In recent years, researchers have oriented their studies towards new technologies based on quantum physics that should resolve complex problems currently considered to be intractable. This new research area is called Quantum Computing. What makes Quantum Computing so attractive is the particular way with which quantum technology operates and the great potential it can offer to solve real-world problems. This work focuses on solving assignment-like combinatorial optimization problems by exploiting this novel computational approach. A case-study, denoted as the Seating Arrangement Optimization problem, is considered. It is modeled through the Quadratic Unconstrained Binary Optimization paradigm and solved through two tools made available by the D-Wave Systems company, QBSolv, and a quantum-classical hybrid system. The obtained experimental results are compared in terms of solution quality and computational efficiency.
In recent years, researchers have oriented their studies towards new technologies based on quantum physics that should resolve complex problems currently considered to be intractable. This new research area is called Quantum Computing. What makes Quantum Computing so attractive is the particular way with which quantum technology operates and the great potential it can offer to solve real-world problems. This work focuses on solving assignment-like combinatorial optimization problems by exploiting this novel computational approach. A case-study, denoted as the Seating Arrangement Optimization problem, is considered. It is modeled through the Quadratic Unconstrained Binary Optimization paradigm and solved through two tools made available by the D-Wave Systems company, QBSolv, and a quantum-classical hybrid system. The obtained experimental results are compared in terms of solution quality and computational efficiency.
2020 year has been a turning point for the entire humanity. The COVID-19 pandemic has not only revolutionized our way of thinking, but it has changed the way we live, leading to having limitations on any aspect of our daily life, from the smallest things to the biggest. This extraordinary situation has afflicted the railway world, too, since the movements have been limited drastically and new rules have been introduced. This thesis focuses on analyzing passenger transport's current situation on high-speed trains in this particular historical period we are experiencing, the COVID-19 Era. It aims to create hypothetical scenarios of passengers' distribution inside a train wagon with current health and hygiene rules. The main goal of what has been defined as the Seating Arrangement Optimization problem is to fill the train wagon as much as possible and therefore transport the largest number of people by maximizing the number of passengers belonging to the same family sitting in nearest seats. In this work, two different optimization models for formalizing the identified problem are presented and compared: a Mixed-Integer Linear Programming (MILP) model, one of the most common formulations in literature in the optimization field, and a Quadratic Unconstrained Binary Optimization (QUBO) model, a novel type of problem that can be solved on a quantum computer. In particular, for the resolution of the first type of model, the Gurobi commercial solver is used while, for the latter one, the QBSolv and a classical-quantum hybrid solver provided by D-Wave Systems Inc., a leader company in the quantum computing field, are considered. Quantum computing is an innovative research field currently still under development, on which time and money have begun to be invested only in recent years. What makes this research field attractive is the particular way with which quantum technology operates and the great potential it can offer to solve real-world problems. Due to the current physical capabilities, quantum computers' computational resources are not sufficient to execute too large optimization problems. Still, even with small instances like the ones considered in this work, it can be seen how much they can find highly optimized solutions in a short time.
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.
Combinatorial optimization problems play a vital role in computer science and engineering, with applications in logistics, network design, finance, and resource allocation. However, many of these problems are NP-hard, making them computationally expensive to solve using classical optimization techniques, especially for large-scale instances. In recent years, quantum computing has emerged as a promising paradigm capable of addressing these limitations by leveraging quantum mechanical principles such as superposition and entanglement. This study investigates the application of quantum computing for solving combinatorial optimization problems, with a focus on algorithm design, complexity analysis, and real-world applicability. The research primarily employs the Quantum Approximate Optimization Algorithm (QAOA) and Grover's search algorithm to solve representative problems such as Max-Cut and the Knapsack problem. The performance of these algorithms is evaluated using key metrics including accuracy, execution time, and approximation ratio, and is compared with classical optimization techniques. The results demonstrate that QAOA is capable of generating near-optimal solutions, achieving accuracy levels of up to 93% for small problem instances. However, the study also highlights the challenges associated with current quantum systems, including noise, limited qubit availability, and increased execution time. Comparative analysis reveals that while classical methods remain more efficient for small-scale problems, quantum algorithms show significant potential for scalability and handling complex optimization tasks. The findings suggest that hybrid quantum-classical approaches offer a practical solution in the current Noisy Intermediate-Scale Quantum (NISQ) era. The study concludes that although quantum computing is still evolving, it holds strong potential for transforming combinatorial optimization in the future.
The Quadratic Assignment Problem is a a classical constrained optimization problem used to model many real-life applications. We present experiments in solving the Quadratic Assignment Problem by means of Quantum Annealing and Quantum-inspired Annealing. We describe how to model this classical combinatorial problem in terms of QUBO (Quadratic Unconstrained Binary optimization) for implementing it on hardware solvers based on quantum or quantum-inspired annealing (D-Wave, Fujitsu Digital Annealing Unit and Fixstars Amplify Annealing Engine). We present performance result for these implementations and compare them with well established metaheuristic solvers on classical hardware, such as Robust Tabu Search and External Optimization.
Quantum computing has emerged as a promising computational paradigm with the potential to solve problems that are intractable for classical computers. This paper provides an overview of the current state of quantum computing, including its historical development, hardware advancements, applications, and challenges. Special attention is given to combinatorial optimization, which is considered one of the most promising application domains. The limitations of current quantum systems and future research directions are also discussed. This paper presents a comparative study between a conventional D-Wave-based simulated annealing approach and a proposed hybrid optimization model for solving largescale combinatorial optimization problems. The study focuses on benchmark problems, including AES, TSP gr24, and a real-world load balancing problem, all formulated as QUBO models. The D-Wave approach employs the dwave-neal simulated annealing engine with various parameter settings, while the proposed model introduces a decomposition-based framework combined with adaptive parameter control and iterative refinement. The experimental results demonstrate that the proposed model consistently outperforms the conventional approach in terms of solution quality, achieving significantly lower energy values across all problem instances. In particular, for the TSP gr24 problem, the proposed model achieves near-optimal solutions with substantially reduced computation time. For large-scale problems such as AES and load balancing, the proposed model maintains scalability and robustness, whereas the conventional approach suffers from increased computational cost and performance degradation. Although the proposed method introduces additional computational steps, its hybrid structure effectively mitigates limitations related to local minima, parameter sensitivity, and scalability. These findings indicate that integrating classical optimization techniques with quantum-inspired methods is essential for practical applications. The proposed model provides a promising framework for solving complex real-world optimization problems and highlights the importance of hybrid approaches in advancing quantum annealing technologies.
Abstract An assignment problem is a mapping between the tasks and agents aiming for the optimal cost. In graph theory, it is represented by a bipartite graph of tasks and agents connected optimally through edges. It is a combinatorial optimization, a type of NP category that makes it hard to solve in a limited time for large inputs. Quantum approximate optimization algorithm (QAOA), a hybrid‐quantum optimization, is a possible way to solve such combinatorial problems in quantum computing. Quantum computation exploits the theory of quantum physics for accelerated computation. In this study, the assignment problem is framed to quadratic unconstrained binary optimization and the Ising model for the execution in QAOA. The details of classical to quantum conversion, modeling, circuit implementation, and various analyses are explained with an example.