Optimizing demand-responsive feeder transit service with modular autonomous vehicles employing fixed and flexible stations

Demand-responsive feeder transit (DRFT), as a significant complement to conventional bus systems, adeptly fulfills the travel needs of passengers. However, DRFT still exhibits shortcomings in controlling costs and managing fluctuating passenger flow. This paper proposes a DRFT scheduling method with modular autonomous vehicles (MAVs) while considering fixed and flexible stations. We construct a MINLP model intending to minimize enterprise operating costs and the generic cost of passenger losses. A two-stage enhanced tabu search with adaptive selection and long-term memory (ETSA-LTM) is employed to solve the model. The first stage rapidly converges to high-quality solutions for fixed-station passengers, while the second stage refines the search to incorporate flexible-station passengers through operator selection and long-term memory strategies. Computational results show that the ETSA-LTM significantly reduces computation time compared to the commercial solver Gurobi and improves solution quality by up to 17% over a conventional tabu search. Furthermore, we perform comparative experiments to validate the effectiveness of setting fixed and flexible stations and using MAVs in reducing DRFT service costs. The results reveal that the proposed scheduling method achieves an overall 16.9% reduction in total costs compared to DRFT approaches. Sensitivity experiments indicate that MAVs are more notably suitable than traditional shuttle buses for hub scenarios with significant demand fluctuations. The MAV system demonstrates robust cost superiority over the non-modular baseline across various rejection penalty settings and unit capacity configurations. Finally, the case study conducted in the proximity of the Nanjing South Railway Station in China validates that the proposed model and algorithm can efficiently address real-scale problems. The findings provide a novel reference for scheduling DRFT services shuttling to transport hubs.