Interval data minmax regret network optimization problems
Discrete Applied Mathematics
An exact algorithm for the robust shortest path problem with interval data
Computers and Operations Research
The robust shortest path problem in series-parallel multidigraphs with interval data
Operations Research Letters
A branch and bound algorithm for the robust shortest path problem with interval data
Operations Research Letters
Using genetic algorithms for navigation planning in dynamic environments
Applied Computational Intelligence and Soft Computing
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We investigate the uncertain versions of two classical combinatorial optimization problems, namely the Single-Pair Shortest Path Problem (SP-SPP) and the Single-Source Shortest Path Problem (SS-SPP). The former consists of finding a path of minimum length connecting two specific nodes in a finite directed graph G; the latter consists of finding the shortest paths from a fixed node to the remaining nodes of G. When considering the uncertain versions of both problems we assume that cycles may occur in G and that arc lengths are (possibly degenerating) nonnegative intervals. We provide sufficient conditions for a node and an arc to be always or never in an optimal solution of the Minimax regret Single-Pair Shortest Path Problem (MSP-SPP). Similarly, we provide sufficient conditions for an arc to be always or never in an optimal solution of the Minimax regret Single-Source Shortest Path Problem (MSS-SPP). We exploit such results to develop pegging tests useful to reduce the overall running time necessary to exactly solve both problems.