Computational Complexity Results of Robust Discrete Optimization Problems
In previous chapters, we have mentioned that the robust discrete optimization problems are in general more difficult to solve than their deterministic counterparts. The major source of complexity comes from the extra degree of freedom — the scenario set. For many polynomially solvable classical optimization problems such as assignment, minimum spanning tree, shortest path, resource allocation, production control, single machine scheduling with sum of flow times criterion, and two machine flow shop scheduling, their corresponding robust versions are weakly or strongly NP-hard. We have found (see Yu and Kouvelis (1995)) that some of the above mentioned problems can be solved by pseudo-polynomial procedures based on dynamic programming if the scenario set is restricted to be bounded (constituting bounded number of scenarios). The well known pseudo-polynomially solvable knapsack problem also remains pseudo-polynormally solvable for bounded scenario set, but becomes strongly NP-hard for unbounded scenario set.
KeywordsMinimum Span Tree Knapsack Problem Complexity Result Resource Allocation Problem Grid Graph
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