Battery Dimensioning for Hybrid Vehicles in a Routing Application. Generalised Duality and Logic-Based Benders Decomposition

Abstract

The Vehicle Routing Problem (VRP), which is defined as to find optimal routes for a fleet of delivery vehicles to various customers, constitute an important class of combinatorial optimisation problems of both practical and theoretical interest. Among the various flavours of VRP, this report specifically focuses on a case with hybrid vehicles with two fuel types, with the goal of finding the optimal battery sizes which minimises the total cost. We present an exact solution method using a generalised Benders decomposition method, known as logic-based Benders decomposition. In this method, the subproblems are generalised to mixed integer linear optimisation problems. The master problem is a simple routing problem, while the subproblems concern resource constraints and battery types. The mixed integer master problem is solved by branch-and-bound, and lower bounds are generated from the solution tree. Only small instances of up to 14 customers are solved to optimality, and the performance of our algorithm is compared with more direct solution methods. As it is, the method is slower than solving the full problem directly, and further work is needed to make it competitive. Keywords: Vehicle routing problem (VRP), hybrid vehicles, battery capacity, logic-based Benders decomposition (LBBD), branch-and-bound iii