This article is a survey paper on solving spacecraft trajectory optimization problems. The solving process is decomposed into four key steps of mathematical modeling of the problem, defining the objective functions, development of an approach and obtaining the solution of the problem. Several subcategories for each step have been identified and described. Subsequently, important classifications and their characteristics have been discussed for solving the problems. Finally, a discussion on how to choose an element of each step for a given problem is provided.
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.
Herein, a model is developed based on energy balance equations to analyze and improve the performance of single‐phase counter‐current and co‐current flow spiral plate heat exchangers (SPHEs). The aim is to comprehensively check the performance and irreversibility factors based on energy, entropy, and entransy methods. First, a new optimization algorithm is proposed to maximize pressure drops and minimize the total cost by considering the geometric proportion of the SPHE. Second, the SPHE spiral turns are modeled as a series‐connected equivalent internal heat exchangers network to determine the temperature boundaries and develop the temperature–enthalpy diagram in analysis. The algorithm and modeling is validated in two stages for different flow arrangement SPHEs. Performance and irreversibility analysis shows similar result trends in different flow patterns. In third stage, a wide range of counter‐current flow SPHEs with constant heat transfer rate is designed, modeled, and analyzed by energy, entropy, and entransy methods. To recapitulate, results assert that SPHEs designed by new algorithm have higher overall heat‐transfer coefficient and compactness. Although entropy and entransy analyses reveal irreversibility trends with effectiveness in SPHEs, entransy analysis is more effective and reliable to analyze the SPHEs.
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