The Maximal Synchronization Problem Of Feeder Buses To Metro

Transfer optimization is an important problem in public transit. Effective transfer can be helpful to not only achieve a smooth convergence among various modes of transport but also improve the attractive of using public transport to travel for the residents. Maximizing the simultaneous arrivals is a research direction of transfer optimization. Synchronization reflects the coordination of the arrival time of the trips from different lines to reach the transfer station. To maximize the number of simultaneous arrivals at transfer stations can support more transfers and minimum the transfer waiting time of passengers. The previous maximal synchronization problem mainly focuses on a single transit mode, without considering different modes. In this paper, we study the transfer problem between two most popular transit modes(i.e. bus and metro) with objective of maximizing the simultaneous arrivals. Given a subway station with known arrival times, this paper aims to maximize the simultaneous arrivals between bus and metro as well as the simultaneous arrivals of bus trips from different bus lines by the means of optimizing the departure time of bus lines, then a model avoiding bus bunching and considering the passenger's walking time is built.To solve the maximal synchronization problem, three solution approaches are developed, which are based on basic genetic algorithm(GA), particle swarm algorithm(PSO) and adaptive differential evolution algorithm(DEMS), respectively. A benchmark instance is employed to verify the effectiveness of the three approaches with the analysis on the computational results. Compared with the benchmark results produced by a heuristic method based on nodes selection, the results of the proposed PSO, GA, DEMS approaches have been improved by 55.77%, 72.03% and 121.37%, respectively. Moreover, the DEMS, which can choose different mutation strategy during various stages of iteration, has better convergence than the other approaches. Furthermore, the DEMS approach is compared with the basic DE using different mutation strategies. Experiments show that this improved DEMS algorithm can get better solution. Finally, the three approaches have also been tested on a real-world problem related to Guanggu Square in the city of Wuhan, the results demonstrate that the proposed DEMS approach can produce good results and is promising with good behavior of convergence.