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Refined ranking relations for selection of solutions in multi objective metaheuristics

Author

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  • Moritz, Ruby L.V.
  • Reich, Enrico
  • Schwarz, Maik
  • Bernt, Matthias
  • Middendorf, Martin

Abstract

Two methods for ranking of solutions of multi objective optimization problems are proposed in this paper. The methods can be used, e.g. by metaheuristics to select good solutions from a set of non dominated solutions. They are suitable for population based metaheuristics to limit the size of the population. It is shown theoretically that the ranking methods possess some interesting properties for such applications. In particular, it is shown that both methods form a total preorder and are both refinements of the Pareto dominance relation. An experimental investigation for a multi objective flow shop problem shows that the use of the new ranking methods in a Population-based Ant Colony Optimization algorithm and in a genetic algorithm leads to good results when compared to other methods.

Suggested Citation

  • Moritz, Ruby L.V. & Reich, Enrico & Schwarz, Maik & Bernt, Matthias & Middendorf, Martin, 2015. "Refined ranking relations for selection of solutions in multi objective metaheuristics," European Journal of Operational Research, Elsevier, vol. 243(2), pages 454-464.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:2:p:454-464
    DOI: 10.1016/j.ejor.2014.10.044
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    1. J. Heller, 1960. "Some Numerical Experiments for an M × J Flow Shop and its Decision-Theoretical Aspects," Operations Research, INFORMS, vol. 8(2), pages 178-184, April.
    2. Taillard, E., 1993. "Benchmarks for basic scheduling problems," European Journal of Operational Research, Elsevier, vol. 64(2), pages 278-285, January.
    3. M. R. Garey & D. S. Johnson & Ravi Sethi, 1976. "The Complexity of Flowshop and Jobshop Scheduling," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 117-129, May.
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    Cited by:

    1. Ding, Jiankun & Han, Deqiang & Yang, Yi, 2018. "Iterative ranking aggregation using quality improvement of subgroup ranking," European Journal of Operational Research, Elsevier, vol. 268(2), pages 596-612.

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