JACIII Vol.21 No.2 pp. 284-292
doi: 10.20965/jaciii.2017.p0284


A Tradeoff-Based Interactive Multi-Objective Optimization Method Driven by Evolutionary Algorithms

Lu Chen*, Bin Xin*,**,***,†, and Jie Chen**,***

*School of Automation, Beijing Institute of Technology
No.5 Zhongguancun South Street, Haidian District, Beijing, China
**Beijing Advanced Innovation Center for Intelligent Robots and Systems, Beijing Institute of Technology
No.5 Zhongguancun South Street, Haidian District, Beijing, China
***State Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology
No.5 Zhongguancun South Street, Haidian District, Beijing, China
Corresponding author

June 27, 2016
November 11, 2016
Online released:
March 15, 2017
March 20, 2017
interactive multi-objective optimization, evolutionary algorithms, indifference tradeoffs, normal vector approximation, most preferred solution

Multi-objective optimization problems involve two or more conflicting objectives, and they have a set of Pareto optimal solutions instead of a single optimal solution. In order to support the decision maker (DM) to find his/her most preferred solution, we propose an interactive multi-objective optimization method based on the DM’s preferences in the form of indifference tradeoffs. The method combines evolutionary algorithms with the gradient-based interactive step tradeoff (GRIST) method. An evolutionary algorithm is used to generate an approximate Pareto optimal solution at each iteration. The DM is asked to provide indifference tradeoffs whose projection onto the tangent hyperplane of the Pareto front provides a tradeoff direction. An approach for approximating the normal vector of the tangent hyperplane is proposed which is used to calculate the projection. A water quality management problem is used to demonstrate the interaction process of the interactive method. In addition, three benchmark problems are used to test the accuracy of the normal vector approximation approach and compare the proposed method with GRIST.

  1. [1] C. L. Hwang and A. S. M. Masud, “Multiple objective decision making methods and applications,” Springer, Berlin, 1979.
  2. [2] K. Miettinen, “Nonlinear multiobjective optimization. Springer, 1999.
  3. [3] J. B. Yang, “Gradient projection and local region search for multiobjective optimisation,” European J. of Operational Research, Vol.112, No.2, pp. 432-459, 1999.
  4. [4] J. B. Yang and D. Li, “Normal vector identification and interactive tradeoff analysis using minimax formulation in multiobjective optimization,” IEEE Trans. on Systems, Man, and Cybernetics- Part A: Systems and Humans, Vol.32, No.3, pp. 305-319, 2002.
  5. [5] M. Luque, J. B. Yang, and B. Y. H. Wong, “PROJECT method for multiobjective optimization based on gradient projection and reference points,” IEEE Trans. on Systems, Man and Cybernetics-Part A: Systems and Humans, Vol.39, No.4, pp. 864-879, 2009.
  6. [6] J. Branke, K. Deb, K. Miettinen, and R. Słowiński, “Multiobjective optimization: interactive and evolutionary approaches,” Springer, 2008.
  7. [7] K. Miettinen, P. Eskelinen, F. Ruiz, and M. Luque, “NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point,” European J. of Operational Research, Vol.206, No.2, pp. 426-434, 2010.
  8. [8] K. Deb, A. Sinha, P. J. Korhonen, and J. Wallenius, “An interactive evolutionary multiobjective optimization method based on progressively approximated value functions,” IEEE Trans. on Evolutionary Computation, Vol.14, No.5, pp. 723-739, 2010.
  9. [9] A. Sinha, K. Deb, P. Korhonen, and J. Wallenius, “Progressively interactive evolutionary multi-objective optimization method using generalized polynomial value functions,” IEEE Congress on Evolutionary Computation, pp. 1-8, 2010.
  10. [10] K. Sindhya, A. B. Ruiz, and K. Miettinen, “A preference based interactive evolutionary algorithm for multi-objective optimization: PIE,” Evolutionary Multi-Criterion Optimization, Springer, 2011.
  11. [11] A. B. Ruiz, M. Luque, K. Miettinen, and R. Saborido, “An interactive evolutionary multiobjective optimization method: Interactive WASF-GA,” Evolutionary Multi-Criterion Optimization, Springer, 2015.
  12. [12] J. Branke, S. Greco, R. Słowiński, and P. Zielniewicz, “Learning value functions in interactive evolutionary multiobjective optimization,” IEEE Trans. on Evolutionary Computation, Vol.19, No.1, pp. 88-102, 2015.
  13. [13] K. Miettinen and F. Ruiz, “NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization,” J. of Business Economics, Vol.86, No.1, pp. 5-21, 2016.
  14. [14] K. Miettinen, J. Hakanen, and D. Podkopaev, “Interactive nonlinear multiobjective optimization methods,” Multiple Criteria Decision Analysis, Springer, 2016.
  15. [15] K. Deb, K. Miettinen, and S. Chaudhuri, “Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches,” IEEE Trans. on Evolutonary Computation, Vol.14, No.6, 821-841, 2010.
  16. [16] R. Storn and K. Price, “Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces,” J. of Global Optimization, Vol.11, No.4, pp. 341-359, 1997.
  17. [17] K. Deb,“An efficient constraint handling method for genetic algorithms,” Computer Methods in Applied Mechanics and Engineering, Vol.186, No.2, pp. 311-338, 2000.
  18. [18] K. V. Price, R. M. Storn, and J. A. Lampinen, Differential evolutionary: a practical approach to global optimization. Springer, 2006.
  19. [19] Y. Aksoy, T. W. Butler, and E. D. Minor, “Comparative studies in interactive multiple objective mathematical programming,” European J. of Operational Research, Vol.89, No.2, pp. 408-422, 1996.
  20. [20] F. Q. Gu, H. L. Liu, and K. C. Tan, “A multiobjective evolutionary algorithm using dynamic weight design method,” Int. J. of Innovative Computing, Information and Control, Vol.8, No.5, pp. 3677-3688, 2012.
  21. [21] K. Deb, L. Thiele, M. Laumanns, and E. Zitzler, “Scalable multi-objective optimization test problems,” Proc. of the IEEE Congress on Evolutionary Computation, pp. 825-830, 2002.

*This site is desgined based on HTML5 and CSS3 for modern browsers, e.g. Chrome, Firefox, Safari, Edge, IE9,10,11, Opera.

Last updated on Mar. 28, 2017