Optimizing Longitudinal Alignment in Railway with Regard to Construction and Operating Costs

Abstract

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.