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Scientific Reports

Quantum Computing for Transport Network Design Problems

Vinayak V. Dixit, Chence Niu

Published Jan 1, 2022• 39 citations
Publisher

Abstract

Transport network design problem (TNDP) is a well-studied problem for planning and operations of transportation systems. They are widely used to determine links for capacity enhancement, link closures to schedule maintenance, identify new road or transit links and more generally network enhancements under resource constraints. As changes in network capacities result in a redistribution of demand on the network, resulting in changes in the congestion patterns, TNDP is generally modelled as a bi-level problem, which is known to be NP-hard. Meta-heuristic methods, such as Tabu Search Method are relied upon to solve these problems, which have been demonstrated to achieve near optimality in reasonable time. The advent of quantum computing has afforded an opportunity to solve these problems faster. We formulate the TNDP problem as a bi-level problem, with the upper level formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem that is solved using quantum annealing on a D-Wave quantum computer. We compare the results with Tabu Search. We find that quantum annealing provides significant computational benefit. The proposed solution has implications for networks across different contexts including communications, traffic, industrial operations, electricity, water, broader supply chains and epidemiology.

DOI
10.1038/s41598-023-38787-2

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Transport network design problem (TNDP) is a well-studied problem for planning and operations of transportation systems. They are widely used to determine links for capacity enhancement, link closures to schedule maintenance, identify new road or transit links and more generally network enhancements under resource constraints. As changes in network capacities result in a redistribution of demand on the network, resulting in changes in the congestion patterns, TNDP is generally modelled as a bi-level problem, which is known to be NP-hard. Meta-heuristic methods, such as Tabu Search Method are relied upon to solve these problems, which have been demonstrated to achieve near optimality in reasonable time. The advent of quantum computing has afforded an opportunity to solve these problems faster. We formulate the TNDP problem as a bi-level problem, with the upper level formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem that is solved using quantum annealing on a D-Wave quantum computer. We compare the results with Tabu Search. We find that quantum annealing provides significant computational benefit. The proposed solution has implications for networks across different contexts including communications, traffic, industrial operations, electricity, water, broader supply chains and epidemiology.
Efficient transportation networks are vital for modern urban environments, where minimizing travel time and reducing congestion are key objectives. The goal of this thesis is to review the applications and benefits of quantum computing in transportation network optimization and to determine whether quantum computing can produce more efficient or accurate solutions than classical computational methods. This thesis is a literature study based on 18 sources, most of which were published between 2017 and 2025 due to the topicality of the subject. Transportation network optimization can be approached from many perspectives, such as adding new roads to existing networks, increasing road capacities, optimizing traffic signals, or improving the computational efficiency of modeling network flows. Transportation networks are modeled using a mathematical framework that divides the optimization problem into an upper level and a lower level. Upper-level optimization focuses on network design, while the lower level focuses on testing the designed upper level. The study examined four applications of quantum computing, focusing on the optimization of lane capacities, traffic signals, and computational efficiency in network flows. The study concluded that quantum computing can achieve significant improvements in network optimization problems. The road capacity optimization method compared a combined classical-quantum hybrid quantum annealing algorithm to a purely classical "Tabu Search" algorithm. The hybrid method achieved a runtime up to 11 times faster than the classical algorithm. The traffic signal optimization method also compared a hybrid quantum computing method to classical methods, producing significantly better results. Network flows were optimized using the qbsolv hybrid quantum annealing algorithm to calculate vehicle flows and redistribute routes, with the goal of reducing congestion and shortening average travel times. The obtained result successfully reduced congestion in targeted areas and generally provided a better way to model network flows compared to the user equilibrium model. Finally, the purely quantum MNDAS algorithm constituted an improved version of the metaheuristic ACO method, producing a quadratic speedup compared to the ACO algorithm. Quantum computing methods were thus computationally faster and produced, on average, shorter travel times by reducing traffic congestion. However, several sources indicated that the full potential of quantum computing is not yet attainable, as scaling quantum computers remains challenging due to qubit instability. If these scalability challenges can be resolved, the benefits offered by the technology will be extensive and significant.
