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arXiv:2306.04414 · IEEE International Conference on Intelligent Transportation Systems (ITSC)

Formulation of the Electric Vehicle Charging and Routing Problem for a Hybrid Quantum-Classical Search Space Reduction Heuristic

Mikel Garcia de Andoin, Alberto Bottarelli, Sebastian Schmitt, Izaskun Oregi, Philipp Hauke, Mikel Sanz

Published Sep 24, 2023• 3 citations
arXivHTMLPDF

Abstract

Combinatorial optimization problems have attracted much interest in the quantum computing community in the recent years as a potential testbed to showcase quantum advantage. In this paper, we show how to exploit multilevel carriers of quantum information—qudits—for the construction of algorithms for constrained quantum optimization. These systems have been recently introduced in the context of quantum optimization and they allow us to treat more general problems than the ones usually mapped into qubit systems. In particular, we propose a hybrid classical quantum heuristic strategy that allows us to sample constrained solutions while greatly reducing the search space of the problem, thus optimizing the use of fewer quantum resources. As an example, we focus on the Electric Vehicle Charging and Routing Problem (EVCRP). We translate the classical problem and map it into a quantum system, obtaining promising results on a toy example which shows the validity of our technique.

DOI
10.1109/itsc57777.2023.10421787

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Combinatorial optimization problems have attracted much interest in the quantum computing community in the recent years as a potential testbed to showcase quantum advantage. In this paper, we show how to exploit multilevel carriers of quantum information—qudits—for the construction of algorithms for constrained quantum optimization. These systems have been recently introduced in the context of quantum optimization and they allow us to treat more general problems than the ones usually mapped into qubit systems. In particular, we propose a hybrid classical quantum heuristic strategy that allows us to sample constrained solutions while greatly reducing the search space of the problem, thus optimizing the use of fewer quantum resources. As an example, we focus on the Electric Vehicle Charging and Routing Problem (EVCRP). We translate the classical problem and map it into a quantum system, obtaining promising results on a toy example which shows the validity of our technique.
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Quantum optimization has recently drawn considerable attention as one of the possible applications of noisy intermediate-scale quantum computation, yet the problem of qubit requirement remains a major bottleneck when combinatorial optimization problems are converted into quantum circuits. This issue becomes especially critical in solving the capacitated vehicle routing problem (CVRP) with the quantum approximate optimization algorithm (QAOA), since the number of required qubits increases polynomially with respect to the number of nodes. This study investigates whether a heuristic divide-and-conquer strategy can be adapted to the quantum setting so as to improve qubit efficiency while preserving the optimization capability to a reasonable extent. The proposed method decomposes a single CVRP into multiple traveling salesman problems (TSPs) by the sweeping-based clustering method, searches for the sector configuration with the smallest angle sum by Grover’s search algorithm, and then solves each sector-wise TSP with the QAOA aided by the gravitational search algorithm. Experiments on five benchmark datasets show that the proposed approach attains feasible solutions within 3.4 to 12.7% of the reinforcement-learning baseline on the main test set. These results suggest that the proposed approach serves as a plausible quantum heuristic framework for constrained routing optimization, with the advantage of reducing the qubit burden by decomposing the original problem into smaller subproblems.
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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.
The Vehicle Routing Problem (VRP) is a crucial combinatorial optimization problem in transportation, logistics, and supply chain management. Quantum computing has gained interest in solving complex optimization issues. This review paper proposes a novel approach that combines quantum computing principles with the Feynman path integral formulation to address the VRP. The paper focuses on limited qubits and how quantum algorithms can circumvent this limitation. Conventional methods, such as Lagrangian and combinatorial optimization, require computational time to solve complex atomic-scale problems. The path integral formulation with the first Born approximation method offers a more elegant explanation of quantum computing. The algorithm investigates quantum system dynamics using the Schrodinger wave equation and computes probability amplitude distributions for optimal vehicle routing techniques. This work will take advantage of entanglement and interference effects for heuristic sampling of high-quality solutions, making the Quantum Path Integral Approach (QPIA) a promising study environment for investigating quantum circuits and algorithms in routing problems with constrained qubits.