A Compositional Algorithm for the Conflict-Free Electric Vehicle Routing Problem

The Conflict-Free Electric Vehicle Routing Problem (CF-EVRP) is an extension of the Vehicle Routing Problem (VRP), a combinatorial optimization problem of designing routes for vehicles to visit customers such that a cost function, typically the number of vehicles or the total travelled distance, is minimized. The problem finds many logistics applications, particularly for highly automated logistic systems for material handling. The CF-EVRP involves constraints such as time windows on the delivery to the customers, limited operating range of the vehicles, and limited capacity on the number of vehicles that a road segment can accommodate at the same time. In this paper, the compositional algorithm ComSat for solving the CF-EVRP is presented. The algorithm iterates through the sub-problems until a globally feasible solution is found. The proposed algorithm is implemented using an optimizing SMT-solver and is evaluated against an implementation of a previously presented monolithic model. The soundness and completeness of the algorithm are proven, and it is benchmarked on a set of generated problems and found to be able to solve problems of industrial size. Note to Practitioners —The need to define and solve the CF-EVRP relates to an industrial application where a fleet of autonomous robots navigates in a heterogeneous environment, shared with humans and other vehicles and obstacles. To allow for a low-level trajectory controller to handle dynamic obstacles, like humans and fork-lifts, the CF-EVRP includes capacity constraints on the road segments. This increases the problem complexity, and thus requires to trade off optimality for feasability; this so to get solutions in reasonable time with respect to how long ahead the jobs to schedule are known. The overall problem is to find feasible solutions that satisfy all constraints while avoiding travelling unnecessarily long routes, and at the same time meet the stipulated time-windows to deliver material just-in-time. The compositional algorithm (ComSat) presented in this work is based on the idea to break down the overall scheduling problem into sub-problems that are easier to solve, and then to build a schedule based on the solutions of the sub-problems. ComSat is designed to work well for industrial scenarios where there are good reasons to believe that feasible solutions do exist. This seems a reasonable assumption as in an industrial setting a sufficient number of mobile robots can typically be assumed to be available.