Quantum annealing technologies aim to solve computational optimization and sampling problems. QPU (Quantum Processing Unit) machines such as the D-Wave system use the QUBO (Quadratic Unconstrained Binary Optimization) formula to define model optimization problems for quantum annealing. This machine uses quantum effects to speed up computing time better than classical computers. We propose a vehicle routing problem that can be formulated in the QUBO model as a combinatorial problem, which gives the possible route solutions increases exponentially. The solution aims to optimize the vehicle's journey to reach a destination. The study presents a QUBO formulation to solve traffic congestion problems on certain roads. The resulting route selection by optimizing the distribution of the flow of alternative road vehicles based on the weighting of road segments. Constraints formulated as a condition for the level of road density. The road weight parameter influences the cost function for each road choice. The simulations on the D-Wave quantum annealer show optimal results on the route deployment of several vehicles. So that each vehicle will be able to go through different road options and reduce road congestion accurately. This solution provides an opportunity to develop QUBO modeling for more complex vehicle routing problems for road congestion.
In planning and scheduling, large-scale optimization problems often have complex limits and a lot of factors, which makes them hard to answer with standard methods. Quantum annealing has become a hopeful way to deal with these problems because it can quickly look into a lot of possible solutions. This essay looks into how quantum annealing might be used to solve optimization problems in transportation and scheduling, with a focus on how it could be used for route planning, inventory management, and arranging workers. To do these optimization jobs, quantum annealing is used. This is a quantum computing method that gets the global minimum of a cost function. We use the D-Wave quantum annealer in this method. It turns the problem's limits and objective function into a quadratic unconstrained binary optimization (QUBO) model. The quantum annealer then works on this model to find the best answers. The suggested method combines traditional preparation methods with quantum annealing to get the best results for big schedule and transportation issues. We use quantum annealing to solve difficult multi-objective optimization problems, like reducing shipping time, cost, and resource use all at the same time. Preliminary results show that quantum annealing can make solutions much better and use computers much more efficiently than traditional methods for optimizing supplies and schedules. Quantum annealing works especially well with problems that have a lot of dimensions. It can provide scalable answers that sometimes work better than standard methods.
Vehicle Routing Problem is a well-known optimization issue, which has many extensions resulting from practical appliances. The problem is NP-hard, therefore it may be impossible to find an optimal solution for big instances, with traditional computation methods. Recent development of quantum technology, may be a response for this challenge, which however requires a different formulation of the model. The problem is then modeled using Quadratic Unconstrained Binary Optimization (QUBO) equations. Such model can be run using quantum annealers (QA), designed specifically for optimization purposes. This paper is a systematic survey of Vehicle Routing Problem models that are formulated using QUBO, to be solved on quantum computers. The main goal of the paper is to check research gaps in this subject, compare and explain different approaches of modeling various problem extensions with QUBO. The results obtained in reviewed papers will be presented and analyzed. Moreover, the theoretical basis for quantum computation will be presented, with focus on D-Wave company solutions.
In this research paper, we employ D-Wave’s quantum annealer to address the NP-hard problem of optimizing new metro station locations while considering both points of interest and existing stations. By formulating the problem as Quadratic Unconstrained Binary Optimization (QUBO) and Binary Quadratic Model (BQM), our approach harnesses the power of quantum computing to yield superior solutions compared to classical methods. This research has the potential to revolutionize urban transportation planning by efficiently balancing accessibility to points of interest and minimizing congestion around existing stations, offering a compelling solution to a complex urban development challenge. Notably, we emphasize the NP-hard nature of this problem, underlining its computational complexity and the significance of our quantum computing approach.
The Traffic Assignment Problem (TAP) is a complex transportation optimisation problem typically solved using meta-heuristics on classical computers. Quantum computers, despite being a nascent technology, have the potential to significantly speed up computation by exploiting quantum parallelism. A quantum annealer (QA) is a quantum computer tailored to solve combinatorial optimisation problems formulated as a Quadratic Unconstrained Binary Optimisation (QUBO). Formulating complex optimisation problems as QUBO is an open challenge. This paper derives a new QUBO formulation for TAP by employing a streamlined methodology of general applicability. It also attempts a direct comparison at solving TAP encompassing a QA (D-WAVE), a hybrid quantum-classical algorithm, and classical methods including Simulated Annealing and Genetic Algorithms. This comparison is difficult and seldom done due to the inherent differences between quantum and classic hardware. As expected from the current quantum technology, our results show that a pure QA suffers from significant noise in qubits and requires significant additional computational time, although we show that the time required solely by the QPU does not increase with problem size. We also show that the hybrid QA mitigates these noise issues and is on a par with traditional methods.