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Combining Lagrangian Decomposition with an Evolutionary Algorithm for the Knapsack Constrained Maximum Spanning Tree Problem

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Book cover Evolutionary Computation in Combinatorial Optimization (EvoCOP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4446))

Abstract

We present a Lagrangian decomposition approach for the Knapsack Constrained Maximum Spanning Tree problem yielding upper bounds as well as heuristic solutions. This method is further combined with an evolutionary algorithm to a sequential hybrid approach. Experimental investigations, including a comparison to a previously suggested simpler Lagrangian relaxation based method, document the advantages of the new approach. Most of the upper bounds derived by Lagrangian decomposition are optimal, and together with the evolutionary algorithm, large instances with up to 12000 nodes can be either solved to provable optimality or with a very small remaining gap in reasonable time.

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Author information

Authors and Affiliations

  1. Institute of Computer Graphics and Algorithms, Vienna University of Technology, Vienna, Austria

    Sandro Pirkwieser & Günther R. Raidl

  2. National ICT Australia (NICTA) Victoria Laboratory, Dep. of Comp. Sci. & Softw. Eng., The University of Melbourne, Australia

    Jakob Puchinger

Authors
  1. Sandro Pirkwieser
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  2. Günther R. Raidl
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  3. Jakob Puchinger
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Editor information

Carlos Cotta Jano van Hemert

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© 2007 Springer Berlin Heidelberg

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Pirkwieser, S., Raidl, G.R., Puchinger, J. (2007). Combining Lagrangian Decomposition with an Evolutionary Algorithm for the Knapsack Constrained Maximum Spanning Tree Problem. In: Cotta, C., van Hemert, J. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2007. Lecture Notes in Computer Science, vol 4446. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71615-0_16

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  • DOI: https://doi.org/10.1007/978-3-540-71615-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71614-3

  • Online ISBN: 978-3-540-71615-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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