Computational Optimization and Applications

, Volume 48, Issue 1, pp 109–138 | Cite as

A fast steady-state ε-dominance multi-objective evolutionary algorithm

  • Minqiang Li
  • Liu Liu
  • Dan Lin


Multi-objective evolutionary algorithms (MOEAs) have become an increasingly popular tool for design and optimization tasks in real-world applications. Most of the popular baseline algorithms are pivoted on the use of Pareto-ranking (that is empirically inefficient) to improve the convergence to the Pareto front of a multi-objective optimization problem. This paper proposes a new ε-dominance MOEA (EDMOEA) which adopts pair-comparison selection and steady-state replacement instead of the Pareto-ranking. The proposed algorithm is an elitist algorithm with a new preservation technique of population diversity based on the ε-dominance relation. It is demonstrated that superior results could be obtained by the EDMOEA compared with other algorithms: NSGA-II, SPEA2, IBEA, ε-MOEA, PESA and PESA-II on test problems. The EDMOEA is able to converge to the Pareto optimal set much faster especially on the ZDT test functions with a large number of decision variables.


Multi-objective optimization ε-dominance Steady-state EAs Diversity preservation 


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  1. 1.
    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
  2. 2.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, Athens, Greece (2001) Google Scholar
  3. 3.
    Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Parallel Problem Solving from Nature, PPSN VIII. Lecture Notes in Computer Science, vol. 3242, pp. 832–842. Springer, Berlin (2004) CrossRefGoogle Scholar
  4. 4.
    Knowles, J., Corne, D.: The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation. In: Proceedings of the Congress on Evolutionary Computation, Washington, DC (1999) Google Scholar
  5. 5.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading (1989) MATHGoogle Scholar
  6. 6.
    Srinivasan, D., Rachmawati, L.: An efficient multi-objective evolutionary algorithm with steady-state replacement model. In: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, Seattle, Washington (2006) Google Scholar
  7. 7.
    Valenzuela, C.L.: A simple evolutionary algorithm for multi-objective optimization (SEAMO). In: Proceedings of the 2002 Congress on Evolutionary Computation, Honolulu, HI (2002) Google Scholar
  8. 8.
    Rajeev, K., Peter, R.: Improved sampling of the Pareto-front in multiobjective genetic optimizations by steady-state evolution: a Pareto converging genetic algorithm. Evol. Comput. 10(3), 283–314 (2002) CrossRefGoogle Scholar
  9. 9.
    Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining convergence and diversity in evolutionary multiobjective optimization. Evol. Comput. 10(3), 263–282 (2002) CrossRefGoogle Scholar
  10. 10.
    Deb, K., Mohan, M., Mishra, S.: Evaluating the epsilon-domination based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions. Evol. Comput. 13(4), 501–525 (2005) CrossRefGoogle Scholar
  11. 11.
    Chinchuluun, A., Pardalos, P.: A survey of recent developments in multiobjective optimization. Ann. Oper. Res. 154(1), 29–50 (2007) MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Coello Coello, C.A.: Evolutionary multi-objective optimization: a historical view of the field. IEEE Comput. Intell. Mag. 1(1), 28–36 (2006) CrossRefMathSciNetGoogle Scholar
  13. 13.
    Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic, Dordrecht (2002) MATHGoogle Scholar
  14. 14.
    Ikeda, K., Kita, H., Kobayashi, S.: Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? In: Proceedings of the 2001 Congress on Evolutionary Computation, Seoul, South Korea (2001) Google Scholar
  15. 15.
    Zitzler, E., Laumanns, M., Bleuler, S.: A tutorial on evolutionary multiobjective optimization. In: Workshop on Multiple Objective Metaheuristics (MOMH 2002), Berlin, Germany (2004) Google Scholar
  16. 16.
    Deb, K.: Multi-Objective Optimization using Evolutionary Algorithm. Wiley, New York (2001) Google Scholar
  17. 17.
    Fonseca, C.M., Fleming, P.J.: An overview of evolutionary algorithms in multiobjective optimization. Evol. Comput. 3(1), 1–16 (1995) CrossRefGoogle Scholar
  18. 18.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999) CrossRefGoogle Scholar
