Evacuation Network Design Under Road Capacity Improvement and Uncertainty: Socp Reformulations and Benders Decomposition

Abstract

This work first presents a stochastic shelter location and evacuation planning problem with considering road capacity improvement strategies, in which the fixed setup cost of shelters and the improvement cost of road capacity are subject to a budget limit. To explicitly capture the impact of traffic volumes and road capacity improvement decisions on evacuation time, the Bureau of Public Roads function is employed. The problem is formulated as a non-convex mixed-integer nonlinear program (MINLP) model that is difficult to solve directly since the objective function is a multivariable non-convex nonlinear function. To tackle the non-convex MINLP, linear approximation and second-order cone programming (SOCP) reformulations that can be directly solved by using the state-of-the-art solvers are developed. Furthermore, a Benders decomposition (BD) approach that utilizes duality results of SOCP and employs acceleration strategies associated with valid inequalities, multi-cut, strengthened Benders cuts, and knapsack inequalities, is proposed to solve large-scale problems. Moreover, extensive numerical experiments and a real-world case study (a potential hurricane risk zone in Texas, U.S.) are conducted to verify the applicability and effectiveness of the proposed model and solution approaches. Computational results show that the derived reformulations are competitive in dealing with small- and medium-scale problems, whereas BD approach demonstrates the best computational performance in solving large-scale problems. The devised acceleration strategies are effective in improving the computational efficiency of the BD approach. In addition, exerting investment for those shelters and arcs that are close to evacuation regions is useful to reduce the expected total evacuation time.

Keywords: evacuation planning, shelter location, road capacity improvement, linear approximation, Second-order cone programming, Benders decomposition