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Dynamic Programming for a Biobjective Search Problem in a Line

  • Conference paper
Combinatorial Optimization and Applications (COCOA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7402))

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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.

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References

  1. Ahuja, R., Magnanti, T., Orlin, J.: Network Flows: Theory, Algorithms and Applications. Prentice-Hall (1993)

    Google Scholar 

  2. Bazgan, C., Hugot, H., Vanderpooten, D.: Solving efficiently the 0-1 multi-objective knapsack problem. Computers & Operations Research 36(1), 260–276 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brown, T., Strauch, R.: Dynamic programming in multiplicative lattices. Journal of Mathematical Analysis and Applications 12, 364–370 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  4. Delling, D., Wagner, D.: Pareto Paths with SHARC. In: Vahrenhold, J. (ed.) SEA 2009. LNCS, vol. 5526, pp. 125–136. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer (2005)

    Google Scholar 

  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. 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. Henig, M.: Vector-value dynamic programming. SIAM Journal on Control and Optimization 21, 490–499 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer (2004)

    Google Scholar 

  10. Klamroth, K., Wiecek, M.: Dynamic programming approaches to the multiple criteria knapsack problem. Naval Research Logistics 47(1), 57–76 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  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. Stone, L.: In search of AF flight 447. ORMS Today 38(4), 22–31 (2011)

    Google Scholar 

  13. Villarreal, B., Karwan, M.: Multicriteria integer programming: A (hybrid) dynamic programming recursive approach. Mathematical Programming 21, 204–223 (1981)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. CISUC, Department of Informatics Engineering, University of Coimbra, Portugal

    Luís Paquete

  2. Department of Mathematics and Natural Sciences, University of Wuppertal, Germany

    Mathias Jaschob, Kathrin Klamroth & Jochen Gorski

Authors
  1. Luís Paquete
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  2. Mathias Jaschob
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  3. Kathrin Klamroth
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  4. Jochen Gorski
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Editor information

Editors and Affiliations

  1. Department of Computing Science, University of Alberta, T6G 2E8, Edmonton, Alberta, Canada

    Guohui Lin

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© 2012 Springer-Verlag Berlin Heidelberg

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Paquete, L., Jaschob, M., Klamroth, K., Gorski, J. (2012). Dynamic Programming for a Biobjective Search Problem in a Line. In: Lin, G. (eds) Combinatorial Optimization and Applications. COCOA 2012. Lecture Notes in Computer Science, vol 7402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31770-5_31

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  • DOI: https://doi.org/10.1007/978-3-642-31770-5_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31769-9

  • Online ISBN: 978-3-642-31770-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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