  19. 19.
    Kukkonen, S., Deb, K.: Improved pruning of non-dominated solutions based on crowding distance for bi-objective optimization problems. In: IEEE Congress on Evolutionary Computation, Canada (2006) Google Scholar
  20. 20.
    Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J.: PESA-II: Region-based selection in evolutionary multiobjective optimization. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001) (2001) Google Scholar
  21. 21.
    Jensen, M.T.: Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms. IEEE Trans. Evol. Comput. 7(5), 503–515 (2003) CrossRefGoogle Scholar
  22. 22.
    Liu, L., Li, M., Lin, D.: A novel epsilon-dominance multi-objective evolutionary algorithms for solving DRS multi-objective optimization problems. In: Third International Conference on Natural Computation, Haikou, HaiNan (2007) Google Scholar
  23. 23.
    Schütze, O., Laumanns, M., Tantar, E., Coello, C.A.C., Talbi, E.: Convergence of stochastic search algorithms to gap-free Pareto front approximations. In: Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation, London, England (2007) Google Scholar
  24. 24.
    Parks, G.T., Miller, I.: Selective breeding in a multiobjective genetic algorithm. In: Parallel Problem Solving from Nature, PPSN V. Lecture Notes in Computer Science, vol. 1498, pp. 250–259. Springer, Berlin (1998) CrossRefGoogle Scholar
  25. 25.
    Deb, K., Goel, T.: Controlled elitist non-dominated sorting genetic algorithms for better convergence. In: First International Conference on Evolutionary Multi-Criterion Optimization, Zurich (2001) Google Scholar
  26. 26.
    Hu, J., Seo, K., Fan, Z., Rosenberg, R.C., Goodman, E.D.: Hemo: A sustainable multi-objective evolutionary optimization framework. In: Genetic and Evolutionary Computation Conference, Washington, DC (2003) Google Scholar
  27. 27.
    Sierra, M.R., Coello, C.A.C.: Improving PSO-based multi-objective optimization using crowding, mutation and e-dominance. In: Evolutionary Multi-Criterion Optimization, vol. 3410, pp. 505–519 (2005) Google Scholar
  28. 28.
    Wu, J., Azarm, S.: Metrics for quality assessment of a multiobjective design optimization solution set. J. Mech. Des. 123(1), 18–25 (2001) CrossRefGoogle Scholar
  29. 29.
    Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: empirical results. Evol. Comput. 8(2), 173–195 (2000) CrossRefGoogle Scholar
  30. 30.
    Deb, K., Agrawal, R.B.: Simulated binary crossover for continuous search space. Complex Syst. 9(1), 115–148 (1995) MATHMathSciNetGoogle Scholar
  31. 31.
    Deb, K., Goyal, M.: A combined genetic adaptive search GeneAS for engineering design. Comput. Sci. Inform. 26(4), 30–45 (1996) Google Scholar
  32. 32.
    Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Fonseca, V.G.: Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7(2), 117–132 (2003) CrossRefGoogle Scholar
  33. 33.
    Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. Technical Report, Computer Engineering and Networks Laboratory (TIK), ETH Zurich, Switzerland (2006) Google Scholar
  34. 34.
    Conover, W.J.: Practical Nonparametric Statistics, 3rd edn. Wiley, New York (1999) Google Scholar
  35. 35.
    Rosner, B.: Fundamentals of Biostatistics, 4th edn. Duxbury, Boston (1995) Google Scholar
  36. 36.
    Fonseca, C.M., Fleming, P.J.: On the performance assessment and comparison of stochastic multiobjective optimizers. In: Proceedings of the 4th International Conference on Parallel Problem Solving from Nature (1996) Google Scholar
  37. 37.
    Laumanns, M., Zitzler, E., Thiele, L.: A unified model for multi-objective evolutionary algorithms with elitism. In: Proceedings of the 2000 Congress on Evolutionary Computation, California (2000) Google Scholar
  38. 38.
    Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. Technical Report, Computer Engineering and Networks Laboratory, ETH Zurich (2001) Google Scholar
  39. 39.
    Wagner, T., Beume, N., Naujoks, B.: Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Evolutionary Multi-Criterion Optimization, vol. 742–756 (2007) Google Scholar

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of ManagementTianjin UniversityTianjinPeople’s Republic of China
  2. 2.School of ScienceTianjin UniversityTianjinPeople’s Republic of China

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