基于非概率可靠性的铁路应急设施选址-路径鲁棒优化

鉴于铁路应急设施选址研究中很难合理估计参数的概率分布或确定其隶属函数的问题，将选址-路径问题与区间非概率可靠性方法结合起来，以复杂网络理论为基础，提出网络节点区间权重的确定方法，同时考虑节点权重、边权及径权区间不确定性的共同作用，构建铁路应急设施选址节点加权网络。基于区间非概率可靠性理论及区间运算规则，提出路径的非概率可靠性度量及最优时间可靠度路径选择方法，建立节点权重、边权及径权均为区间数的非概率可靠性铁路应急设施选址-路径鲁棒优化模型，并给出了求解算法，确定了基于区间模型的铁路应急设施鲁棒选址的最优方案。算例表明，本文的优化方案能更好地保证救援的时间鲁棒性，能有效地规避不确定因素波动对设施选址的长期风险，具有很好的实际应用价值。

Robust Optimization for Railway Emergency Location-Routing Based on Non-probabilistic Reliability

In view of that it is difficult to reasonably estimate the probability distribution of parameters or determine the membership function in the study of location selection of railway emergency facilities, combining the site-path problem with the interval non-probabilistic reliability method, and based on the complex network theory, a method to determine the interval weight of network nodes is proposed. Considering the confluence of interval uncertainties in node weight, edge weight and path weight, a weighted network of railway emergency facility location nodes is constructed. Based on the interval non-probabilistic reliability theory and interval operation rules, the path non-probabilistic reliability measurement and optimal time reliability path selection method are proposed, and a robust optimization model for railway emergency location-routing based on non-probabilistic reliability was established, in which node weights, edge weights and path weights were all interval numbers. As well as the solution algorithm is given. Furthermore, the optimal scheme of robust location of railway emergency facilities based on interval model is determined. Numerical examples show that the optimization scheme in this paper can better ensure the time robustness of rescue, effectively avoid the long-term risk of uncertain factors fluctuations on facility location, and have good practical application value.