AbstractWith the wide use of smartphone travel apps, a new hybrid transit system (HTS) that integrates fixed-route transit (FRT) and app-based demand-responsive feeder transit (DRFT) services have recently emerged in many cities over the world. App-based DRFT services are coordinated with FRT to offer fast, comfortable, and well-connected mobility services to travelers. The study investigates a new variant of HTS, termed flexible HTS (FHTS), allowing FRT to have flexible vehicle departure times and capacitated vehicle loads and DRFT to have flexible feeder stations, so as to further enhance the coordination between FRT and DRFT. The coordinated operation optimization problem of such an FHTS in a travel corridor is formulated as a mixed-integer linear programming model. A novel hybrid metaheuristic algorithm is developed to solve it. In the hybrid algorithm, a constrained compass search method is used to optimize FRT vehicle departure times, and an adaptive large neighborhood search algorithm, coupled with a tailored forward time slack algorithm, is applied to solve the DRFT routing and scheduling problems. A case study in Shucheng County, China is conducted to examine the performance of the model and solution algorithms. Sensitivity analyses on feeder station layout and vehicle size are also conducted. The results show that flexible FRT vehicle departure times and flexible DRFT feeder stations have a great potential of enhancing the coordination of FRT and DRFT services by reducing operators’ costs and passengers’ total travel time. Managerial implications are to set feeder transit stations downstream of an FRT line and to keep a reasonable station spacing.