利用两阶段稳健优化进行基于对称性的城市轨道交通网络规划

Symmetry Pub Date : 2024-09-04 DOI:10.3390/sym16091149
Zhaoguo Huang, Changxi Ma
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引用次数: 0

摘要

为了解决城市轨道交通网络中与车站和线路对称性相关的弹性问题,我们提出了一种基于两阶段稳健优化的城市轨道交通网络规划方法。在此背景下,弹性被概念化为网络在正常和干扰条件下保持运营对称性的能力。首先,我们将客流分布作为决策变量,构建了一个基于两阶段对称性的城市轨道交通网络规划模型,旨在同时最小化网络的总成本和总运营时间,并保持其功能对称性。其次,我们设计了一种染色体具有两层编码结构的混合进化算法,其中尼切帕累托遗传算法作为主要算法框架,并设计了大邻域搜索机制来优化个体的连接基因层,确保网络连接的对称性。最后,我们对随机生成的实例进行了计算验证,以确认模型和算法的有效性。实验结果表明,我们的方法可以找到成本偏好和时间偏好的两组帕累托最优解,从而保持了网络在正常和受损条件下的运行对称性,并减少了总运行时间。这有效提高了网络的整体效率和弹性。我们设计的混合进化算法在早期迭代中就收敛到了满意的目标值,表现出很强的搜索和优化性能,有效地解决了基于两阶段对称性的城市轨道交通网络规划模型。
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Symmetry-Based Urban Rail Transit Network Planning Using Two-Stage Robust Optimization
To address the symmetry-related resilience issues of stations and lines in urban rail transit networks, we propose a two-stage robust optimization-based approach for urban rail transit network planning. In this context, resilience is conceptualized as the ability of the network to maintain its operational symmetry under normal and disruptive conditions. Firstly, we used passenger flow distributions as decision variables to construct a two-stage symmetry-based urban rail transit network planning model, aiming to simultaneously minimize the total cost and total operating time of the network while preserving its functional symmetry. Secondly, we designed a hybrid evolutionary algorithm with chromosomes having a two-layer encoding structure, where the Niched Pareto Genetic Algorithm served as the main algorithmic framework, and a Large Neighborhood Search mechanism was designed to optimize the connectivity gene layer of individuals, ensuring the symmetry of network connectivity. Finally, we conducted computational verification on randomly generated instances to confirm the effectiveness of the model and algorithm. The experimental results demonstrated that our method could find two sets of Pareto optimal solutions for cost preference and time preference, thereby preserving the operational symmetry of the network under normal and damaged conditions, as well as reducing the total operating time. This effectively improved the overall efficiency and resilience of the network. Our designed hybrid evolutionary algorithm converged to satisfactory objective values in the early iterations, exhibiting strong search and optimization performance and effectively solving the two-stage symmetry-based urban rail transit network planning model.
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