Research on railway emergency resource scheduling strategy under multiple uncertainty coupling

To address the multiple sources of uncertainty in railway emergency resource scheduling, this study uses interval numbers to characterize uncertainty in scheduling time, models resource demand as a fuzzy-random variable, and integrates fuzzy credibility constraints with interval programming within a unified optimization framework. Based on interval fuzzy credibility-constrained programming, an emergency resource scheduling model is developed to minimize both scheduling time and scheduling cost. Given the characteristics of the model constructed in this paper, an improved solution strategy based on the VEPSO algorithm is designed. By using the mean of existing feasible solutions to repair infeasible solutions generated during the optimization process, the proposed method ensures that all particles satisfy the constraints. This approach effectively addresses the complex and discontinuous Pareto front characteristics inherent in multi-objective programming involving multiple uncertain variables, enabling rapid search and selection of Pareto-optimal solutions. The results of the case study indicate that the VEPSO algorithm outperforms PSO, NSGA-II, VEGA, and MOEA/D in terms of convergence efficiency and solution quality. Its average number of convergence iterations is only 385, which is approximately 26.0% lower than that of MOEA/D, with an average runtime of 273 seconds, a convergence success rate of 93.3%, and a total demand fulfillment credibility of 0.983. By introducing a satisfaction evaluation method, this study quantifies the degree of alignment between resource allocation and actual demand under different confidence levels across various accident scenarios, revealing the distribution patterns by which both factors jointly determine resource satisfaction. This provides a quantitative basis for dynamically adjusting emergency resource scheduling strategies. Furthermore, a sensitivity analysis of resource demand was conducted at a fixed confidence level. The results indicate that when the demand scaling factor k increases from 1.0 to 1.2, the rate of change in total scheduling cost is 16.0529%, and the rate of change in total scheduling time is 50%. The model exhibits a stable and approximately linear response, indicating good robustness. This study provides quantifiable decision support for railway emergency resource scheduling in environments with multiple uncertainties, offering both theoretical value and practical significance.