Efficient negative cycle-canceling algorithm for finding the optimal traffic routing for network evacuation with nonuniform threats

A new network flow solution method is designed to determine optimal traffic routing efficiently for the evacuation of networks with several threat zones and with nonuniform threat levels across zones. The objective is to minimize total exposure (as duration and severity) to the threat for all evacuees during the evacuation. The problem is formulated as a minimum cost dynamic flow problem coupled with traffic dynamic constraints. The traffic flow dynamic constraints are enforced by the well-known point queue and spatial queue models in a time-expanded network presentation. The key to the efficiency of the proposed method is that, for any feasible solution, the algorithm can find and can cancel multiple negative cycles (including the cycle with the largest negative cost) with a single shortest path calculation made possible by applying a proposed transformation to the original problem. A cost transformation function and a multisource shortest path algorithm are proposed to facilitate the efficient detection and cancelation of negative cycles. Zone by zone, negative cycles are canceled at the border links of the zones. The solution method is proved to be optimal. The algorithm is implemented, tested, and verified to be optimal for a midsized example problem

Network flow solution method for optimal evacuation traffic routing and signal control with nonuniform threat

An efficient two-stage network flow approach is proposed for the determination of optimal scenarios for integrated traffic routing and signal timing in the evacuation of real-sized urban networks with several threat zones, where the threat levels may be nonuniform across zones. The objective is to minimize total exposure to the threat (severity multiplied by duration) for all evacuees during the evacuation. In the problem formulation, traffic flow dynamics are based on the well-known point queue model in a time-expanded network representation. The proposed solution approach is adapted from a general relaxation-based decomposition method in a network flow formulation. The decomposition method is developed on the basis of insights into the optimal flow of traffic at intersections in the solution of the evacuation routing problem. As for efficiency, the computation time associated with the decomposition method for solving the integrated optimal routing and signal control problem is equivalent to the time required for solving the same optimal routing problem (without optimizing the intersection control plan) because the computation time required for determining the optimal signal control is negligible. The proposed solution method proves to be optimal. The method is implemented and applied to a real-sized evacuation scenario in the transportation network of Tucson, Arizona. The method is stress-tested with some inflated demand scenarios, and computation aspects are reported