Optimal Subgraph on Disturbed Network

TL;DR

This paper addresses the challenge of designing an optimal subnetwork in a disrupted urban transportation system, balancing access time, delay, and network reduction, using mixed integer programming and real-world data.

Contribution

It introduces a novel optimization model for selecting subgraphs in disturbed networks, ensuring minimal delays and reduced nodes, with practical application to Lyon's bus network.

Findings

The model effectively balances access time and delay constraints.

Application to Lyon's network demonstrates practical viability.

Optimal subnetwork reduces nodes while maintaining service quality.

Abstract

During the pandemic of COVID-19, the demand of the transportation systems are drastically changed both qualitatively and quantitatively and the network has become obsolete. In this article, we study the problem of finding an optimal subnetwork that guarantee that (i) the minimal access time from any node of the urban network to the new network is not {\em too large} compared to the original transportation network; (ii) for any itinerary, the delay caused by the deletion of nodes of the transportation network is not {\em too big}; and (iii) the number of nodes of the transportation network has been reduced at least by a known factor. A solution is optimal if it induces a minimal global delay. We model this problem as a Mixed Integer Linear Program before applying the model on a real-case application on the Lyon's buses transportation network.