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Implementing an efficient fptas for the 0-1 multi-objective knapsack problem

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  • Bazgan, Cristina
  • Hugot, Hadrien
  • Vanderpooten, Daniel

Abstract

In the present work, we are interested in the practical behavior of a new fully polynomial time approximation schemes (fptas) to solve the approximation version of the 0-1 multi-objective knapsack problem. The proposed methodology makes use of very general techniques (such as dominance relations in dynamic programming) and thus may be applicable in the implementation of fptas for other problems as well. Extensive numerical experiments on various types of instances in the bi and tri-objective cases establish that our method performs very well both in terms of CPU time and size of solved instances. We point out some reasons for the good practical performance of our algorithm. A comparison with an exact method and the fptas proposed in [Erlebach, T., Kellerer, H., Pferschy, U., 2002. Approximating multiobjective knapsack problems. Management Science 48 (12), 1603-1612] is also performed.

Suggested Citation

  • Bazgan, Cristina & Hugot, Hadrien & Vanderpooten, Daniel, 2009. "Implementing an efficient fptas for the 0-1 multi-objective knapsack problem," European Journal of Operational Research, Elsevier, vol. 198(1), pages 47-56, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:1:p:47-56
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    1. Thomas Erlebach & Hans Kellerer & Ulrich Pferschy, 2002. "Approximating Multiobjective Knapsack Problems," Management Science, INFORMS, vol. 48(12), pages 1603-1612, December.
    2. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria combinatorial optimization," Working papers 3756-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
    4. G. L. Nemhauser & Z. Ullmann, 1969. "Discrete Dynamic Programming and Capital Allocation," Management Science, INFORMS, vol. 15(9), pages 494-505, May.
    5. Safer, Hershel M. & Orlin, James B., 1953-, 1995. "Fast approximation schemes for multi-criteria flow, knapsack, and scheduling problems," Working papers 3757-95., Massachusetts Institute of Technology (MIT), Sloan School of Management.
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    1. Rong, Aiying & Figueira, José Rui, 2013. "A reduction dynamic programming algorithm for the bi-objective integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 231(2), pages 299-313.
    2. Rong, Aiying & Figueira, José Rui, 2014. "Dynamic programming algorithms for the bi-objective integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 236(1), pages 85-99.
    3. Bazgan, Cristina & Jamain, Florian & Vanderpooten, Daniel, 2017. "Discrete representation of the non-dominated set for multi-objective optimization problems using kernels," European Journal of Operational Research, Elsevier, vol. 260(3), pages 814-827.
    4. Florios, Kostas & Mavrotas, George & Diakoulaki, Danae, 2010. "Solving multiobjective, multiconstraint knapsack problems using mathematical programming and evolutionary algorithms," European Journal of Operational Research, Elsevier, vol. 203(1), pages 14-21, May.
    5. Justkowiak, Jan-Erik & Kovalev, Sergey & Kovalyov, Mikhail Y. & Pesch, Erwin, 2023. "Single machine scheduling with assignable due dates to minimize maximum and total late work," European Journal of Operational Research, Elsevier, vol. 308(1), pages 76-83.
    6. Daniel Vanderpooten & Lakmali Weerasena & Margaret M. Wiecek, 2017. "Covers and approximations in multiobjective optimization," Journal of Global Optimization, Springer, vol. 67(3), pages 601-619, March.
    7. Bas, Esra, 2011. "An investment plan for preventing child injuries using risk priority number of failure mode and effects analysis methodology and a multi-objective, multi-dimensional mixed 0-1 knapsack model," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 748-756.
    8. Shah, Ruchit & Reed, Patrick, 2011. "Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems," European Journal of Operational Research, Elsevier, vol. 211(3), pages 466-479, June.
    9. José Figueira & Luís Paquete & Marco Simões & Daniel Vanderpooten, 2013. "Algorithmic improvements on dynamic programming for the bi-objective {0,1} knapsack problem," Computational Optimization and Applications, Springer, vol. 56(1), pages 97-111, September.

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