Visualizing the Optimization Process for Multi-objective Optimization Problems

  • Bayanda Chakuma
  • Mardé HelbigEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10841)


Visualization techniques used to visualize the optimization process of multi-objective evolutionary algorithms (MOEAs) have been discussed in the literature, predominantly in the context of aiding domain experts in decision making and in improving the effectiveness of the design optimization process. These techniques provide the decision maker with the ability to directly observe the performance of individual solutions, as well as their distribution in the approximated Pareto-optimal front. In this paper a visualization technique to study the mechanics of a MOEA, as it is solving multi-objective optimization problems (MOOPs), is discussed. The visualization technique uses a scatterplot animation to visualize the evolutionary process of the algorithms search, focusing on the changes in the population of non-dominated solutions obtained for each generation. The ability to visualize the optimization process of the algorithm provides the means to evaluate the performance of the algorithm, as well as visually observing the trade-offs between objectives.


Visualization Scatterplot Multi-objective optimization Multi-objective evolutionary algorithms 



This work is based on the research supported by the National Research Foundation (NRF) of South Africa (Grant Number 46712). The opinions, findings and conclusions or recommendations expressed in this article is that of the author(s) alone, and not that of the NRF. The NRF accepts no liability whatsoever in this regard.


  1. 1.
    Coello Coello, C.: Evolutionary multi-objective optimization: a historical view of the field. IEEE Comput. Intell. Mag. 1(1), 28–36 (2006)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Konak, A., Coit, D., Smith, A.: Multi-objective optimization using genetic algorithms: a tutorial. Reliab. Eng. Syst. Saf. 91(9), 992–1007 (2006)CrossRefGoogle Scholar
  3. 3.
    Coello Coello, C., Lamont, G., van Veldhuizen, D.: Evolutionary Algorithms for Solving Multi-Objective Problems, vol. 5. Springer, New York (2007). Scholar
  4. 4.
    Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms, vol. 16. Wiley, Hoboken (2001)zbMATHGoogle Scholar
  5. 5.
    Jones, D., Mirrazavi, S., Tamiz, M.: Multi-objective meta-heuristics: an overview of the current state-of-the-art. Eur. J. Oper. Res. 137(1), 1–9 (2002)zbMATHCrossRefGoogle Scholar
  6. 6.
    Messac, A., Chen, X.: Visualizing the optimization process in real-time using physical programming. Eng. Optim. 32(6), 721–747 (2000)CrossRefGoogle Scholar
  7. 7.
    Jones, C.: Visualization and optimization. ORSA J. Comput. 6(3), 221–257 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Tuar, T., Filipi, B.: Visualization of Pareto front approximations in evolutionary multiobjective optimization: a critical review and the prosection method. IEEE Trans. Evol. Comput. 19(2), 225–245 (2015)CrossRefGoogle Scholar
  9. 9.
    Ashby, M.: Multi-objective optimization in material design and selection. Acta Mater. 48(1), 359–369 (2000)CrossRefGoogle Scholar
  10. 10.
    He, Z., Yen, G.: Visualization and performance metric in many-objective optimization. IEEE Trans. Evol. Comput. 20, 386–402 (2016)CrossRefGoogle Scholar
  11. 11.
    Inselberg, A., Dimsdale, B.: Parallel coordinates: a tool for visualizing multi-dimensional geometry. In: Proceedings of the Conference on Visualization, pp. 361–378 (1990)Google Scholar
  12. 12.
    Pryke, A., Mostaghim, S., Nazemi, A.: Heatmap visualization of population based multi objective algorithms. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 361–375. Springer, Heidelberg (2007). Scholar
  13. 13.
    Kudo, F., Yoshikawa, T.: Knowledge extraction in multi-objective optimization problem based on visualization of Pareto solutions. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1–6, June 2012Google Scholar
  14. 14.
    Yamashiro, D., Yoshikawa, T., Furuhashi, T.: Efficiency of search performance through visualizing search process. In: Proceedings of the IEEE International Conference in Systems, Man and Cybernetics, pp. 1114–1119, October 2006Google Scholar
  15. 15.
    Lotif, M.: Visualizing the population of meta-heuristics during the optimization process using self-organizing maps. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 313–319, July 2014Google Scholar
  16. 16.
    Kobayashi, Y., Okamoto, T., Koakutsu, S.: A Pareto optimal solution visualization method using SOM-NG with learning parameter optimization. In: Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, pp. 4525–4531 (2016)Google Scholar
  17. 17.
    Taghavi, T., Pimentel, A.: VMODEX: a visualization tool for multi-objective design space exploration. In: Proceedings of the International Conference on Field-Programmable Technology, pp. 357–360 (2010)Google Scholar
  18. 18.
    Madetoja, E., Ruotsalainen, H., Monkkonen, V., Hamalainen, J., Deb, K.: Visualizing multi-dimensional Pareto-optimal fronts with a 3D virtual reality system. In: Proceedings of the International Multiconference on Computer Science and Information Technology, pp. 907–913 (2008)Google Scholar
  19. 19.
    Ang, K., Chong, G., Li, Y.: Visualization technique for analyzing non-dominated set comparison. In: Proceedings of the Asia-Pacific Conference on Simulated Evolution and Learning, vol. 1 (2002)Google Scholar
  20. 20.
    Shine, W., Eick, C.: Visualizing the evolution of genetic algorithm search processes. In: Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 367–372, April 1997Google Scholar
  21. 21.
    Elmqvist, N., Dragicevic, P., Fekete, J.: Rolling the dice: multidimensional visual exploration using scatterplot matrix navigation. IEEE Trans. Vis. Comput. Graph. 14(6), 1141–1148 (2008)CrossRefGoogle Scholar
  22. 22.
    Heer, J., Robertson, G.: Animated transitions in statistical data graphics. IEEE Trans. Vis. Comput. Graph. 13(6), 1240–1247 (2007)CrossRefGoogle Scholar
  23. 23.
    Pohlheim, H.: Visualization of evolutionary algorithms-set of standard techniques and multidimensional visualization. In: Proceedings of the Annual Conference on Genetic and Evolutionary Computation, vol. 1, pp. 533–540, July 1999Google Scholar
  24. 24.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  25. 25.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the 2002 Congress on Evolutionary Computation, pp. 825–830, May 2002Google Scholar
  26. 26.
    Fleischer, M.: The measure of Pareto optima applications to multi-objective metaheuristics. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds.) EMO 2003. LNCS, vol. 2632, pp. 519–533. Springer, Heidelberg (2003). Scholar
  27. 27.
    Fortin, F., Rainville, F., Gardner, M., Parizeau, M., Gagné, C.: DEAP: evolutionary algorithms made easy. J. Mach. Learn. Res. 13, 2171–2175 (2012)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of PretoriaPretoriaSouth Africa

Personalised recommendations