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.

在本文中，我们开发了一种新工具，通过从旅行者的角度优化路线多样性冗余来增强交通网络的弹性。决定在何处添加新链路是为了生成尽可能多的起点-终点 (OD) 对，以及尽可能多的替代不同路线，以潜在地减轻中断的影响。在数学上，我们将问题表述为一个二进制整数双级程序 (BLP)，其中上级子程序最大化 OD 对的总数，并具有受预算约束的替代不同路线，而下级子程序计算最大值在给定设计方案下，每个 OD 对之间不同路径的数量。在计算上，通过使用低级子程序的等效连续松弛和最优条件以及互补条件的线性化技术，BLP ​​模型可以等效地重新表述为单级混合整数线性程序 (MILP)。可以使用商业软件包中的现有算法获得重构模型的 MILP 结构的全局最优解。提供了数值例子来证明所提出的面向路由多样性的网络设计模型在优化网络冗余方面的有效性、特征和灵活性。所提出的路线多样性冗余网络设计有助于增强网络在交通网络规划的灾前阶段抵御中断的能力，并有助于以冗余为导向的时间相关网络增长。当在设计过程中考虑旅行者的路线选择行为和旅行需求时，它也可以作为长期网络设计问题的上限解决方案。