Society General Meeting, pp. 1–8 (2010)Google Scholar
  6. 6.
    Voss, T., Beume, N., Rudolph, G., Igel, C.: Scalarization versus indicator-based selection in multi-objective CMA evolution strategies. In: Proc (IEEE World Congress on Computational Intelligence). IEEE Congress on Evolutionary Computation, CEC 2008, pp. 3036–3043 (2008)Google Scholar
  7. 7.
    Miettinen, K.: Nonlinear Multiojective Optimization. Kluwer, Norwell (1999)Google Scholar
  8. 8.
    Qi, Y.T., Ma, X.L., Liu, F., Jiao, L.C., Sun, J.Y., Wu, J.S.: MOEA/D with Adaptive Weight Adjustment. Evolutionary Computation 22(2), 231–264 (2014)CrossRefGoogle Scholar
  9. 9.
    Zhang, Q., Zhou, A., Zhao, S., Suganthan, P.N., Liu, W., Tiwari, S.: Multiobjective optimization test instances for the CEC 2009 special session and competition. Tech. Rep. CES-487, University of Essex and Nanyang Technological University (2008)Google Scholar
  10. 10.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multi-Objective Optimization, Zurich, Switzerland, Tech. Rep. 112 (2001)Google Scholar
  11. 11.
    Veldhuizen, D.A.V., Lamont, G.B.: On measuring multiobjective evolutionary algorithm performance. In: 2000 Congress on Evolutionary Compuation, vol. 1, IEEE Service Center, Piscataway (2000)Google Scholar
  12. 12.
    Veldhuizen, D.A.V., Lamont, G.B.: Multiobjective evolutionary algorithm research: A history and analysis. Technical Report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH (1998)Google Scholar
  13. 13.
    Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9, 115–148 (1995)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Xin Qiu
    • 1
  • Ye Huang
    • 2
  • Jian-Xin Xu
    • 2
  • Kay Chen Tan
    • 2
  1. 1.NUS Graduate School for Integrative Sciences and EngineeringNational University of SingaporeSingaporeSingapore
  2. 2.Department of Electrical and Computer EngineeringNational University of SingaporeSingaporeSingapore

Personalised recommendations