This paper presents a global optimization framework for identifying the most critical combination of vulnerable links in a transportation network. The problem is formulated as a mixed-integer nonlinear program with equilibrium constraints, aiming to determine the combination of links whose deterioration would induce the most increase in total travel cost in the network. A global optimization solution method applying a piecewise linearization approach and range reduction technique is developed to solve the model. From the numerical results, it is interesting and counterintuitive to note that the set of most vulnerable links when simultaneous multiple-link failure occurs are not simply the combination of the most vulnerable links with single-link failure, and the links in the critical combination of vulnerable links are not necessarily connected or even in the neighbourhood of each other. The numerical results also show that the ranking of vulnerable links will be significantly affected by certain input parameters.
a b s t r a c tConventional discrete transportation network design problem deals with the optimal decision on new link addition, assuming the capacity of each candidate link addition is predetermined and fixed. In this paper, we address a novel yet general discrete network design problem formulation that aims to determine the optimal new link addition and their optimal capacities simultaneously, which answers the questions on whether a new link should be added or not, and if added, what should be the optimal link capacity. A global optimization method employing linearization, outer approximation and range reduction techniques is developed to solve the formulated model.
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