A Brief Review on Mathematical Tools Applicable to Quantum Computing for Modelling and Optimization Problems in Engineering

Since its emergence, quantum computing has enabled a wide spectrum of new possibilities and advantages, including its efficiency in accelerating computational processes exponentially. This has directed much research towards completely novel ways of solving a wide variety of engineering problems, especially through describing quantum versions of many mathematical tools such as Fourier and Laplace transforms, differential equations, systems of linear equations, and optimization techniques, among others. Exploration and development in this direction will revolutionize the world of engineering. In this manuscript, we review the state of the art of these emerging techniques from the perspective of quantum computer development and performance optimization, with a focus on the most common mathematical tools that support engineering applications. This review focuses on the application of these mathematical tools to quantum computer development and performance improvement/optimization. It also identifies the challenges and limitations related to the exploitation of quantum computing and outlines the main opportunities for future contributions. This review aims at offering a valuable reference for researchers in fields of engineering that are likely to turn to quantum computing for solutions. Doi: 10.28991/ESJ-2023-07-01-020 Full Text: PD

Optimal control problems solved via swarm intelligence

Questa tesi descrive come risolvere problemi di controllo ottimo tramite swarm in telligence. Grande enfasi viene posta circa la formulazione del problema di controllo ottimo, in particolare riguardo a punti fondamentali come l’identificazione delle incognite, la trascrizione numerica e la scelta del risolutore per la programmazione non lineare. L’algoritmo Particle Swarm Optimization viene preso in considerazione e la maggior parte dei problemi proposti sono risolti utilizzando una formulazione differential flatness. Quando viene usato l’approccio di dinamica inversa, il problema di ottimo relativo ai parametri di trascrizione è risolto assumendo che le traiettorie da identificare siano approssimate con curve B-splines. La tecnica Inverse-dynamics Particle Swarm Optimization, che viene impiegata nella maggior parte delle applicazioni numeriche di questa tesi, è una combinazione del Particle Swarm e della formulazione differential flatness. La tesi investiga anche altre opportunità di risolvere problemi di controllo ottimo tramite swarm intelligence, per esempio usando un approccio di dinamica diretta e imponendo a priori le condizioni necessarie di ottimalitá alla legge di controllo. Per tutti i problemi proposti, i risultati sono analizzati e confrontati con altri lavori in letteratura. Questa tesi mostra quindi the algoritmi metaeuristici possono essere usati per risolvere problemi di controllo ottimo, ma soluzioni ottime o quasi-ottime possono essere ottenute al variare della formulazione del problema.This thesis deals with solving optimal control problems via swarm intelligence. Great emphasis is given to the formulation of the optimal control problem regarding fundamental issues such as unknowns identification, numerical transcription and choice of the nonlinear programming solver. The Particle Swarm Optimization is taken into account, and most of the proposed problems are solved using a differential flatness formulation. When the inverse-dynamics approach is used, the transcribed parameter optimization problem is solved assuming that the unknown trajectories are approximated with B-spline curves. The Inverse-dynamics Particle Swarm Optimization technique, which is employed in the majority of the numerical applications in this work, is a combination of Particle Swarm and differential flatness formulation. This thesis also investigates other opportunities to solve optimal control problems with swarm intelligence, for instance using a direct dynamics approach and imposing a-priori the necessary optimality conditions to the control policy. For all the proposed problems, results are analyzed and compared with other works in the literature. This thesis shows that metaheuristic algorithms can be used to solve optimal control problems, but near-optimal or optimal solutions can be attained depending on the problem formulation

