A Provably Asymptotically Fast Version of the Generalized Jensen Algorithm for Non-dominated Sorting

  • Maxim Buzdalov
  • Anatoly Shalyto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8672)

Abstract

The non-dominated sorting algorithm by Jensen, generalized by Fortin et al to handle the cases of equal objective values, has the running time complexity of O(N logK − 1N) in the general case. Here N is the number of points, K is the number of objectives and K is thought to be a constant when N varies. However, the complexity was not proven to be the same in the worst case.

A slightly modified version of the algorithm is presented, for which it is proven that its worst-case running time complexity is O(N logK − 1N).

Keywords

Non-dominated sorting worst-case running time complexity multi-objective optimization 

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References

  1. 1.
    Source code for the implementation (a part of this paper), https://github.com/mbuzdalov/papers/tree/master/2014-ppsn-jensen-fortin
  2. 2.
    Abbass, H.A., Sarker, R., Newton, C.: PDE: A Pareto Frontier Differential Evolution Approach for Multiobjective Optimization Problems. In: Proceedings of the Congress on Evolutionary Computation, pp. 971–978. IEEE Press (2001)Google Scholar
  3. 3.
    Bentley, J.L.: Multidimensional Divide-and-conquer. Communications of ACM 23(4), 214–229 (1980)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Corne, D.W., Jerram, N.R., Knowles, J.D., Oates, M.J.: PESA-II: Region-based Selection in Evolutionary Multiobjective Optimization. In: Proceedings of Genetic and Evolutionary Computation Conference, pp. 283–290. Morgan Kaufmann Publishers (2001)Google Scholar
  5. 5.
    Corne, D.W., Knowles, J.D., Oates, M.J.: The Pareto Envelope-based Selection Algorithm for Multiobjective Optimization. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN VI. LNCS, vol. 1917, pp. 839–848. Springer, Heidelberg (2000)Google Scholar
  6. 6.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast Elitist Multi-Objective Genetic Algorithm: NSGA-II. Transactions on Evolutionary Computation 6, 182–197 (2000)CrossRefGoogle Scholar
  7. 7.
    Fortin, F.A., Grenier, S., Parizeau, M.: Generalizing the Improved Run-time Complexity Algorithm for Non-dominated Sorting. In: Proceeding of the Fifteenth Annual Conference on Genetic and Evolutionary Computation Conference, GECCO 2013, pp. 615–622. ACM (2013)Google Scholar
  8. 8.
    Jensen, M.T.: Reducing the Run-time Complexity of Multiobjective EAs: The NSGA-II and Other Algorithms. Transactions on Evolutionary Computation 7(5), 503–515 (2003)CrossRefGoogle Scholar
  9. 9.
    Knowles, J.D., Corne, D.W.: Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation 8(2), 149–172 (2000)CrossRefGoogle Scholar
  10. 10.
    Kung, H.T., Luccio, F., Preparata, F.P.: On finding the maxima of a set of vectors. Journal of ACM 22(4), 469–476 (1975)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In: Proceedings of the EUROGEN 2001 Conference, pp. 95–100 (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Maxim Buzdalov
    • 1
  • Anatoly Shalyto
    • 1
  1. 1.ITMO UniversitySaint-PetersburgRussia

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