An optimization method for railway alignment schemes based on game-theoretic combination weighting and an interval number model

Optimal selection of railway alignment schemes is a critical phase in railway line design. However, existing studies primarily adopt an engineering perspective, often overlooking economic and social factors. Current decision-making models also face limitations in quantifying qualitative indicators and balancing subjective and objective weights, thereby undermining the scientific rigor and effectiveness of the evaluation process. To address these issues, this study proposes a multi-attribute optimization model for railway alignment selection based on combined weighting and the interval number model. First, the key factors influencing railway alignment are systematically identified through expert consultations and an extensive literature review. On this basis, a multi-dimensional evaluation index system comprising 20 indicators is established, encompassing four dimensions: technical feasibility, economic rationality, environmental impact, and regional coordinated development. Subjective weights are derived using the Analytic Hierarchy Process (AHP), while objective weights are calculated through an improved CRITIC method. Game theory is then employed to integrate them. To further enhance the objectivity and robustness of the evaluation, the study develops a decision-making model based on interval number distance. This model quantifies qualitative indicators using interval numbers and ranks alternative schemes by computing their distances to an ideal solution. A case study on the Jieshipu-Pingliang section of the Dingxi-Pingliang railway confirms the method's validity. The results show that the comprehensive weighting method reduces the influence of weight factor sensitivity on route selection. Furthermore, the scheme ranking derived from the interval number model closely aligns with the scheme recommended by the design institute and demonstrates stability. The research findings can provide a scientific reference for optimizing railway alignment in economically underdeveloped regions.