Efficient meta-heuristics for spacecraft trajectory optimization

Meta-heuristics has a long tradition in computer science. During the past few years, different types of meta-heuristics, specially evolutionary algorithms got noticeable attention in dealing with real-world optimization problems. Recent advances in this field along with rapid development of high processing computers, make it possible to tackle various engineering optimization problems with relative ease, omitting the barrier of unknown global optimal solutions due to the complexity of the problems. Following this rapid advancements, scientific communities shifted their attention towards the development of novel algorithms and techniques to satisfy their need in optimization. Among different research areas, astrodynamics and space engineering witnessed many trends in evolutionary algorithms for various types of problems. By having a look at the amount of publications regarding the development of meta-heuristics in aerospace sciences, it can be seen that a high amount of efforts are dedicated to develop novel stochastic techniques and more specifically, innovative evolutionary algorithms on a variety of subjects. In the past decade, one of the challenging problems in space engineering, which is tackled mainly by novel evolutionary algorithms by the researchers in the aerospace community is spacecraft trajectory optimization. Spacecraft trajectory optimization problem can be simply described as the discovery of a space trajectory for satellites and space vehicles that satisfies some criteria. While a space vehicle travels in space to reach a destination, either around the Earth or any other celestial body, it is crucial to maintain or change its flight path precisely to reach the desired final destination. Such travels between space orbits, called orbital maneuvers, need to be accomplished, while minimizing some objectives such as fuel consumption or the transfer time. In the engineering point of view, spacecraft trajectory optimization can be described as a black-box optimization problem, which can be constrained or unconstrained, depending on the formulation of the problem. In order to clarify the main motivation of the research in this thesis, first, it is necessary to discuss the status of the current trends in the development of evolutionary algorithms and tackling spacecraft trajectory optimization problems. Over the past decade, numerous research are dedicated to these subjects, mainly from two groups of scientific communities. The first group is the space engineering community. Having an overall look into the publications confirms that the focus in the developed methods in this group is mainly regarding the mathematical modeling and numerical approaches in dealing with spacecraft trajectory optimization problems. The majority of the strategies interact with mixed concepts of semi-analytical methods, discretization, interpolation and approximation techniques. When it comes to optimization, usually traditional algorithms are utilized and less attention is paid to the algorithm development. In some cases, researchers tried to tune the algorithms and make them more efficient. However, their efforts are mainly based on try-and-error and repetitions rather than analyzing the landscape of the optimization problem. The second group is the computer science community. Unlike the first group, the majority of the efforts in the research from this group has been dedicated to algorithm development, rather than developing novel techniques and approaches in trajectory optimization such as interpolation and approximation techniques. Research in this group generally ends in very efficient and robust optimization algorithms with high performance. However, they failed to put their algorithms in challenge with complex real-world optimization problems, with novel ideas as their model and approach. Instead, usually the standard optimization benchmark problems are selected to verify the algorithm performance. In particular, when it comes to solve a spacecraft trajectory optimization problem, this group mainly treats the problem as a black-box with not much concentration on the mathematical model or the approximation techniques. Taking into account the two aforementioned research perspectives, it can be seen that there is a missing link between these two schemes in dealing with spacecraft trajectory optimization problems. On one hand, we can see noticeable advances in mathematical models and approximation techniques on this subject, but with no efforts on the optimization algorithms. On the other hand, we have newly developed evolutionary algorithms for black-box optimization problems, which do not take advantage of novel approaches to increase the efficiency of the optimization process. In other words, there seems to be a missing connection between the characteristics of the problem in spacecraft trajectory optimization, which controls the shape of the solution domain, and the algorithm components, which controls the efficiency of the optimization process. This missing connection motivated us in developing efficient meta-heuristics for solving spacecraft trajectory optimization problems. By having the knowledge about the type of space mission, the features of the orbital maneuver, the mathematical modeling of the system dynamics, and the features of the employed approximation techniques, it is possible to adapt the performance of the algorithms. Knowing these features of the spacecraft trajectory optimization problem, the shape of the solution domain can be realized. In other words, it is possible to see how sensitive the problem is relative to each of its feature. This information can be used to develop efficient optimization algorithms with adaptive mechanisms, which take advantage of the features of the problem to conduct the optimization process toward better solutions. Such flexible adaptiveness, makes the algorithm robust to any changes of the space mission features. Therefore, within the perspective of space system design, the developed algorithms will be useful tools for obtaining optimal or near-optimal transfer trajectories within the conceptual and preliminary design of a spacecraft for a space mission. Having this motivation, the main goal in this research was the development of efficient meta-heuristics for spacecraft trajectory optimization. Regarding the type of the problem, we focused on space rendezvous problems, which covers the majority of orbital maneuvers, including long-range and short-range space rendezvous. Also, regarding the meta-heuristics, we concentrated mainly on evolutionary algorithms based on probabilistic modeling and hybridization. Following the research, two algorithms have been developed. First, a hybrid self adaptive evolutionary algorithm has been developed for multi-impulse long-range space rendezvous problems. The algorithm is a hybrid method, combined with auto-tuning techniques and an individual refinement procedure based on probabilistic distribution. Then, for the short-range space rendezvous trajectory optimization problems, an estimation of distribution algorithm with feasibility conserving mechanisms for constrained continuous optimization is developed. The proposed mechanisms implement seeding, learning and mapping methods within the optimization process. They include mixtures of probabilistic models, outlier detection algorithms and some heuristic techniques within the mapping process. Parallel to the development of algorithms, a simulation software is also developed as a complementary application. This tool is designed for visualization of the obtained results from the experiments in this research. It has been used mainly to obtain high-quality illustrations while simulating the trajectory of the spacecraft within the orbital maneuvers.La Caixa TIN2016-78365R PID2019-1064536A-I00 Basque Government consolidated groups 2019-2021 IT1244-1

Efficient meta-heuristics for spacecraft trajectory optimization

190 p.Uno de los problemas más difíciles de la ingeniería espacial es la optimización de la trayectoria de las naves espaciales. Dicha optimización puede formularse como un problema de optimización que dependiendo del tipo de trayectoria, puede contener además restricciones de diversa índole. El principal objetivo de esta tesis fue el desarrollo de algoritmos metaheurísticos eficientes para la optimización de la trayectoria de las naves espaciales. Concretamente, nos hemos centrado en plantear soluciones a maniobras de naves espaciales que contemplan cambios de orbitas de largo y coto alcance. En lo que respecta a la investigación llevada a cabo, inicialmente se ha realizado una revisión de estado del arte sobre optimización de cambios de orbitas de naves espaciales. Según el estudio realizado, la optimización de trayectorias para el cambio de orbitas cuenta con cuatro claves, que incluyen la modelización matemática del problema, la definición de las funciones objetivo, el diseño del enfoque a utilizar y la obtención de la solución del problema. Una vez realizada la revisión del estado del arte, se han desarrollado dos algoritmos metaheurísticos. En primer lugar, se ha desarrollado un algoritmo evolutivo híbrido auto-adaptativo para problemas de cambio de orbitas de largo alcance y multi-impulso. El algoritmo es un método híbrido, combinado con técnicas de autoajuste y un procedimiento derefinamiento individual basado en el uso de distribuciones de probabilidad. Posteriormente, en lo que respecta a los problemas de optimización de trayectoria de los encuentros espaciales de corto alcance, se desarrolla un algoritmo de estimación de distribuciones con mecanismos de conservación de viabilidad. Los mecanismos propuestos aplican métodos innovadores de inicialización, aprendizaje y mapeo dentro del proceso de optimización. Incluyen mixturas de modelos probabilísticos, algoritmos de detección de soluciones atípicas y algunas técnicas heurísticas dentro del proceso de mapeo. Paralelamente al desarrollo de los algoritmos, se ha desarrollado un software de simulación para la visualización de los resultados obtenidos en el cambio de orbitas de las naves espaciales