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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]

The implication of firefly and fuzzy firefly optimization algorithms has been greatly witnessed in clustering techniques and extensively used in applications such as Image segmentation. Parameters such as step factor and attractiveness have been kept constant in these algorithms, which affect the convergence rate and accuracy of the clustering process. Though fuzzy adaptive firefly algorithm tackled this problem by making those parameters an adaptive one, issues such as low convergence rate, and provision of non-optimal solutions are still there. To tackle these issues, this paper proposed a novel fuzzy adaptive fuzzy firefly algorithm that significantly improves the accuracy and convergence rate while comparing with the existing optimization algorithms. Further, the proposed algorithm fused with existing hybrid clustering algorithms involving fuzzy set, intuitionistic fuzzy set, and rough set resulted in eight novel hybrid clustering algorithms which lead to better performance in optimizing the selection of initial centroids. To validate the proposal, experimental studies have been conducted on datasets found in bench-marking data repositories such as UCI, and Kaggle. The performance and accuracy evaluation of proposed algorithms have been carried out with the aid of seven accuracy measures. Results clearly indicate the improved accuracy and convergence rate of the proposed algorithms. [ABSTRACT FROM AUTHOR]