New Formulations and Solution Methods for the Dial-a-ride Problem

Abstract

The classic Dial-A-Ride Problem (DARP) aims at designing the minimum-cost routing solution that accommodates a set of user requests under constraints at the operations planning level. It is a highly constrained combinatorial optimization problem initially designed for providing door-to-door transportation for people with limited mobility (e.g. the elderly or disabled). It consists of routing and scheduling a fleet of capacitated vehicles to service a set of requests with specified pickup and drop-off locations and time windows. With the details of requests obtained either beforehand (static DARP) or en-route (dynamic DARP), dial-a-ride operators strive to deliver efficient and yet high-quality transport services that satisfy each passenger's individual travel needs. The goal of this thesis is threefold: (1) to propose rich DARP formulations where users' preferences are taken into account, in order to improve service quality of Demand-Responsive Transport (DRT) services and promote ridership strategically; (2) to develop novel and efficient solution methods where local search, column generation, metaheuristics and machine learning techniques are integrated to solve large-scale DARPs; and (3) to conduct real-life DARP case studies (using data extracted from NYC Yellow Taxi trip records) to test the practicality of proposed models and solution methods, as well as to emphasise the importance of connecting algorithms with real-world datasets. These aims are achieved and presented in the three core chapters of this thesis. In the first core chapter (Chapter 3), two Mixed Integer Programming (MIP) formulations (link-based and path-based) of DARP are presented, alongside with their objective functions and standard solution methods. This chapter builds the foundation of the thesis by elaborating the base models and algorithms that this thesis is based on, and by running benchmark experiments and reporting numerical results as the base line of the whole thesis. In the second core chapter (Chapter 4), two DARP models (one deterministic, one stochastic) integrated with users' preferences from dial-a-ride service operators' perspective are proposed, facilitating them to optimise their overall profit while maintaining service quality. In these models, users' utility users' preferences are considered within a dial-a-ride problem. A customized local search based heuristic and a matheuristic are developed to solve the proposed Chance-Constrained DARP (CC-DARP). Numerical results are reported for both DARP benchmark instances and a realistic case study based on New York City yellow taxi trip data. This chapter also explores the design of revenue/fleet management and pricing differentiation. The proposed chance-constrained DARP formulation provides a new decision-support tool to inform on revenue and fleet management, including fleet sizing, for DRT systems at a strategic planning level. In the last core chapter (Chapter 5), three hybrid metaheuristic algorithms integrated with Reinforcement Learning (RL) techniques are proposed and implemented, aiming to increase the scale-up capability of existing DARP solution methods. Machine learning techniques and/or a branching scheme are incorporated with various metaheuristic algorithms including VNS and LNS, providing innovative methodologies to solve large-instance DARPs in a more efficient manner. Thompson Sampling (TS) is applied to model dual values of requests under a column generation setting to negate the effect of dual oscillation (i.e. promote faster converging). The performance of proposed algorithms is tested benchmark datasets, and strengths and weaknesses across different algorithms are reported