A Branch and Bound algorithm for the minimax regret spanning arborescence
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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.
KeywordsSpanning arborescences Robust optimization Branch and Bound algorithms
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- 1.Aron I., Van Hentenryck P. (2003) On the complexity of the robust spanning tree with interval data. Oper. Res. Lett. 32(1): 136–140Google Scholar
- 2.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)Google Scholar
- 4.Conde, E., Candia, A.: Minimax regret spanning arborescences under uncertain costs. Eur. J. Operational Res. (in Press) (2006)Google Scholar
- 5.Edmonds J. (1967) Optimum branching. J. Res. Nat. Bureau of Standards, 71B: 233–240Google Scholar
- 6.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)Google Scholar