Battery-time-space fragment-based formulation for the Electric Autonomous Dial-a-Ride Problem

The Electric Autonomous Dial-A-Ride Problem (E-ADARP) optimizes routing and scheduling for electric autonomous vehicles to transport customers from origins to destinations. It features a combined objective that minimizes travel cost and excess user ride time, and allows partial recharging. Motivated by practical scenarios where time and battery data are available with limited precision, we introduce a discrete variant of the problem, termed D-E-ADARP, in which all time and battery parameters are discretized. This enables the development of our alternative solution approach: the discrete battery-time-space fragment-based formulation (BTSFF). In this framework, a fragment represents a subpath with an associated cost that accounts for both travel cost and excess user ride time. The BTSFF network integrates spatial, temporal, and battery dimensions, with the latter two discretized into finite indices. Computational results show that BTSFF solves D-E-ADARP significantly more efficiently than existing methods applied to the original E-ADARP. In addition, BTSFF efficiently provides high-quality lower bounds for E-ADARP and accelerates solving its battery swap variants. For E-ADARP, a relaxed network is constructed by rounding down travel times and battery consumptions, enabling a valid lower bound. For battery swap variants, BTSFF integrates lazy constraints via callbacks to correct time discretization errors, guaranteeing optimal solutions. Experiments show BTSFF outperforms benchmark methods in efficiency.