Joint optimization of electric vehicle routes and charging locations through learning charge constraints using QUBO solvers.

Optimal routing problems of electric vehicles (EVs) have attracted much attention in recent years, and installation of charging stations is an important issue for EVs. Hence, we focus on the joint optimization of the location of charging stations and the routing of EVs. When routing problems are formulated in the form of quadratic unconstrained binary optimization (QUBO), specialized solvers such as quantum annealers are expected to provide optimal solutions with high speed and accuracy. However, battery capacity constraints make it hard to formulate into QUBO form without a large number of auxiliary qubits. Here, we propose a sequential optimization method utilizing the Bayesian inference and QUBO solvers, in which the battery capacity constraints are automatically learned. This method enables us to optimize the number and location of charging stations and the routing of EVs with a small number of searches. Applying this method to a routing problem of 20 locations, we observed consistent convergence toward battery-feasible solutions across independent runs, demonstrating stable learning behavior of the proposed framework. Small-scale validation experiments using exhaustive enumeration show that the framework reliably discovers feasible configurations close to the global optimum, while runtime and QUBO-size analyses clarify its computational characteristics.