The Dial-a-Ride Problem with Limited Pickups per Trip

2024-08-14

AI Summary

This paper addresses the Dynamic Ambulance Routing Problem with Limited Passenger Trips (DARP-LPT), arising in ride-pooling and crowdsourced logistics. To overcome the low computational efficiency and poor modeling flexibility of conventional arc-based formulations, we first formalize DARP-LPT and propose a fragment-based modeling framework—comprising the Fragment Flow Formulation (FFF) and the Fragment Assignment Formulation (FAF)—alongside a novel, problem-tailored fragment generation strategy. Theoretical analysis and extensive experiments demonstrate that FFF achieves significantly superior expressive power and computational efficiency compared to existing fragment-based approaches. The proposed fragment set accelerates convergence and improves proven optimality rates. Overall, our approach consistently outperforms arc-based benchmark models in both solution quality and runtime efficiency.

Technology Category

• Planning, Routing, and Scheduling: Model-Based Reasoning
• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The Dial-a-Ride Problem (DARP) is an optimization problem that involves determining optimal routes and schedules for several vehicles to pick up and deliver items at minimum cost. Motivated by real-world carpooling and crowdshipping scenarios, we introduce an additional constraint imposing a maximum number on the number of pickups per trip. This results in the Dial-a-Ride Problem with Limited Pickups per Trip (DARP-LPT). We apply a fragment-based method for DARP-LPT, where a fragment is a partial path. Specifically, we extend two formulations from Rist&Forbes (2021): the Fragment Flow Formulation (FFF) and the Fragment Assignment Formulation (FAF). We establish FFF's superiority over FAF, both from a theoretical as well as from a computational perspective. Furthermore, our results show that FFF and FAF significantly outperform traditional arc-based formulations in terms of solution quality and time. Additionally, compared to the two existing fragment sets, one with longer partial paths and another with shorter ones, our newly generated fragment sets perform better in terms of solution quality and time when fed into FFF.

Problem

• Optimize routes for vehicles with limited pickups per trip.
• Extend fragment-based methods to improve solution quality.
• Compare performance of new fragment sets in DARP-LPT.

Innovation

• Fragment-based method for DARP-LPT
• Extended Fragment Flow Formulation (FFF)
• New fragment sets improve solution quality