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Dynamic Programming for a Biobjective Search Problem in a Line

  • Luís Paquete
  • Mathias Jaschob
  • Kathrin Klamroth
  • Jochen Gorski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7402)

Abstract

In this article we study the performance of multiobjective dynamic programming for a biobjective combinatorial optimization problem under several formulations. Based on our theoretical and computational results we argue that a clever definition of the recursion, allowing for strong dominance criteria, is crucial in the design of a multiobjective dynamic programming algorithm.

Keywords

Multiobjective combinatorial optimization dynamic programming shortest path problems knapsack problems 

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References

  1. 1.
    Ahuja, R., Magnanti, T., Orlin, J.: Network Flows: Theory, Algorithms and Applications. Prentice-Hall (1993)Google Scholar
  2. 2.
    Bazgan, C., Hugot, H., Vanderpooten, D.: Solving efficiently the 0-1 multi-objective knapsack problem. Computers & Operations Research 36(1), 260–276 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Brown, T., Strauch, R.: Dynamic programming in multiplicative lattices. Journal of Mathematical Analysis and Applications 12, 364–370 (1965)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Delling, D., Wagner, D.: Pareto Paths with SHARC. In: Vahrenhold, J. (ed.) SEA 2009. LNCS, vol. 5526, pp. 125–136. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer (2005)Google Scholar
  6. 6.
    Gaver, D., Jacobs, P., Pilnick, S.: On minefield transit by detection, avoidance and demining. In: Bottoms, A., Scandrett, C. (eds.) Applications of Technology to Demining, an Anthology of Scientific Papers 1995-2005, Part 3 – Naval Mine Countermeasures, Society for Countermine Technology (2005)Google Scholar
  7. 7.
    Hansen, P.: Bicriterion path problems. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making, Theory and Application. Lecture Notes in Economics and Mathematical Systems, vol. 177, pp. 109–127. Springer (1980)Google Scholar
  8. 8.
    Henig, M.: Vector-value dynamic programming. SIAM Journal on Control and Optimization 21, 490–499 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer (2004)Google Scholar
  10. 10.
    Klamroth, K., Wiecek, M.: Dynamic programming approaches to the multiple criteria knapsack problem. Naval Research Logistics 47(1), 57–76 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Sodhi, M., Swaszek, P., Bovio, E.: Stochastic line search using UUVs. In: 9th International Conference on Information Fusion (ICIF 2006), pp. 1–5 (2006)Google Scholar
  12. 12.
    Stone, L.: In search of AF flight 447. ORMS Today 38(4), 22–31 (2011)Google Scholar
  13. 13.
    Villarreal, B., Karwan, M.: Multicriteria integer programming: A (hybrid) dynamic programming recursive approach. Mathematical Programming 21, 204–223 (1981)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Luís Paquete
    • 1
  • Mathias Jaschob
    • 2
  • Kathrin Klamroth
    • 2
  • Jochen Gorski
    • 2
  1. 1.CISUC, Department of Informatics EngineeringUniversity of CoimbraPortugal
  2. 2.Department of Mathematics and Natural SciencesUniversity of WuppertalGermany

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