Abstract
In this article, the beam search approach is extended to multicriteria combinatorial optimization, with particular emphasis on its application to bicriteria {0,1} knapsack problems. The beam search uses several definitions of upper bounds of knapsack solutions as well as a new selection procedure based on ε-indicator that allows to discard uninteresting solutions. An in-depth experimental analysis on a wide benchmark set of instances suggests that this approach can achieve very good solution quality in a small fraction of time needed to solve the problem to optimality by state-of-the-art algorithms.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aneja, Y., Nair, K.: Bicriteria transportation problem. Management Science 25(1), 73–78 (1979)
Bazgan, C., Hugot, H., Vanderpooten, D.: Solving efficiently the 0-1 multi-objective knapsack problem. Computers & Operations Research 36(1), 260–279 (2009)
Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181(3), 1653–1669 (2007)
Blum, C., Cotta, C., Férnandez, A., Gallardo, J., Mastrolilli, M.: Hybridizations of Metaheuristics with Branch & Bound Derivates. In: Blum, C., et al. (eds.) Hybrid Metaheuristics: An Emerging Approach to Optimization. SCI, vol. 114, pp. 85–116. Springer, Heidelberg (2008)
Blunck, H., Vahrenhold, J.: In-place algorithms for computing (layers of) maxima. Algorithmica 57(1), 1–21 (2010)
Captivo, M., Clímaco, J., Figueira, J., Martins, E., dos Santos, J.: Solving bicriteria 0-1 knapsack problems using a labeling algorithm. Computers & Operations Research 30(12), 1865–1886 (2003)
Chvátal, V.: A greedy heuristic for the set-covering problem. Mathematics of Operations Research 4(3), 233–235 (1979)
Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms. MIT Press (2001)
Ehrgott, M., Gandibleux, X.: Bound sets for biobjective combinatorial optimization problems. Computers & Operations Research 34(9), 2674–2694 (2007)
Erlebach, T., Kellerer, H., Pferschy, U.: Approximating multiobjective knapsack problems. Management Science 48(12), 1603–1612 (2002)
Figueira, J., Paquete, L., Simões, M., Vanderpooten, D.: Algorithmic improvements on dynamic programming for the bi-objective {0,1} knapsack problem. Tech. Rep. TR2011/03, CISUC, University of Coimbra (2011)
Gandibleux, X., Freville, A.: Tabu search based procedure for solving the 0-1 multiobjective knapsack problem: The two objectives case. Journal of Heuristics 6(3), 361–383 (2000)
da Silva, G., Clímaco, C., Figueira, J.: A scatter search method for bi-criteria {0, 1}-knapsack problems. European Journal of Operational Research 169(2), 373–391 (2006)
Honda, N.: Backtrack beam search for multiobjective scheduling problem. In: Tanino, T., et al. (eds.) Multi-Objective Programming and Goal Programming: Theory and Applications. AISC, pp. 147–152. Springer, Heidelberg (2003)
Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer (2004)
Klamroth, K., Wiecek, M.: Dynamic programming approaches to the multiple criteria knapsack problem. Naval Research Logistics 47(1), 57–76 (2000)
Kung, H., Luccio, F., Preparata, F.: On finding the maxima of a set of vectors. Journal of the ACM 22(4), 469–476 (1975)
Martello, S., Toth, P.: Knapsack Problems – Algorithms and Computer Implementations. John Wiley & Sons (1990)
Papadimitriou, C., Yannakakis, M.: On the approximability of trade-offs and optimal access of web sources. In: IEEE Symposium on Foundation of Computer Science, pp. 86–92 (2000)
Sabuncuoğlu, I., Gocgun, Y., Eerl, E.: Backtracking and exchange of information: Methods to enhance a beam search algorithm for assembly line scheduling. European Journal of Operational Research 186, 915–930 (2008)
Schöbel, A.: Set covering problems with consecutive ones property. Tech. Rep. 2005-03, Georg-August Universität Göttingen, Institut für Numerische und Angewandte Mathematik (2005)
Steuer, R.: Multiple Criteria Optimization: Theory, Computation and Application, p. 546. John Wiley, New York (1986)
Visée, M., Teghem, J., Pirlot, M., Ulungu, E.L.: Two-phases method and branch and bound procedures to solve the bi–objective knapsack problem. Journal of Global Optimization 12(2), 139–155 (1998)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., da Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 529–533 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ponte, A., Paquete, L., Figueira, J.R. (2012). On Beam Search for Multicriteria Combinatorial Optimization Problems. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds) Integration of AI and OR Techniques in Contraint Programming for Combinatorial Optimzation Problems. CPAIOR 2012. Lecture Notes in Computer Science, vol 7298. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29828-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-29828-8_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29827-1
Online ISBN: 978-3-642-29828-8
eBook Packages: Computer ScienceComputer Science (R0)