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Improved Dynamic Lexicographic Ordering for Multi-Objective Optimisation

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6239)


There is a variety of methods for ranking objectives in multi-objective optimization and some are difficult to define because they require information a priori (e.g. establishing weights in a weighted approach or setting the ordering in a lexicographic approach). In many-objective optimization problems, those methods may exhibit poor diversification and intensification performance. We propose the Dynamic Lexicographic Approach (DLA). In this ranking method, the priorities are not fixed, but they change throughout the search process. As a result, the search process is less liable to get stuck in local optima and therefore, DLA offers a wider exploration in the objective space. In this work, DLA is compared to Pareto dominance and lexicographic ordering as ranking methods within a Discrete Particle Swarm Optimization algorithm tackling the Vehicle Routing Problem with Time Windows.


  • Multi-objective Optimization
  • Swarm Optimization
  • Combinatorial Optimization
  • Vehicle Routing Problem

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  • DOI: 10.1007/978-3-642-15871-1_4
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  1. Banks, A., Vincent, J., Anyakoha, C.: A review of particle swarm optimization. part II: hybridisation, combinatorial, multicriteria and constrained optimization, and indicative applications. Natural Computing 7(1), 109–124 (2008)

    MathSciNet  MATH  CrossRef  Google Scholar 

  2. Castro-Gutierrez, J., Landa-Silva, D., Moreno Perez, J.: Dynamic lexicographic approach for heuristic multi-objective optimization. In: Proceedings of the Workshop on Intelligent Metaheuristics for Logistic Planning (CAEPIA-TTIA 2009) (Seville (Spain)), pp. 153–163 (2009)

    Google Scholar 

  3. Coello, C., Lamont, G., Veldhuizen, D.: Evolutionary algorithms for solving Multi-Objective problems. In: Genetic and Evolutionary Computation, Springer, Heidelberg (2007)

    Google Scholar 

  4. Consoli, S., Moreno-Pérez, J.A., Darby-Dowman, K., Mladenović, N.: Discrete particle swarm optimization for the minimum labelling steiner tree problem. Natural Computing 9(1), 29–46 (2010)

    MathSciNet  MATH  CrossRef  Google Scholar 

  5. Dantzig, G., Ramser, J.: The truck dispatching problem. Management Science 6(1), 80–91 (1959)

    MathSciNet  MATH  CrossRef  Google Scholar 

  6. Dorronsoro Díaz, B.: VRP web (2009),

  7. Ehrgott, M., Gandibleux, X.: Multiple criteria optimization: State of the art annotated bibliographic survey. International Series in Operations Research and Management Science, vol. (52) Springer/Kluwer (2002)

    Google Scholar 

  8. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks - Proceedings, vol. 4, pp. 1942–1948 (1995)

    Google Scholar 

  9. Kokolo, I., Hajime, K., Shigenobu, K.: Failure of pareto-based MOEAs, does non-dominated really mean near to optimal? In: Proceedings of the 2001 Congress on Evolutionary Computation (CEC 2001), pp. 957–962. IEEE press, Los Alamitos (2001)

    Google Scholar 

  10. Laporte, G., Golden, B., Grazia, M., Melissa, A.: The vehicle routing problem: Latest advances and new challenges. Operations Research/Computer Science Interfaces Series, vol. 43. Springer, Heidelberg (2008)

    Google Scholar 

  11. Zitzler, E., Brockhoff, D., Thiele, L.: The hypervolume indicator revisited: On the design of pareto-compliant indicators via weighted integration. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 862–876. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

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Castro-Gutierrez, J., Landa-Silva, D., Pérez, J.M. (2010). Improved Dynamic Lexicographic Ordering for Multi-Objective Optimisation. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds) Parallel Problem Solving from Nature, PPSN XI. PPSN 2010. Lecture Notes in Computer Science, vol 6239. Springer, Berlin, Heidelberg.

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  • Print ISBN: 978-3-642-15870-4

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