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The Electric Autonomous Dial-A-Ride Problem (E-ADARP) consists in schedulinga fleet of electric autonomous vehicles to provide ride-sharing services forcustomers that specify their origins and destinations. The E-ADARP differs fromthe classical DARP in two aspects: (i) a weighted-sum objective that minimizesboth total travel time and total excess user ride time; (ii) the employment ofelectric autonomous vehicles and a partial recharging policy. This paperpresents a highly-efficient labeling algorithm, which is integrated intoBranch-and-Price (B&P) algorithms to solve the E-ADARP. To handle (i), weintroduce a fragment-based representation of paths. A novel approach is invokedto abstract fragments to arcs while ensuring excess-user-ride-time optimality.We then construct a new graph that preserves all feasible routes of theoriginal graph by enumerating all feasible fragments, abstracting them to arcs,and connecting them with each other, depots, and recharging stations in afeasible way. On the new graph, partial recharging (ii) is tackled exactly bytailored Resource Extension Functions (REFs). We apply strong dominance rulesand constant-time feasibility checks to compute the shortest paths efficiently.These methods construct the first labeling algorithm that can deal withminimizing (excess) user ride time. In the computational experiments, the B&Palgorithm achieves optimality in 71 out of 84 instances. Remarkably, amongthese 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 vehiclesand 96 requests. In total 42 new best solutions are generated on previouslysolved and unsolved instances.

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