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.
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.
Quantum computers are early-stage technology, but are progressing rapidly. Here, we compare metaheuristics with a quantum annealer (QA), a quantum computer tailored to solve combinatorial optimisation problems formulated as a Quadratic Unconstrained Binary Optimisation (QUBO) problem. Formulating non-trivial optimisation problems as QUBOs is a challenge, so it is to ensure that the direct comparison of classical and quantum search algorithms is conducted fairly. This paper illustrates the use of a streamlined methodology to derive a QUBO for a classical optimisation problem – the Steiner tree problem – and provides comprehensive experiments comparing D-WAVE pure QA and hybrid QA with classical methods including Simulated Annealing and Genetic Algorithms. We find that the pure QA suffers from considerable qubit noise but the hybrid QA is on a par with traditional methods.
Traffic congestion continues to pose a significant challenge in urban environments, necessitating innovative approaches to traffic management. This paper explores the application of Quantum Annealing (QA) for real-world traffic optimization, expanding on the pioneering work of Volkswagen and D-Wave. In 2017, a collaborative team demonstrated the potential of QA to optimize traffic flow by solving a complex Quadratic Unconstrained Binary Optimization (QUBO) problem involving 418 cars, which required 1,254 qubits. Later, this research culminated in a pilot project at the Web Summit conference in Lisbon, one of Europe's largest technology events, showcasing quantum computing-based traffic optimization. Since the QPU alone could not directly handle the full problem size, the team employed a hybrid classical-quantum approach, leading to significant improvements in traffic distribution. This paper builds on that foundation by investigating potential speedups using a purely quantum approach, particularly by utilizing the QPU for smaller QUBO problems. The proposed method (MTF) enhances traffic management by decomposing the overall optimization problem into smaller, more manageable subproblems. This decomposition enables us to harness the advantages of the QPU while tackling more complex traffic scenarios that previous approaches struggled to manage. By breaking the problem into smaller parts, we mitigate the challenges associated with embedding large-scale problems into the QPU, which often presents computational difficulties. To evaluate our approach, we conducted experiments involving 100, 200, 300, 400, and 500 cars on a complex traffic map featuring multiple start and end points. We successfully embedded the problem into the D-Wave Advantage Quantum Processing Unit, utilizing the "Pegasus" topology, which resulted in a significant acceleration of the solution process. The experiment results show improved speed and effectiveness in real-world scenarios by leveraging the QPU for better traffic optimization.
In more recent years, there has been increasing research interest in exploiting the use of application specific hardware for solving optimisation problems. Examples of solvers that use specialised hardware are IBM's Quantum System One and D-wave's Quantum Annealer (QA) and Fujitsu's Digital Annealer (DA). These solvers have been developed to optimise problems faster than traditional meta-heuristics implemented on general purpose machines. Previous research has shown that these solvers (can optimise many problems much quicker than exact solvers such as GUROBI and CPLEX. Such conclusions have not been made when comparing hardware solvers with classical evolutionary algorithms. Making a fair comparison between traditional evolutionary algorithms, such as Genetic Algorithm (GA), and the DA (or other similar solvers) is challenging because the later benefits from the use of application specific hardware while evolutionary algorithms are often implemented on general-purpose machines. Moreover, quantum or quantum-inspired solvers are limited to solving problems in a specific format. A common formulation used is Quadratic Unconstrained Binary Optimisation (QUBO). Many optimisation problems are however constrained and have natural representations that are non-binary. Converting such problems to QUBO can lead to more problem difficulty and/or larger search space. The question addressed in this paper is whether quantum or quantum-inspired solvers can optimise QUBO transformations of combinatorial optimisation problems faster than classical evolutionary algorithms applied to the same problems in their natural representations. We show that the DA often present better average objective function values than GA on Travelling Salesman, Quadratic Assignment and Multi-dimensional Knapsack Problem instances.
Airline companies struggle every day trying to schedule crew, flights and aircraft.Tail Assignment is the problem of allocating individual aircraft to a set of flights, while ensuring multiple constraints and aiming to minimise an objective function, such as operational costs.Given the enormous amount of possibilities and constraints involved, this problem has been a study case for the last decade.Many solutions have emerged using classical computing, but with limitations regarding performance.Quantum Annealing (QA) is a heuristic technique for finding global minimum energy levels over an energy landscape using quantum mechanics.Due to its characteristics, it has been proved to have a clear advantage in solving some complex optimisation problems, being a promising technique to apply in multiple fields.In this study, Tail Assignment Problem was set as a Quadratic Unconstrained Binary Optimisation (QUBO) model, using two different techniques, and was solved using a classical and two hybrid solvers.Tests were run based on extractions from real-world data, analysing the performance of the implementation in terms of time, scalability and quality (i.e., the lowest operational costs) of the obtained solutions.We concluded that using a library for modelling the problem as well as considering individual flights rather than pre-aggregating them in strings can be a bottleneck when it comes to its scalability.Furthermore, we found out that there was a higher probability of obtaining better solutions for this problem using one of the hybrid solvers when compared with the classical heuristic algorithms such as Simulated Annealing (SA).These findings can serve as foundations for further studies.
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.
Quantum annealing algorithms belong to the class of meta-heuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum processing units (QPUs) produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. In this paper, we present a real-world application that uses quantum technologies. Specifically, we show how to map certain parts of a real-world traffic flow optimization problem to be suitable for quantum annealing. We show that time-critical optimization tasks, such as continuous redistribution of position data for cars in dense road networks, are suitable candidates for quantum computing. Due to the limited size and connectivity of current-generation D-Wave QPUs, we use a hybrid quantum and classical approach to solve the traffic flow problem.