Identifying key station nodes for suppressing delay propagation in high-speed rail networks

Nowadays, high-speed rail (HSR) has become an increasingly popular choice for travel. However, delays occasionally occur during HSR trips, and these delays can propagate throughout the network, causing widespread disruptions. Therefore, controlling delay propagation is a critical task in HSR network maintenance. Given the limited resources available for delay control in real-world applications (such as budgets, personnel, and facilities), it is crucial to identify the optimal set of station nodes, of a given size, that can most effectively resist the spread of delays when controlled. In this paper, we formulate an optimization problem for immune node selection to control delay propagation. To solve this problem, we propose a node propagation centrality metric that integrates both the susceptibility and infectivity of a node to quantify the importance of nodes in delay propagation. Furthermore, we develop a genetic algorithm to find an approximately optimal set of immune nodes, using centrality-based initialization and a one-hop neighbor-based variable neighborhood search strategy. Comparative experiments on real-world HSR networks demonstrate the effectiveness of our algorithm. Our work helps identify the most influential nodes in HSR networks for limiting delay propagation, assisting railway personnel in making informed decisions.