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arXiv:2112.15408

Analysis of Vehicle Routing Problem in Presence of Noisy Channels

Nishikanta Mohanty, Bikash K. Behera

Published Dec 28, 2021• 0 citations
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Abstract

Vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver a fixed number of customers with optimal efficiency. Classical tools and methods provide good approximations to reach the optimal global solution. Quantum computing and quantum machine learning provide a new approach to solving combinatorial optimization of problems faster due to inherent speedups of quantum effects. Many solutions of VRP are offered across different quantum computing platforms using hybrid algorithms such as quantum approximate optimization algorithm and quadratic unconstrained binary optimization. Quantum computers such as IBM-Q experience along with Qiskit framework offer tools to solve combinatorial optimization problems. This work proposed here builds a basic VRP solution for 3 and 4 cities using variational quantum eigensolver on a variable ANSATZ. The work is further extended to evaluate the robustness of the solution in noisy channels available within the ambit of Qiskit framework.

DOI
10.48550/arxiv.2112.15408

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Vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver a fixed number of customers with optimal efficiency. Classical tools and methods provide good approximations to reach the optimal global solution. Quantum computing and quantum machine learning provide a new approach to solving combinatorial optimization of problems faster due to inherent speedups of quantum effects. Many solutions of VRP are offered across different quantum computing platforms using hybrid algorithms such as quantum approximate optimization algorithm and quadratic unconstrained binary optimization. Quantum computers such as IBM-Q experience along with Qiskit framework offer tools to solve combinatorial optimization problems. This work proposed here builds a basic VRP solution for 3 and 4 cities using variational quantum eigensolver on a variable ANSATZ. The work is further extended to evaluate the robustness of the solution in noisy channels available within the ambit of Qiskit framework.
The vehicle routing problem (VRP) is an NP-hard optimization problem that has been an interest of research for decades in science and industry. The objective is to plan routes of vehicles to deliver goods to a fixed number of customers with optimal efficiency. Classical tools and methods provide good approximations to reach the optimal global solution. Quantum computing and quantum machine learning provide a new approach to solving combinatorial optimization of problems faster due to inherent speedups of quantum effects. Many solutions of VRP are offered across different quantum computing platforms using hybrid algorithms such as quantum approximate optimization algorithm and quadratic unconstrained binary optimization. In this work, we build a basic VRP solver for 3 and 4 cities using the variational quantum eigensolver on a fixed ansatz. The work is further extended to evaluate the robustness of the solution in several examples of noisy quantum channels. We find that the performance of the quantum algorithm depends heavily on what noise model is used. In general, noise is detrimental, but not equally so among different noise sources.
Abstract The vehicle routing problem (VRP) is an example of a combinatorial optimization problem that has attracted academic attention due to its potential use in various contexts. VRP aims to arrange vehicle deliveries to several sites in the most efficient and economical manner possible. Quantum machine learning offers a new way to obtain solutions by harnessing the natural speedups of quantum effects, although many solutions and methodologies are modified using classical tools to provide excellent approximations of the VRP. In this paper, we employ 6 and 12 qubit circuits, respectively, to build and evaluate a hybrid quantum machine learning approach for solving VRP of 3- and 4-city scenarios. The approach employs quantum support vector machines (QSVMs) trained using a variational quantum eigensolver on a static or dynamic ansatz. Different encoding strategies are used in the experiment to transform the VRP formulation into a QSVM and solve it. Multiple optimizers from the IBM Qiskit framework are also evaluated and compared
Vehicle Routing Problem (VRP) is considered one of the most challenging problems with application in several domains, including transportation and logistics distribution. VRP is known to be NP-Hard problem. Several algorithms have been proposed to solve VRP in polynomial time. However, these algorithms are inefficient if the VRP instance increases. Recently, researchers investigated how quantum computing can be used to solve VRP. In particular, two promising variational quantum algorithms have been studied, i.e., Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA). In this paper, we implement both algorithms on IBM Qiskit and compare their evaluation in solving several instances of VRP. We observe that current Noisy-Intermediate Scale Quantum (NISQ) devices cannot solve VRP instances beyond 5 nodes and 2 vehicles. Furthermore, we observe that classical optimizers still provide better results. However, we believe that with the rapid advancement of quantum computing manufacturing, VQE and QAOA can provide better performance as compared to classical computing,
Intelligent transportation systems (ITS) are a critical component of Industry 4.0 and 5.0, particularly having applications in logistic management. One of their crucial utilization is in supply-chain management and scheduling for optimally routing transportation of goods by vehicles at a given set of locations. This paper discusses the broader problem of vehicle traffic management, more popularly known as the Vehicle Routing Problem (VRP), and investigates the possible use of near-term quantum devices for solving it. For this purpose, we give the Ising formulation for VRP and some of its constrained variants. Then, we present a detailed procedure to solve VRP by minimizing its corresponding Ising Hamiltonian using a hybrid quantum-classical heuristic called Quantum Approximate Optimization Algorithm (QAOA), implemented on the IBM Qiskit platform. We compare the performance of QAOA with classical solvers such as CPLEX on problem instances of up to 15 qubits. We find that performance of QAOA has a multifaceted dependence on the classical optimization routine used, the depth of the ansatz parameterized byppp, initialization of variational parameters, and problem instance itself.
Vehicle Routing Problem (VRP) is one of the most complex NP-hard combinatorial optimization problem in transportation and logistics that requires a dynamic solution approach. In this paper we present a new hybrid approach that combines the Quantum Approximate Optimization Algorithm (QAOA) into the QRL policy network, instead of the usual variational layers, QAOA mixing and cost Hamiltonian layers. This enhancement enables the agent to exploit problem specific particular quantum correlations when learning policies, and so richer exploration of the routing solution space. The QAOA-augmented QRL framework shows quicker convergence in training and can tackle larger VRP instances that are beyond the reach of Grover's Adaptive Search (GAS) and Quantum Reinforcement Learning (QRL) approaches. Experiments on standard VRP instances demonstrate better solutions, fewer episodes to converge and good memory usage on near term quantum hardware simulators. These findings demonstrate QAOA- integrated QRL as a viable approach to scalable, high quality quantum-assisted combinatorial optimization.
Introduction Finding the most efficient routes for a fleet of delivery vehicles remains a critical and costly challenge for nearly any logistics business. This core idea is known as the Vehicle Routing Problem (VRP). The primary goal is to minimize operational costs, such as the total travel distance or the number of trucks deployed, while ensuring all the customers are served. Because VRP is NP-hard, finding a perfect solution is often impossible, forcing industries to rely on classical approximate algorithms. However, quantum variational algorithms offer a new paradigm by iteratively optimizing parameters to navigate the solution space, presenting a new and promising avenue for finding better and faster solutions. Methods In this paper, we introduce Symmetric Arc Reduction in Quantum Approximate Optimization Algorithm (SAR-QAOA), which systematically eliminates redundant symmetric routing variables in the binary integer programming formulation prior to the Quadratic Unconstrained Binary Optimization (QUBO) formulation. The proposed SAR-QAOA encodes edge-based VRP while reducing the qubit requirement from n ( n −1) to n ( n −1)/2, thereby improving the resource efficiency of the QUBO formulation by prioritizing regions of the solution space that are more likely to contain high-quality solutions; SAR enhances both search accuracy and computational efficiency. Results Experimental results on noiseless quantum simulators validate the feasibility of the proposed formulation and its integration with the QAOA framework, providing a promising foundation for future investigations on larger routing problems and evolving quantum hardware.