An Analysis of Local Search for the Bi-objective Bidimensional Knapsack Problem

  • Leonardo C. T. Bezerra
  • Manuel López-Ibáñez
  • Thomas Stützle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7832)


Local search techniques are increasingly often used in multi-objective combinatorial optimization due to their ability to improve the performance of metaheuristics. The efficiency of multi-objective local search techniques heavily depends on factors such as (i) neighborhood operators, (ii) pivoting rules and (iii) bias towards good regions of the objective space. In this work, we conduct an extensive experimental campaign to analyze such factors in a Pareto local search (PLS) algorithm for the bi-objective bidimensional knapsack problem (bBKP). In the first set of experiments, we investigate PLS as a stand-alone algorithm, starting from random and greedy solutions. In the second set, we analyze PLS as a post-optimization procedure.


Local Search Candidate List Nondominated Solution Stochastic Local Search Input Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alsheddy, A., Tsang, E.: Guided Pareto local search and its application to the 0/1 multi-objective knapsack problems. In: Caserta, M., Voß, S. (eds.) MIC 2009. University of Hamburg, Hamburg (2010)Google Scholar
  2. 2.
    Bezerra, L.C.T., López-Ibáñez, M., Stützle, T.: Automatic Generation of Multi-objective ACO Algorithms for the Bi-objective Knapsack. In: Dorigo, M., Birattari, M., Blum, C., Christensen, A.L., Engelbrecht, A.P., Groß, R., Stützle, T. (eds.) ANTS 2012. LNCS, vol. 7461, pp. 37–48. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Bezerra, L.C.T., López-Ibáñez, M., Stützle, T.: An analysis of local search for the bi-objective bidimensional knapsack: Supplementary material (2012),
  4. 4.
    Drugan, M.M., Thierens, D.: Path-Guided Mutation for Stochastic Pareto Local Search Algorithms. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 485–495. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Dubois-Lacoste, J., López-Ibáñez, M., Stützle, T.: A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems. Computers & Operations Research 38(8), 1219–1236 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Dubois-Lacoste, J., López-Ibáñez, M., Stützle, T.: Pareto Local Search Algorithms for Anytime Bi-objective Optimization. In: Hao, J.-K., Middendorf, M. (eds.) EvoCOP 2012. LNCS, vol. 7245, pp. 206–217. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Dubois-Lacoste, J., López-Ibáñez, M., Stützle, T.: Combining Two Search Paradigms for Multi-objective Optimization: Two-Phase and Pareto Local Search. In: Talbi, E.-G. (ed.) Hybrid Metaheuristics. SCI, vol. 434, pp. 97–117. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  8. 8.
    Fonseca, C.M., Paquete, L., López-Ibáñez, M.: An improved dimension-sweep algorithm for the hypervolume indicator. In: CEC 2006, pp. 1157–1163. IEEE Press, Piscataway (2006)Google Scholar
  9. 9.
    Geiger, M.J.: Decision support for multi-objective flow shop scheduling by the Pareto iterated local search methodology. Computers and Industrial Engineering 61(3), 805–812 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Liefooghe, A., Humeau, J., Mesmoudi, S., Jourdan, L., Talbi, E.G.: On dominance-based multiobjective local search: design, implementation and experimental analysis on scheduling and traveling salesman problems. Journal of Heuristics 18(2), 317–352 (2011)CrossRefGoogle Scholar
  11. 11.
    López-Ibáñez, M., Paquete, L., Stützle, T.: Exploratory analysis of stochastic local search algorithms in biobjective optimization. In: Bartz-Beielstein, T., et al. (eds.) Experimental Methods for the Analysis of Optimization Algorithms, pp. 209–222. Springer, Berlin (2010)CrossRefGoogle Scholar
  12. 12.
    Lust, T., Teghem, J.: The multiobjective multidimensional knapsack problem: a survey and a new approach. Intern. Trans. in Oper. Res. 19(4), 495–520 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Paquete, L., Chiarandini, M., Stützle, T.: Pareto local optimum sets in the biobjective traveling salesman problem: An experimental study. In: Gandibleux, et al. (eds.) Metaheuristics for Multiobjective Optimisation. LNEMS, pp. 177–200. Springer, Berlin (2004)CrossRefGoogle Scholar
  14. 14.
    Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto evolutionary algorithm. IEEE Transactions on Evolutionary Computation 3(4), 257–271 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Leonardo C. T. Bezerra
    • 1
  • Manuel López-Ibáñez
    • 1
  • Thomas Stützle
    • 1
  1. 1.IRIDIAUniversité Libre de BruxellesBrusselsBelgium

Personalised recommendations