EDA++: Estimation of Distribution Algorithms with Feasibility Conserving Mechanisms for Constrained Continuous Optimization

Handling non-linear constraints in continuous optimization is challenging, and finding a feasible solution is usually a difficult task. In the past few decades, various techniques have been developed to deal with linear and non-linear constraints. However, reaching feasible solutions has been a challenging task for most of these methods. In this paper, we adopt the framework of Estimation of Distribution Algorithms (EDAs) and propose a new algorithm (EDA++) equipped with some mechanisms to deal with non-linear constraints. These mechanisms are associated with different stages of the EDA, including seeding, learning and mapping. It is shown that, besides increasing the quality of the solutions in terms of objective values, the feasibility of the final solutions is guaranteed if an initial population of feasible solutions is seeded to the algorithm. The EDA with the proposed mechanisms is applied to two suites of benchmark problems for constrained continuous optimization and its performance is compared with some state-of-the-art algorithms and constraint handling methods. Conducted experiments confirm the speed, robustness and efficiency of the proposed algorithm in tackling various problems with linear and non-linear constraints.La Caixa Foundatio

Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL) optimization framework

Simplicity and flexibility of meta-heuristic optimization algorithms have attracted lots of attention in the field of optimization. Different optimization methods, however, hold algorithm-specific strengths and limitations, and selecting the best-performing algorithm for a specific problem is a tedious task. We introduce a new hybrid optimization framework, entitled Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL), which combines the strengths of different evolutionary algorithms (EAs) in a parallel computing scheme. SC-SAHEL explores performance of different EAs, such as the capability to escape local attractions, speed, convergence, etc., during population evolution as each individual EA suits differently to various response surfaces. The SC-SAHEL algorithm is benchmarked over 29 conceptual test functions, and a real-world hydropower reservoir model case study. Results show that the hybrid SC-SAHEL algorithm is rigorous and effective in finding global optimum for a majority of test cases, and that it is computationally efficient in comparison to algorithms with individual EA

Process Knowledge-guided Autonomous Evolutionary Optimization for Constrained Multiobjective Problems

Various real-world problems can be attributed to constrained multi-objective optimization problems. Although there are various solution methods, it is still very challenging to automatically select efficient solving strategies for constrained multi-objective optimization problems. Given this, a process knowledge-guided constrained multi-objective autonomous evolutionary optimization method is proposed. Firstly, the effects of different solving strategies on population states are evaluated in the early evolutionary stage. Then, the mapping model of population states and solving strategies is established. Finally, the model recommends subsequent solving strategies based on the current population state. This method can be embedded into existing evolutionary algorithms, which can improve their performances to different degrees. The proposed method is applied to 41 benchmarks and 30 dispatch optimization problems of the integrated coal mine energy system. Experimental results verify the effectiveness and superiority of the proposed method in solving constrained multi-objective optimization problems.The National Key R&D Program of China, the National Natural Science Foundation of China, Shandong Provincial Natural Science Foundation, Fundamental Research Funds for the Central Universities and the Open Research Project of The Hubei Key Laboratory of Intelligent Geo-Information Processing.http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=4235hj2023Electrical, Electronic and Computer Engineerin

Fuzzy Differential Evolution Algorithm

The Differential Evolution (DE) algorithm is a powerful search technique for solving global optimization problems over continuous space. The search initialization for this algorithm does not adequately capture vague preliminary knowledge from the problem domain. This thesis proposes a novel Fuzzy Differential Evolution (FDE) algorithm, as an alternative approach, where the vague information of the search space can be represented and used to deliver a more efficient search. The proposed FDE algorithm utilizes fuzzy set theory concepts to modify the traditional DE algorithm search initialization and mutation components. FDE, alongside other key DE features, is implemented in a convenient decision support system software package. Four benchmark functions are used to demonstrate performance of the new FDE and its practical utility. Additionally, the application of the algorithm is illustrated through a water management case study problem. The new algorithm shows faster convergence for most of the benchmark functions

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

Hybrid of memory andprediction strategies for dynamic multiobjective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Dynamic multiobjective optimization problems (DMOPs) are characterized by a time-variant Pareto optimal front (PF) and/or Pareto optimal set (PS). To handle DMOPs, an algorithm should be able to track the movement of the PF/PS over time efficiently. In this paper, a novel dynamic multiobjective evolutionary algorithm (DMOEA) is proposed for solving DMOPs, which includes a hybrid of memory and prediction strategies (HMPS) and the multiobjective evolutionary algorithm based on decomposition (MOEA/D). In particular, the resultant algorithm (MOEA/D-HMPS) detects environmental changes and identifies the similarity of a change to the historical changes, based on which two different response strategies are applied. If a detected change is dissimilar to any historical changes, a differential prediction based on the previous two consecutive population centers is utilized to relocate the population individuals in the new environment; otherwise, a memory-based technique devised to predict the new locations of the population members is applied. Both response mechanisms mix a portion of existing solutions with randomly generated solutions to alleviate the effect of prediction errors caused by sharp or irregular changes. MOEA/D-HMPS was tested on 14 benchmark problems and compared with state-of-the-art DMOEAs. The experimental results demonstrate the efficiency of MOEA/D-HMPS in solving various DMOPs