Abstract
The paper considers the problem of finding a spanning arborescence on a directed network whose arc costs are partially known. It is assumed that each arc cost can take on values from a known interval defining a possible economic scenario. In this context, the problem of finding the spanning arborescence which better approaches to that of minimum overall cost under each possible scenario is studied. The minimax regret criterion is proposed in order to obtain such a robust solution of the problem. As it is shown, the bounds on the optimal value of the minimax regret optimization problem obtained in a previous paper, can be used here in a Branch and Bound algorithm in order to give an optimal solution. The computational behavior of the algorithm is tested through numerical experiments.
Similar content being viewed by others
References
Aron I., Van Hentenryck P. (2003) On the complexity of the robust spanning tree with interval data. Oper. Res. Lett. 32(1): 136–140
Aron, I., Van Hentenryck, P.: A constraint satisfaction approach to the robust spanning tree with interval data. Proceedings of the 18th conference on uncertainty in artificial intelligence (UAI), (August 2002)
Averbakh I., Lebedev V. (2004) Interval data minmax regret network optimization problems. Discrete Applied Mathematics, 138, 289–301
Conde, E., Candia, A.: Minimax regret spanning arborescences under uncertain costs. Eur. J. Operational Res. (in Press) (2006)
Edmonds J. (1967) Optimum branching. J. Res. Nat. Bureau of Standards, 71B: 233–240
Magnanti, T.L., Wolsey, L.: Optimal trees, in: Network models, handbook in operations research and management science. In: Ball, M.O. et al. (eds.), vol. 7, pp. 503–615. North-Holland Amsterdam (1995)
Montemanni R. (2006) A Benders decomposition approach for the robust spanning tree problem with interval data. Eur. J. Operational Res. 174(3): 1479–1490
Montemanni R., Gambardella L.M. (2005) A branch and bound algorithm for the robust spanning tree problem with interval data. Eur. J. Operational Res. 161(3): 771–779
Yaman H., Karasan O.E., Pinar M.Ç. (2001) The robust spanning tree problem with interval data. Operations Res. Lett. 29(1): 31–40
Author information
Authors and Affiliations
Corresponding author
Additional information
This research has been supported by the Spanish Ministry of Education and Science and FEDER Grant No. MTM2006-04393 and by the European Alfa Project, “Engineering System for Preparing and Making Decisions Under Multiple Criteria”, II-0321-FA.
Rights and permissions
About this article
Cite this article
Conde, E. A Branch and Bound algorithm for the minimax regret spanning arborescence. J Glob Optim 37, 467–480 (2007). https://doi.org/10.1007/s10898-006-9074-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-006-9074-4