In recent years, with the development of high-speed railway in China, the railway operating mileages and passenger transport capacity have increased rapidly. Due to the high density of trains and the limited capacity of railways, it is necessary to solve market shares of different railway traffic modes in order to adjust the operation plans appropriately and run railway passenger transport products in line with passenger demand. Therefore, the purpose of this paper is to calculate market shares by formulating a mixed logit model based on improved nonlinear utility functions taking different factors into consideration, such as seat grades, fares, running time, passenger income levels and so on. Firstly according to maximum likelihood estimation, the likelihood function of this mixed logit model is proposed to maximize utility of all passenger groups. After that, we propose two improved algorithms based on the simulated annealing algorithm (ISAA-CC and ISAA-SS) to estimate the unknown parameters and solve the optimal solution of this model in order to enhance the computational efficiency. Finally, a real-world instance with related data of Beijing–Tianjin corridor, is implemented to demonstrate the performance and effectiveness of the proposed approaches. In addition, by performing this numerical experiment and comparing these two improved algorithms with the traditional Newton method, the ant colony algorithm and the simulated annealing algorithm, we prove that the improved algorithms we developed are superior to others in the optimal solution.
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