Mathematical models and a constructive heuristic for finding minimum fundamental cycle bases

Authors

  • Leo Liberti DEI, Politecnico di Milano, Milano, Italy
  • Edoardo Amaldi DEI, Politecnico di Milano, Milano, Italy
  • Francesco Maffioli DEI, Politecnico di Milano, Milano, Italy
  • Nelson Maculan COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil

DOI:

https://doi.org/10.2298/YJOR0501015L

Keywords:

fundamental cycle, cycle basis, IP formulation, tree-growing heuristic

Abstract

The problem of finding a fundamental cycle basis with minimum total cost in a graph arises in many application fields. In this paper we present some integer linear programming formulations and we compare their performances, in terms of instance size, CPU time required for the solution, and quality of the associated lower bound derived by solving the corresponding continuous relaxations. Since only very small instances can be solved to optimality with these formulations and very large instances occur in a number of applications, we present a new constructive heuristic and compare it with alternative heuristics.

References

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Published

2005-03-01

Issue

Vol. 15 No. 1 (2005)

Section

Research Articles

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