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Greedy heuristics and evolutionary algorithms for the bounded minimum-label spanning tree problem

Published: 12 July 2008 Publication History

Abstract

Given an edge-labeled, connected, undirected graph G and a bound r>1, the bounded minimum-label spanning tree problem seeks a spanning tree on G whose edges carry the fewest possible labels and in which no label appears more than r times. Two greedy heuristics for the unbounded version of the problem are adapted to the bounded version. Two genetic algorithms for the problem encode labeled spanning trees as permutations of G's edges. A simple GA performs poorly, but the addition of local search enables consistently good results.

References

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T. Brüggemann, J. Monnot, and G. J. Woeginger. Local search for the minimum label spanning tree problem with bounded color classes. Operations Research Letters, 31:195--201, 2003.
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J. B. Kruskal. On the shortest spanning subtree and the traveling salesman problem. Proceedings of the American Mathematical Society, 7:48--50, 1956.
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J. Nummela and B. A. Julstrom. An effective genetic algorithm for the minimum-label spanning tree problem. In M. Keijzer et al., editors, Proceedings of the 2006 Genetic and Evolutionary Computation Conference, volume 1, pages 553--557, New York, 2006. ACM Press.
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I. M. Oliver, D. J. Smith, and J. R. C. Holland. A study of permutation operators on the Traveling Salesman Problem. In J. J. Grefenstette, editor, Proceedings of the Second International Conference on Genetic Algorithms, pages 224--230, Hillsdale, NJ, 1987. Lawrence Erlbaum.
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Y. Xiong, B. Golden, and E. Wasil. A one-parameter genetic algorithm for the minimum labeling spanning tree problem. IEEE Transactions on Evolutionary Computation, 9(1):55--60, 2005.

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Published In

cover image ACM Conferences
GECCO '08: Proceedings of the 10th annual conference on Genetic and evolutionary computation
July 2008
1814 pages
ISBN:9781605581309
DOI:10.1145/1389095
  • Conference Chair:
  • Conor Ryan,
  • Editor:
  • Maarten Keijzer
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 July 2008

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Author Tags

  1. bounded labels
  2. genetic algorithms
  3. greedy heuristics
  4. labeled spanning trees
  5. local search

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