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• Propose a transfer-based customized bus network design with passenger-route assignment and a modular fleet. • Formulate the problem into a mixed-integer non-linear programming model. • Propose an exact solution method by reformulating the problem into a linear model. • Present a customized Particle Swarm Optimization (PSO) algorithm for large-scale problems. • