Bilevel Optimization and Heuristic Algorithms for Integrating Latent Demand into the Design of Large-Scale Transit Systems

TL;DR

This paper develops a bilevel optimization model for transit network design that incorporates latent demand, proposes heuristic algorithms for large-scale problems, and validates them through extensive real-world case studies.

Contribution

It introduces a novel bilevel model for integrating latent demand into transit design and provides efficient heuristics with proven properties for large-scale applications.

Findings

Heuristic algorithms achieve high-quality solutions faster than exact methods.

The model captures rider adoption behavior effectively.

Case studies demonstrate practical applicability and solution quality.

Abstract

Capturing latent demand has a pivotal role in designing transit services as omitting these riders can lead to poor quality of service and/or additional costs. This paper explores this topic in the design of transit networks by considering the perspectives of both the transit agencies and riders. The paper presents a generic bilevel optimization model, namely the Transit Networks Design with Adoptions (TN-DA), that considers the network design decisions in the leader problem, and routing of the riders in the follower problem under the given network design, while allowing a black-box choice function for representing the adoption behavior of latent demand. The paper then identifies structural properties of the optimal solution of the TN-DA problem, which are desirable for transit agencies for capturing adoption behavior of the riders. The paper further provides guideline metrics for the transit agencies based on these desired adoption properties. Due to the computational complexity of this bilevel problem, the paper proposes five efficient heuristic algorithms to solve large-scale instances, which leverage an iterative procedure by solving a simpler version of the TN-DA problem and integrating the evaluation of rider choices. These algorithms either satisfy the desired properties of the optimal solution or provide fast approximations. The paper presents extensive large-scale case studies on two different transit systems by utilizing real datasets: (i) On-demand Multimodal Transit Systems (ODMTS) and (ii) Scooters-Connected Transit Systems (SCTS). The results demonstrate that the heuristic algorithms can find high-quality solutions much faster than exact approaches over various instances, while satisfying key adoption properties of the optimal solutions.