Computational Optimization and Applications
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Many real problems in transportation and telecommunications can be modelled in mathematical terms as shortest path problems on interval digraphs, where an interval of costs is associated with each arc. Intervals represent uncertainty, typical of real situations, about the exact values of costs. In this context, a robust shortest path is a path which is ideally not too far from the best one, whatever the exact values of arc costs are. We use this optimality concept, expressed in mathematical terms, to drive optimization. In this paper a branch and bound algorithm for the robust shortest path problem is described. It is based on a new lower bound and on some new reduction rules which exploit the properties of the branching strategy adopted. Computational results obtained by the algorithm are finally presented.