Sensitivity analysis for minimum Hamiltonian path and traveling salesman problems
ARIDAM III Selected papers on Third advanced research institute of discrete applied mathematics
Some concepts of stability analysis in combinatorial optimization
Proceedings of the workshop on Discrete algorithms
Advances in computational and stochastic optimization, logic programming, and heuristic search
Mathematics of Operations Research
On the complexity of postoptimality analysis of 0/1 programs
Discrete Applied Mathematics
Tolerance Sensitivity and Optimality Bounds in Linear Programming
Management Science
Calculation of stability radii for combinatorial optimization problems
Operations Research Letters
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We consider so-called generic combinatorial optimization problem, where the set of feasible solutions is some family of nonempty subsets of a finite ground set with specified positive initial weights of elements, and the objective function represents the total weight of elements of the feasible solution. We assume that the set of feasible solutions is fixed, but the weights of elements may be perturbed or are given with errors. All possible realizations of weights form the set of scenarios. A feasible solution, which for a given set of scenarios guarantees the minimum value of the worst-case relative regret among all the feasible solutions, is called a robust solution. The maximum percentage perturbation of a single weight, which does not destroy the robustness of a given solution, is called the robustness tolerance of this weight with respect to the solution considered. In this paper we give formulae for computing the robustness tolerances with respect to an optimal solution obtained for some initial weights and we show that this can be done in polynomial time whenever the optimization problem is polynomially solvable itself.