A multi-period asymmetric transit frequency design problem

Transit frequency design is critical in determining the performance of public transit services. In the literature, single-period frequency design is often considered but ignores the demand variation over time of day. Moreover, in high-demand bus networks, the demand patterns are asymmetric in both directions of some bus routes. This study investigates a bus operation strategy to address these two issues. In this strategy, for each route, a class of buses serves both directions while the other class only serves one direction with high travel demand, leading to the two directions having different frequencies. A bilevel optimization problem is formulated for this strategy. The upper level problem is a multi-period asymmetric transit frequency design problem, which aims to determine the route frequencies of different classes of buses associated with each period to maximize the operating profit or social welfare. This upper level problem also considers deadhead trips between the bus depot and terminals or between terminals of different routes across periods. The lower level problem is a schedule-based user equilibrium transit assignment problem, taking elastic demand, the common line choice of passengers, and capacity constraints into account. A hybrid algorithm combining an enhanced artificial bee colony algorithm with the method of successive averages is proposed to tackle the bilevel optimization problem and then applied to the study of the Tin Shui Wai bus network to demonstrate the model properties. The effectiveness of the proposed algorithm is also examined. The results indicate that the proposed algorithm can produce better solutions compared with the modified hybrid genetic algorithm. Moreover, the proposed multi-period asymmetric design outperforms the existing design, which can achieve less passenger travel time and greater demand satisfaction, operating profit, and social welfare.