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A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms

  • Conference paper
Evolutionary Multi-Criterion Optimization (EMO 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6576))

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Abstract

The use of multi-objective evolutionary algorithms for solving black-box problems with multiple conflicting objectives has become an important research area. However, when no gradient information is available, the examination of formal convergence or optimality criteria is often impossible. Thus, sophisticated heuristic online stopping criteria (OSC) have recently become subject of intensive research. In order to establish formal guidelines for a systematic research, we present a taxonomy of OSC in this paper. We integrate the known approaches within the taxonomy and discuss them by extracting their building blocks. The formal structure of the taxonomy is used as a basis for the implementation of a comprehensive MATLAB toolbox. Both contributions, the formal taxonomy and the MATLAB implementation, provide a framework for the analysis and evaluation of existing and new OSC approaches.

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References

  1. Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181(3), 1653–1669 (2007)

    Article  MATH  Google Scholar 

  2. Beume, N., Laumanns, M., Rudolph, G.: Convergence rates of (1+1) evolutionary multiobjective optimization algorithms. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 597–606. Springer, Heidelberg (2010)

    Google Scholar 

  3. Bui, L.T., Wesolkowski, S., Bender, A., Abbass, H.A., Barlow, M.: A dominance-based stability measure for multi-objective evolutionary algorithms. In: Tyrrell, A., et al. (eds.) Proc. Int’l. Congress on Evolutionary Computation (CEC 2009), pp. 749–756. IEEE Press, Piscataway (2009)

    Google Scholar 

  4. Deb, K., Jain, S.: Running performance metrics for evolutionary multi-objective optimization. In: Simulated Evolution and Learning (SEAL), pp. 13–20 (2002)

    Google Scholar 

  5. Deb, K., Pratap, A., Agarwal, S.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6(8) (2002)

    Google Scholar 

  6. Deb, K., Miettinen, K., Chaudhuri, S.: Toward an estimation of nadir objective vector using a hybrid of evolutionary and local search approaches. Trans. Evol. Comp. 14, 821–841 (2010)

    Article  Google Scholar 

  7. Efron, B.: Bootstrap methods: Another look at the jackknife. Annals of Statistics 7(1), 1–26 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  8. Goel, T., Stander, N.: A non-dominance-based online stopping criterion for multi–objective evolutionary algorithms. International Journal for Numerical Methods in Engineering (Online access) (2010) doi: 10.1002/nme.2909

    Google Scholar 

  9. Guerrero, J.L., Martí, L., García, J., Berlanga, A., Molina, J.M.: Introducing a robust and efficient stopping criterion for MOEAs. In: Fogel, G., Ishibuchi, H. (eds.) Proc. Int’l. Congress on Evolutionary Computation (CEC 2010), pp. 1–8. IEEE Press, Piscataway (2010)

    Google Scholar 

  10. Hansen, M.P., Jaszkiewicz, A.: Evaluating the quality of approximations to the non-dominated set. Tech. Rep. IMM-REP-1998-7, Institute of Mathematical Modelling, Technical University of Denmark (1998)

    Google Scholar 

  11. Martí, L., García, J., Berlanga, A., Molina, J.M.: A cumulative evidential stopping criterion for multiobjective optimization evolutionary algorithms. In: Thierens, D., et al. (eds.) Proc. of the 9th Annual Conference on Genetic and Evolutionary Computation (GECCO 2007), p. 911. ACM Press, New York (2007)

    Chapter  Google Scholar 

  12. Martí, L., García, J., Berlanga, A., Molina, J.M.: An approach to stopping criteria for multi-objective optimization evolutionary algorithms: The MGBM criterion. In: Tyrrell, A., et al. (eds.) Proc. Int’l. Congress on Evolutionary Computation (CEC 2009), pp. 1263–1270. IEEE Press, Piscataway (2009)

    Google Scholar 

  13. Mersmann, O., Trautmann, H., Naujoks, B., Weihs, C.: On the distribution of EMOA hypervolumes. In: Blum, C., Battiti, R. (eds.) LION 4. LNCS, vol. 6073, pp. 333–337. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Naujoks, B., Trautmann, H.: Online convergence detection for multiobjective aerodynamic applications. In: Tyrrell, A., et al. (eds.) Proc. Int’l. Congress on Evolutionary Computation (CEC 2009), pp. 332–339. IEEE press, Piscataway (2009)

    Google Scholar 

  15. Rudenko, O., Schoenauer, M.: A steady performance stopping criterion for pareto-based evolutionary algorithms. In: The 6th International Multi-Objective Programming and Goal Programming Conference, Hammamet, Tunisia (2004)

    Google Scholar 

  16. Trautmann, H., Wagner, T., Preuss, M., Mehnen, J.: Statistical methods for convergence detection of multiobjective evolutionary algorithms. Evolutionary Computation Journal, Special Issue: Twelve Years of EC Research in Dortmund 17(4), 493–509 (2009)

    Article  Google Scholar 

  17. Wagner, T., Beume, N., Naujoks, B.: Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Obayashi, S., et al. (eds.) EMO 2007. LNCS, vol. 4403, pp. 742–756. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Wagner, T., Martí, L.: Taxonomy-based matlab framework for online stopping criteria (2010), http://www.giaa.inf.uc3m.es/miembros/lmarti/stopping

  19. Wagner, T., Trautmann, H.: Online convergence detection for evolutionary multi-objective algorithms revisited. In: Fogel, G., Ishibuchi, H. (eds.) Proc. Int’l. Congress on Evolutionary Computation (CEC 2010), pp. 3554–3561. IEEE press, Piscataway (2010)

    Google Scholar 

  20. Wagner, T., Trautmann, H., Naujoks, B.: OCD: Online convergence detection for evolutionary multi-objective algorithms based on statistical testing. In: Ehrgott, M., et al. (eds.) EMO 2009. LNCS, vol. 5467, pp. 198–215. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 8(2), 117–132 (2003)

    Article  Google Scholar 

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Wagner, T., Trautmann, H., Martí, L. (2011). A Taxonomy of Online Stopping Criteria for Multi-Objective Evolutionary Algorithms. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds) Evolutionary Multi-Criterion Optimization. EMO 2011. Lecture Notes in Computer Science, vol 6576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19893-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-19893-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19892-2

  • Online ISBN: 978-3-642-19893-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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