A Branch-and-Price Algorithm for the Electric Autonomous Dial-A-Ride Problem

TL;DR

The paper addresses the Electric Autonomous DARP (E-ADARP), introducing a highly efficient Branch-and-Price framework that solves a weighted-sum objective combining total travel time and excess user ride time. A fragment-based path representation is developed, with fragments abstracted to arcs on a new sparse graph $G_{sp}$ to guarantee excess-ride-time optimality and enable exact REFs for partial recharging. The pricing subproblem is solved via a tailored ESPPRC-MERT labeling algorithm with strong dominance and constant-time feasibility checks, complemented by cutting planes and branches. Computational results show the approach solving 71 of 84 instances to optimality, with substantial improvements over prior B&C and state-of-the-art heuristics, and provide managerial insights on the trade-offs between service quality and operational cost, as well as the benefits of unlimited charging visits. The methodology also yields a first exact scheduling procedure for minimal excess ride time on a given E-ADARP route, with potential applications to dynamic DARP/E-ADARP and more energy-realistic battery models.

Abstract

The Electric Autonomous Dial-A-Ride Problem (E-ADARP) consists in scheduling a fleet of electric autonomous vehicles to provide ride-sharing services for customers that specify their origins and destinations. The E-ADARP differs from the classical DARP in two aspects: (i) a weighted-sum objective that minimizes both total travel time and total excess user ride time; (ii) the employment of electric autonomous vehicles and a partial recharging policy. This paper presents a highly-efficient labeling algorithm, which is integrated into Branch-and-Price (B&P) algorithms to solve the E-ADARP. To handle (i), we introduce a fragment-based representation of paths. A novel approach is invoked to abstract fragments to arcs while ensuring excess-user-ride-time optimality. We then construct a new graph that preserves all feasible routes of the original graph by enumerating all feasible fragments, abstracting them to arcs, and connecting them with each other, depots, and recharging stations in a feasible way. On the new graph, partial recharging (ii) is tackled exactly by tailored Resource Extension Functions (REFs). We apply strong dominance rules and constant-time feasibility checks to compute the shortest paths efficiently. These methods construct the first labeling algorithm that can deal with minimizing (excess) user ride time. In the computational experiments, the B&P algorithm achieves optimality in 71 out of 84 instances. Remarkably, among these instances, 50 were solved optimally at the root node without branching. We identify 26 new best solutions, improve 30 previously reported lower bounds, and provide 17 new lower bounds for large-scale instances with up to 8 vehicles and 96 requests. In total 42 new best solutions are generated on previously solved and unsolved instances.

Figures (3)

• Figure 1: Example of abstracting a fragment to an arc
• Figure 2: Example of any excess-user-ride-time optimal schedule on a fragment
• Figure 3: Example of constructing arcs in the new graph $G_{sp}$

Theorems & Definitions (13)

• Definition 1: E-ADARP route
• Definition 2: Battery-restricted fragment, su2023deterministic
• Definition 3
• Example 1
• Example 2: Example \ref{['example2']} continued
• Theorem 1
• proof : Proof of Theorem \ref{['thm:segment scheduling']}
• Theorem 2
• proof : Proof of Theorem \ref{['thm:optimization']}
• Lemma 1