A demand-responsive feeder service with a maximum headway at mandatory stops

Public transportation out of suburban or rural areas is crucial. Feeder transportation services offer a solution by transporting passengers to areas where more options for public transport are available. On one hand, fully flexible demand-responsive feeder services (DRFSs) efficiently tailor their service to the needs of the passengers. On the other hand, traditional feeder services provide predictability and easier cost control. In this article, a semi-flexible DRFS is considered, which combines positive characteristics of both traditional services as well as fully flexible services. This feeder service has two types of bus stops: mandatory bus stops and optional bus stops. Mandatory bus stops are guaranteed to be visited by a bus within a certain time interval. Optional stops are only visited when there is demand for transportation nearby. The performance of this feeder service is optimized with the use of a new type of metaheuristic framework, which we denote as parameter space search. Experimental results on small benchmark instances indicate that the heuristic performs on average 12.42% better than LocalSolver, a commercial optimization solver, with an average runtime of 2.1 s. Larger instances can also be solved, typically within 2 min.