Design and application of quantum algorithms for railway optimisation problems ; Conception et application d’algorithmes quantiques pour la résolution de problèmes d’optimisation ferroviaire
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| Název: | Design and application of quantum algorithms for railway optimisation problems ; Conception et application d’algorithmes quantiques pour la résolution de problèmes d’optimisation ferroviaire |
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| Autoři: | Grange, Camille |
| Přispěvatelé: | Methods, Algorithms for Operations REsearch (LIRMM, Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier (LIRMM), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Université de Montpellier, Michael Poss |
| Zdroj: | https://hal.science/tel-04671228 ; Infrastructures de transport. Université de Montpellier, 2024. English. ⟨NNT : 2024UMONS009⟩. |
| Informace o vydavateli: | CCSD |
| Rok vydání: | 2024 |
| Sbírka: | Université de Montpellier: HAL |
| Témata: | Railway problems, Quantum algorithms, Combinatorial optimization, Problèmes ferroviaires, Algorithmes quantiques, Optimisation combinatoire, [SPI.GCIV.IT]Engineering Sciences [physics]/Civil Engineering/Infrastructures de transport |
| Popis: | This thesis is dedicated to the conception and application of quantum algorithms for railway combinatorial optimization problems. Today, the optimization problems that SNCF faces are complex, often prohibiting finding the optimal solution for industrial instances with classical methods within a reasonable amount of time. Quantum computing is expected to improve the quality of solutions and reduce the computation time for some of these problems. Quantum algorithms for optimization are divided into two classes: exact algorithms and heuristics. The former demonstrate theoretical advantages for several problems but cannot be implemented on current quantum machines because they require too high-quality quantum resources. On the contrary, the latter can be implemented, at least for small instances, but there are no performance guarantees or proven quantum advantages yet. In this thesis, we analyze and propose algorithms that belong to each of these two classes.On the one hand, we study the Variational Quantum Algorithms, which belong to the class of heuristics. These are hybrid quantum-classical algorithms that alternate between a parametrized quantum circuit and a classical optimizer. They allow solving unconstrained problems with binary variables, and we propose a general method to reformulate constrained integer problems into such problems. We highlight some properties of Variational Quantum Algorithms necessary for potential theoretical guarantees. In particular, we study QAOA (Quantum Approximate Optimization Algorithm) in light of the previous properties, and we provide a universal decomposition of the quantum circuit for problems whose objective function is polynomial. We solve with this algorithm a railway timetabling problem of SNCF. It consists of finding the transportation plan maximizing the operating profit according to the customers' demand taking into account the availability and cost of both the network and the rolling stock. To solve it with QAOA, we propose two simplifications with different ... |
| Druh dokumentu: | doctoral or postdoctoral thesis |
| Jazyk: | English |
| Relation: | NNT: 2024UMONS009 |
| Dostupnost: | https://hal.science/tel-04671228 https://hal.science/tel-04671228v2/document https://hal.science/tel-04671228v2/file/GRANGE_2024_archivage.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| Přístupové číslo: | edsbas.BB7FB529 |
| Databáze: | BASE |
Nájsť tento článok vo Web of Science | Abstrakt: | This thesis is dedicated to the conception and application of quantum algorithms for railway combinatorial optimization problems. Today, the optimization problems that SNCF faces are complex, often prohibiting finding the optimal solution for industrial instances with classical methods within a reasonable amount of time. Quantum computing is expected to improve the quality of solutions and reduce the computation time for some of these problems. Quantum algorithms for optimization are divided into two classes: exact algorithms and heuristics. The former demonstrate theoretical advantages for several problems but cannot be implemented on current quantum machines because they require too high-quality quantum resources. On the contrary, the latter can be implemented, at least for small instances, but there are no performance guarantees or proven quantum advantages yet. In this thesis, we analyze and propose algorithms that belong to each of these two classes.On the one hand, we study the Variational Quantum Algorithms, which belong to the class of heuristics. These are hybrid quantum-classical algorithms that alternate between a parametrized quantum circuit and a classical optimizer. They allow solving unconstrained problems with binary variables, and we propose a general method to reformulate constrained integer problems into such problems. We highlight some properties of Variational Quantum Algorithms necessary for potential theoretical guarantees. In particular, we study QAOA (Quantum Approximate Optimization Algorithm) in light of the previous properties, and we provide a universal decomposition of the quantum circuit for problems whose objective function is polynomial. We solve with this algorithm a railway timetabling problem of SNCF. It consists of finding the transportation plan maximizing the operating profit according to the customers' demand taking into account the availability and cost of both the network and the rolling stock. To solve it with QAOA, we propose two simplifications with different ... |
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