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Designing baseline or vertical alignment in railways greatly depends on the designer's experience. An inaccurate design imposes unreasonable costs during construction and operations. This paper presents a program to find the best vertical alignment for a track with a given horizontal layout. First, the vertical alignment is formulated using mathematical equations, and then an algorithm is developed to produce its geometric configuration. Construction and operating costs, which are sensitive to gradient changes, are expressed as vertical alignment variables and included in the model. A direct search method is employed to solve the objective function, and a genetic algorithm encodes solution algorithms in a program, whereas certain heuristic operators are utilized to cover operational situations. The program also provides railway engineers and planners with practical information on the resulting alignment such as time and speed graph, total traction force, and block capacity. Moreover, the model is evaluated using a real example to verify the algorithms' ability to find the optimal alignment. [ABSTRACT FROM AUTHOR]

In this paper, an optimization model for force finding of tensegrity systems with considerations of the geometrical stability condition, the unilateral property of members, and the evenness requirement of internal forces was developed. The simulated annealing algorithm was used to solve this optimization problem. Force finding of several typical tensegrity systems was carried out with the proposed method. It was found that the optimized solutions were very close to the analytical solutions and able to reflect the geometrical symmetry of the structures. It also verified that the proposed method is applicable to tensegrity systems under consideration including simple two-dimensional structures and complex three-dimensional multimodular structures. [ABSTRACT FROM AUTHOR]