Micro-mobility dispatch optimization via quantum annealing incorporating historical data

TL;DR

The dispatch problem for micro-mobility services is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling efficient solving through QA, and the proposed formulation incorporates historical usage data to enhance operational efficiency.

Abstract

This paper proposes a novel dispatch formulation for micro-mobility vehicles using a Quantum Annealer (QA). In recent years, QA has gained increasing attention as a high-performance solver for combinatorial optimization problems. Meanwhile, micro-mobility services have been rapidly developed as a promising means of realizing efficient and sustainable urban transportation. In this study, the dispatch problem for such micro-mobility services is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling efficient solving through QA. Furthermore, the proposed formulation incorporates historical usage data to enhance operational efficiency. Specifically, customer arrival frequencies and destination distributions are modeled into the QUBO formulation through a Bayesian approach, which guides the allocation of vacant vehicles to designated stations for waiting and charging. Simulation experiments are conducted to evaluate the effectiveness of the proposed method, with comparisons to conventional formulations such as the vehicle routing problem. Additionally, the performance of QA is compared with that of classical solvers to reveal its potential advantages for the proposed dispatch formulation. The effect of reverse annealing on improving solution quality is also investigated.

Figures (7)

• Figure 1: Overview of the proposed micro-mobility dispatch system. Customer demand triggers the dispatch process, in which the system predicts travel times for vehicle–customer and vehicle–station pairs. The QUBO matrix is then constructed using the predicted travel times together with historical distribution data, and the resulting QUBO is solved by a quantum annealer.
• Figure 2: Simulation environment for validating the proposed vehicle dispatch problem. The map consists of a $4 \times 4$ grid with six vehicles. The vehicle speed is $4~\mathrm{m/s}$. The average customer appearance interval is 50 seconds. High-frequency areas for both appearances and destinations have a 10-fold higher probability than other areas.
• Figure 3: Average waiting time of the customers according to the weight $B_1$ compared to $B_0$. We measured 10 trials, and each trial lasted for 10,000 seconds.
• Figure 4: Comparison of vehicle position statistics under different dispatch strategies. Each panel shows a heatmap of vacant vehicle positions along with the fitted Gaussian distribution. The customer request rate is high $40~\mathrm{s/request}$.
• Figure 5: Parameter tuning of the minimum anneal fraction $s_{\mathrm{min}}$. We generated 30 random instances using the simulator and solved them using the proposed static formulation. (a) Annealing schedules. We adopted the default D-Wave FA schedule as a baseline. The RA schedule follows Ref. haba2022travel, where the pause point $s_{\mathrm{min}}$ is a tunable parameter. The total annealing time for RA is set to match the FA duration. (b) Distribution of solution quality relative to initial states as a function of $s_{\mathrm{min}}$.