  The rise of battery-powered vehicles for mobility-on-demand leads to many
technical and methodological hurdles. Among these, the efficient planning of a
shared electric fleet to fulfill passenger transportation requests still
represents a major challenge. This is due to the specific constraints of
electric vehicles, bound by their autonomy and necessity of recharge planning,
and the typical large scale of these systems, which challenges existing
optimization algorithms. The purpose of this paper is to introduce a scalable
column generation approach for the problem of managing electric
mobility-on-demand fleets. Our algorithm relies on three ingredients: (i) an
algebraic framework leading to an efficient algorithm for the pricing
subproblem despite its non-linearity, (ii) sparsification approaches permitting
to decrease the size of the subjacent graphs dramatically, and (iii) a diving
heuristic, which locates near-optimal solutions in a fraction of the time
needed for a complete branch-and-price. Through extensive computational
experiments, we demonstrate that our approach significantly outperforms
previous algorithms for this setting, leading to accurate solutions for
problems counting several hundreds of requests.
