Enhancing network resilience by adding redundancy to road networks

In this paper, we develop a new tool to enhance the resilience of transportation networks by optimizing route diversity redundancy from travelers’ perspective. The decision of where to add new links is made to generate as many origin–destination (O-D) pairs with alternative distinct routes as possible to potentially alleviate the impact of disruptions. Mathematically, we formulate the problem as a binary integer bi-level program (BLP), where the upper-level subprogram maximizes the total number of O-D pairs with alternative distinct routes subject to a budgetary constraint, and the lower-level subprogram counts the maximum number of distinct routes between each O-D pair under a given design scheme. Computationally, the BLP model can be equivalently reformulated as a single-level mixed-integer linear program (MILP) by using the equivalent continuous relaxation and optimality conditions of the lower-level subprogram and linearization techniques for the complementarity conditions. The globally optimum solution of the MILP structure of the reformulated model can be obtained using existing algorithms in commercial software packages. Numerical examples are provided to demonstrate the validity, features, and flexibility of the proposed route diversity-oriented network design model in terms of optimizing the network redundancy. The proposed route diversity redundant network design contributes toward enhancing network resilience against disruptions in the pre-disaster stage of transportation network planning and assists in redundancy-oriented time-dependent network growth. It can also serve as an upper-bound solution for the long-term network design problem when travelers’ route choice behaviors and travel demands are considered in the design process.