Scalable Test Problems for Evolutionary Multiobjective Optimization

  • Kalyanmoy Deb
  • Lothar Thiele
  • Marco Laumanns
  • Eckart Zitzler
Part of the Advanced Information and Knowledge Processing book series (AI&KP)


After adequately demonstrating the ability to solve different two-objective optimization problems, multiobjective evolutionary algorithms (MOEAs) must demonstrate their efficacy in handling problems having more than two objectives. In this study, we have suggested three different approaches for systematically designing test problems for this purpose. The simplicity of construction, scalability to any number of decision variables and objectives, knowledge of the shape and the location of the resulting Pareto-optimal front, and introduction of controlled difficulties in both converging to the true Pareto-optimal front and maintaining a widely distributed set of solutions are the main features of the suggested test problems. Because of the above features, they should be found useful in various research activities on MOEAs, such as testing the performance of a new MOEA, comparing different MOEAs, and better understanding of the working principles of MOEAs.


Test Problem Multiobjective Optimization Objective Space Multiobjective Evolutionary Algorithm Feasible Search Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Schaffer, JD Some Experiments in Machine Learning Using Vector Evaluated Genetic Algorithms. PhD thesis, Nashville, TN: Vanderbilt University, 1984.Google Scholar
  2. 2.
    Kursawe, F A Variant of Evolution Strategies for Vector Optimization. In Parellel Problem Solving from Nature I (PPSN-I), pp. 193–197, 1990.Google Scholar
  3. 3.
    Fonseca, CM and Fleming, PJ An Overview of Evolutionary Algorithms in Multi-objective Optimization. Evolutionary Computation Journal, 1995; 3(1):1–16.Google Scholar
  4. 4.
    Poloni, C, Giurgevich, A, Onesti, L and Pediroda, V Hybridization of a Multiobjective Genetic Algorithm, a Neural Network and a Classical Optimizer for Complex Design Problem in Fluid Dynamics. Computer Methods in Applied Mechanics and Engineering, 2000; 186(2–4): 403–420.CrossRefGoogle Scholar
  5. 5.
    Viennet, R Multicriteria Optimization Using a Genetic Algorithm for Determining the Pareto Set. International Journal of Systems Science, 1996;27(2): 255–260.Google Scholar
  6. 6.
    Deb, K Multi-objective Optimization Using Evolutionary Algorithms. Chichester, UK: Wiley, 2001.Google Scholar
  7. 7.
    Van Veldhuizen, D Multiobjective Evolutionary Algorithms: Classifications, Analyses, and New Innovations. PhD Thesis, Dayton, OH: Air Force Institute of Technology, 1999. Technical Report No. AFIT/DS/ENG/99-01.Google Scholar
  8. 8.
    Deb, K Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems. Evolutionary Computation Journal, 1999; 7(3):205–230.Google Scholar
  9. 9.
    Zitzler, E, Deb, K and Thiele, L Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation Journal, 2000; 8(2):125–148.CrossRefGoogle Scholar
  10. 10.
    Deb, K, Thiele, L, Laumanns, M and Zitzler, E Scalable Multi-objective Optimization Test Problems. In Proceedings of the Congress on Evolutionary Computation (CEC-2002), pp. 825–830, 2002.Google Scholar
  11. 11.
    Coello, CAC, VanVeldhuizen, DA, and Lamont G Evolutionary Algorithms for Solving Multi-Objective Problems. Boston, MA: Kluwer Academic Publishers, 2002.Google Scholar
  12. 12.
    Bleuler, S, Laumanns, M, Thiele, L and Zitzler, E PISA-A Platform and Programming Language Independent Interface for Search Algorithms. In Evolutionary Multi-Criterion Optimization (EMO 2003), Lecture Notes in Computer Science, Berlin, 2003. Springer.Google Scholar
  13. 13.
    Laumanns, M, Rudolph, G and Schwefel, HP A Spatial Predator-prey Approach to Multi-objective Optimization: A Preliminary Study. In Proceedings of the Parallel Problem Solving from Nature, V, pp. 241–249, 1998.Google Scholar
  14. 14.
    Laumanns, M, Thiele, L, Ziztler, E, Welzl, E and Deb, K Running Time Analysis of Multi-objective Evolutionary Algorithms on a Simple Discrete Optimization Problem. In Proceedings of the Seventh Conference on Parallel Problem Solving from Nature (PPSN-VII), pp. 44–53, 2002.Google Scholar
  15. 15.
    Zitzler, E and Thiele, L Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Transactions on Evolutionary Computation, 1999; 3(4): 257–271.CrossRefGoogle Scholar
  16. 16.
    Deb, K and Jain, S Multi-speed Gearbox Design Using Multi-objective Evolutionary Algorithms. ASME Transactions on Mechanical Design, 2003; 125(3): 609–619.Google Scholar
  17. 17.
    Laumanns, M, Thiele, L and Zitzler, E Running Time Analysis of Multiobjective Evolutionary Algorithms on Pseudo-boolean Functions. IEEE Transactions on Evolutionary Computation, 2004. Accepted for publication.Google Scholar
  18. 18.
    Tanaka, M GA-based Decision Support System for Multi-criteria Optimization. In Proceedings of the International Conference on Systems, Man and Cybernetics, Volume 2: pp. 1556–1561, 1995.Google Scholar
  19. 19.
    Tamaki, H Multi-objective Optimization by Genetic Algorithms: A Review. In Proceedings of the Third IEEE Conference on Evolutionary Computation, pp. 517–522, 1996.Google Scholar
  20. 20.
    Knowles, JD and Corne, DW Approximating the Non-dominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation Journal, 2000; 8(2): 149–172.CrossRefGoogle Scholar
  21. 21.
    Deb, K, Agrawal, S, Pratap, A and Meyarivan, T A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 2002; 6(2):182–197.CrossRefGoogle Scholar
  22. 22.
    Kokolo, I, Kita, H, and Kobayashi, S Failure of Pareto-based Moeas: Does Non-dominated Really Mean Near to Optimal? In Proceedings of the Congress on Evolutionary Computation 2001, pp. 957–962, 2001.Google Scholar
  23. 23.
    Laumanns, M, Thiele, L, Deb, K and Zitzler, E Combining Convergence and Diversity in Evolutionary Multi-objective Optimization. Evolutionary Computation, 2002; 10(3): 263–282.Google Scholar
  24. 24.
    Deb, K, Mohan, M, and Mishra, S Towards a Quick Computation of Well-spread Pareto-optimal Solutions. In Proceedings of the Second Evolutionary Multi-Criterion Optimization (EMO-03) Conference (LNCS 2632), pp. 222–236, 2003.Google Scholar
  25. 25.
    Deb, K, Pratap, A and Meyarivan, T Constrained Test Problems for Multiobjective Evolutionary Optimization. In Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization (EMO-01), pp. 284–298, 2001.Google Scholar
  26. 26.
    Miettinen, K, Nonlinear Multiobjective Optimization, Boston, Kluwer, 1999.Google Scholar

Copyright information

© Springer-Verlag London Limited 2005

Authors and Affiliations

  • Kalyanmoy Deb
  • Lothar Thiele
  • Marco Laumanns
  • Eckart Zitzler

There are no affiliations available

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