A variable neighborhood search algorithm for a public bus line with a demand-responsive operation during peak hours

In this study, we propose a variable neighborhood search (VNS) algorithm to optimize the performance of a single bus line during peak hours where the passenger flows in one direction are typically much larger than the flows in the opposite direction. The system we propose aims to increase the frequency of the service towards the city center during morning peak hours, by allowing some of the vehicles to perform short-cut trips away from the city center. Just before the morning peak hours and based on the expected demand, the VNS algorithm decides which buses should visit all the stops ahead or take a short-cut during its return trip. Experiments show that with the demand-responsive system, total passenger travel time improves about 10% on average for a real-size benchmark instance. The performance of the system is also analyzed under different fleet size and capacity, duration of peak hours, and demand scenarios