Time-Dependent Shortest Path Optimization in Urban Multimodal Transportation Networks with Integrated Timetables

Urban transportation systems evolve toward greater diversification, scalability, and complexity. To address the escalating issue of urban traffic congestion, leveraging modern information technologies to enhance the integration of multiple transportation modes and maximize overall efficiency has emerged as a promising strategy. This study focuses on the decision making problem of urban multimodal transportation travel paths, integrating the time-varying characteristics of public transportation schedules and networks. We consider passengers’ diverse needs and systematically investigate how to optimize travel paths to minimize travel time while adhering to constraints, such as the number of interchanges and travel costs. To address this NP-hard problem, we propose and implement two optimization algorithms: a variable-length coding genetic algorithm (V-GA) and a full permutation coding genetic algorithm (F-GA). Detailed numerical analysis validates the effectiveness of both algorithms, with the V-GA demonstrating significant advantages over the F-GA in terms of solution efficiency. Our findings provide novel perspectives and methodologies for optimizing urban multimodal transportation travel paths, offering robust theoretical foundations and practical tools for enhancing urban traffic planning and travel service efficiency.