Resilient Transportation Network Design under Uncertain Link Capacity Using a Trilevel Optimization Model

Mohammad Rahdar,Lizhi Wang,Jing Dong,Guiping Hu,Meaad Saberi

doi:10.1155/2022/5023518

Abstract

This study addresses uncertainty in a transportation network by proposing a trilevel optimization model, which improves resiliency against uncertain disruptions. The goal is to minimize the total travel time by designing a resilient transportation network under uncertain disruptions and deterministic origin-destination demands. The trilevel optimization model has three levels. The lower level determines the network flow, and the middle level assesses the network’s resiliency by identifying the worst-case scenario disruptions that could lead to maximal travel time. The upper-level takes the system perspective to expand the existing transportation network to enhance resiliency. We also propose a formulation for the network flow problem to significantly reduce the number of variables and constraints. Two algorithms have been developed to solve the trilevel model. The results of solving the highway network in Iowa show that the trilevel optimization model improves the total travel time by an average of 41%.

Highlights

Academic Editor: Meaad Saberi is study addresses uncertainty in a transportation network by proposing a trilevel optimization model, which improves resiliency against uncertain disruptions. e goal is to minimize the total travel time by designing a resilient transportation network under uncertain disruptions and deterministic origin-destination demands. e trilevel optimization model has three levels. e lower level determines the network flow, and the middle level assesses the network’s resiliency by identifying the worstcase scenario disruptions that could lead to maximal travel time. e upper-level takes the system perspective to expand the existing transportation network to enhance resiliency
We developed a trilevel optimization model for the resilient network design problem. e lower-level determines the network flow to minimize the total travel time; the middle-level assesses the resiliency of the network by identifying the worst-case scenario disruptions that could lead to a maximal cost to the transportation system, and the upper-level designs the optimal strategy to expand the existing transportation network so that it enhances the resiliency of the network
We reformulated the network flow problem to reduce the number of variables and constraints significantly. ird, we designed a heuristic algorithm for solving the trilevel optimization model to efficiently enhance the resiliency of the network

Summary

Model Formulation

The lower level, minz∈Z(x,y)c⊤z, solves a deterministic problem to minimize the total travel cost given the expansion decision, x, made at the upper level and the worst-case scenario of disruptions, y, identified by the middle level. E algorithm of solving subproblem (17) reduces the capacity of links in the network up to the total disruption limit (Q) to find a worst-case scenario It has two steps in each iteration: first, we find a worst-case scenario for disruption; second, we solve the lower-level problem to find the network flow under this scenario. E algorithm to find the initial traffic disruption starts with disconnecting the (r, s) pairs with the highest demands and continues to separate them until it reaches the network disruption upper bound Q After having this initial disruption, the lower-level problem is solved to find the network flow. The resiliency of the network is assessed again by solving the bilevel programming problem. e steps of the greedy method are represented in Algorithm 2

Case Study

Findings

Conclusions