Leveraging Conflicting Constraints in Solving Vehicle Routing Problems

The Conflict-Free Electric Vehicle Routing Problem (CF-EVRP) is 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 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 simultaneously accommodate. In previous work, the compositional algorithm ComSat was introduced and that solves the CF-EVRP by breaking it down into sub-problems and iteratively solve them to build an overall solution. Though ComSat showed good performance in general, some problems took significant time to solve due to the high number of iterations required to find solutions that satisfy the road segments' capacity constraints. The bottleneck is the Path Changing Problem, i.e., the sub-problem of finding a new set of shortest paths to connect a subset of the customers, disregarding previously found shortest paths. This paper presents an improved version of the PathsChanger function to solve the Path Changing Problem that exploits the unsatisfiable core, i.e., information on which constraints conflict, to guide the search for feasible solutions. Experiments show faster convergence to feasible solutions compared to the previous version of PathsChanger.