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This paper deals with fuzzy multi-depot bus scheduling (FMDBS) problem in which the objective function and constraints are defined with fuzzy attributes. Credibility relation is used to formulate the problem as an integer multicommodity flow problem. A novel combination of branch-and-price and heuristic algorithms, is proposed to efficiently solve FMDBS problem. In the proposed algorithm, the heuristic algorithm is applied to generate initial columns for the column generation method. Also, a heuristic algorithm is used to improve the generated solutions in each node of the branch-and-price tree. Two sets of benchmark examples are applied to demonstrate the efficiency of the proposed algorithm for large-scale instances. Also, the algorithm is applied to solve the classical multi-depot bus scheduling problem. The results show that the proposed algorithm decreases integrality gap and computational time in comparison with the state-of-the-art algorithms and normal branch-and-price algorithm. Finally, as a case study, the bus schedules in Tehran BRT network are generated. [ABSTRACT FROM AUTHOR]

In order to rationally formulate a customized bus route plan to improve the operation efficiency of customized buses, in view of the problem of ignoring the distance between the boarding area and the alighting area, and setting it as a fixed value when performing custom bus route optimization modeling, as well as solving the problem of multiple custom bus parking lots. This paper proposes a method based on the NSGA-II algorithm using a three-stage hybrid coding method to solve. First, according to real life, the entire operation process of customized buses is divided into four phases. Second, based on the four stages, a multi-objective optimization model of customized bus routes that satisfies multiple parking lots, multiple cars, and multiple boarding and alighting stations is constructed to pursue the minimum total travel time of passengers and minimizes the operating costs of customized bus companies. Third, the NSGA-II algorithm is employed to solve the model, including three-stage hybrid coding, segmented crossover, and segmented mutation operators. Finally, the local road network in Lanzhou City is adopted for simulation research. The results show that it is feasible to use NSGA-II algorithm to solve the problem of customizing bus routes for multiple parking lots, multiple vehicles, and multiple boarding and alighting stations. The research results are of great value for exploring the optimization methods of customized bus routes and improving the operating efficiency of custom buses. [ABSTRACT FROM AUTHOR]