Transit Network Design and Frequency Setting Model Driven by Interchange Stations and Improved NSGA-II Algorithm

Abstract

The core of the transit network design and frequency setting problem lies in balancing passenger travel efficiency and operator operating costs. However, existing methods generally rely on physical distance to measure site relevance, which makes it difficult to reflect the actual connections between passenger flows. At the same time, existing algorithms are inefficient and produce poor-quality solutions when dealing with multiobjective strong constraint optimization in networks, making it difficult to effectively coordinate the optimization of complex decision variables such as route paths, station attributes, and interchange relationships. To this end, we propose a collaborative optimization framework that integrates graph representation learning and improved multiobjective evolutionary algorithms from the perspective of interchange stations. First, improved graph convolutional networks are used to deeply mine network topology and passenger flow allocation information. Through third-order neighborhood aggregation, high-order feature vectors of nodes are learned, overcoming the limitations of traditional physical distance measurements. Second, a three-layer multipopulation chromosome coding mechanism (route path, station attributes, interchange relationship) and customized genetic operators (chromosome-to-chromosome/intrachromosome crossover, perturbation strategy) based on NSGA-II were designed to effectively handle complex decision variables and construct a mathematical model containing seven types of constraints, including network topology connectivity, passenger flow allocation rules, and operational coordination. Finally, experiments on the Mandl benchmark network showed that this method achieved a minimum total travel time of 199,825.65 min, a maximum direct rate of 98.89%, and a minimum average travel time of 12.76 min on a network with six lines. The proposed method eliminates secondary and higher interchanges and unmet demand in all scenarios, with a single interchange rate controlled between 1.11% and 4.41%. By adjusting the interchange penalty coefficient through sensitive parameters, the Pareto equilibrium between operator costs and passenger travel time is significantly optimized. Compared with existing methods, we show significant advantages in solution efficiency and plan quality, providing a reference for transit network optimization.