Robust solutions of uncertain linear programs
Operations Research Letters
An exact algorithm for the robust shortest path problem with interval data
Computers and Operations Research
Annals of Mathematics and Artificial Intelligence
An approximation algorithm for interval data minmax regret combinatorial optimization problems
Information Processing Letters
A Branch and Bound algorithm for the minimax regret spanning arborescence
Journal of Global Optimization
The minimum spanning tree problem with fuzzy costs
Fuzzy Optimization and Decision Making
Simulated annealing algorithm for the robust spanning tree problem
Journal of Heuristics
Choosing robust solutions in discrete optimization problems with fuzzy costs
Fuzzy Sets and Systems
Some methods for evaluating the optimality of elements in matroids with ill-known weights
Fuzzy Sets and Systems
Combinatorial optimization in system configuration design
Automation and Remote Control
Interval-parameter optimization problems on graphs
Cybernetics and Systems Analysis
An approximation algorithm for interval data minmax regret combinatorial optimization problems
Information Processing Letters
The minimum risk spanning tree problem
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
Heuristics for the central tree problem
Journal of Heuristics
A relaxation algorithm with a probabilistic guarantee for robust deviation optimization
Computational Optimization and Applications
Connection situations under uncertainty and cost monotonic solutions
Computers and Operations Research
A constraint satisfaction approach to the robust spanning tree problem with interval data
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
Complexity of the min-max (regret) versions of cut problems
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
A possibilistic approach to combinatorial optimization problems on fuzzy-valued matroids
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
The robust minimum spanning tree problem: Compact and convex uncertainty
Operations Research Letters
Operations Research Letters
Minmax regret bottleneck problems with solution-induced interval uncertainty structure
Discrete Optimization
Complexity of the min-max (regret) versions of min cut problems
Discrete Optimization
Pinpointing the complexity of the interval min-max regret knapsack problem
Discrete Optimization
Complexity of the min-max and min-max regret assignment problems
Operations Research Letters
On the complexity of the robust spanning tree problem with interval data
Operations Research Letters
Minmax regret linear resource allocation problems
Operations Research Letters
On the hardness of evaluating criticality of activities in a planar network with duration intervals
Operations Research Letters
A branch and bound algorithm for the robust shortest path problem with interval data
Operations Research Letters
Robust optimization of graph partitioning involving interval uncertainty
Theoretical Computer Science
The balanced minimum evolution problem under uncertain data
Discrete Applied Mathematics
On exact solutions for the Minmax Regret Spanning Tree problem
Computers and Operations Research
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Motivated by telecommunications applications we investigate the minimum spanning tree problem where edge costs are interval numbers. Since minimum spanning trees depend on the realization of the edge costs, we define the robust spanning tree problem to hedge against the worst case contingency, and present a mixed integer programming formulation of the problem. We also define some useful optimality concepts, and present characterizations for these entities leading to polynomial time recognition algorithms. These entities are then used to preprocess a given graph with interval data prior to the solution of the robust spanning tree problem. Computational results show that these preprocessing procedures are quite effective in reducing the time to compute a robust spanning tree.