We study the routing problem for vehicles with limited energy through a
network of inhomogeneous charging nodes. This is substantially more complicated
than the homogeneous node case studied in [1]. We seek to minimize the total
elapsed time for vehicles to reach their destinations considering both
traveling and recharging times at nodes when the vehicles do not have adequate
energy for the entire journey. We study two versions of the problem. In the
single vehicle routing problem, we formulate a mixed-integer nonlinear
programming (MINLP) problem and show that it can be reduced to a lower
dimensionality problem by exploiting properties of an optimal solution. We also
obtain a Linear Programming (LP) formulation allowing us to decompose it into
two simpler problems yielding near-optimal solutions. For a multi-vehicle
problem, where traffic congestion effects are included, we use a similar
approach by grouping vehicles into "subflows". We also provide an alternative
flow optimization formulation leading to a computationally simpler problem
solution with minimal loss in accuracy. Numerical results are included to
illustrate these approaches.Comment: To appear in proceeding of 22nd Mediterranean Conference on Control
and Automation, MED'1
