An Improved Particle Swarm Optimization Algorithm for the Urban Transit Routing Problem

The Urban Transit Routing Problem (UTRP) is a challenging discrete problem that revolves around designing efficient routes for public transport systems. It falls under the category of NP-hard problems, characterized by its complexity and numerous constraints. Evaluating potential route sets for feasibility is a demanding and time-consuming task, often resulting in the rejection of many solutions. Given its difficulty, metaheuristic methods, such as swarm intelligence algorithms, are considered highly suitable for addressing the UTRP. However, the effectiveness of these methods depends heavily on appropriately adapting them to discrete problems, as well as employing suitable initialization procedures and solution-evaluation methods. In this study, a new variant of the particle swarm optimization algorithm is proposed as an efficient solution approach for the UTRP. We present an improved initialization function and improved modification operators, along with a post-optimization routine to further improve solutions. The algorithm's performance is then compared to the state of the art using Mandl's widely recognized benchmark, a standard for evaluating UTRP solutions. By comparing the generated solutions to published results from 10 studies on Mandl's benchmark network, we demonstrate that the developed algorithm outperforms existing techniques, providing superior outcomes.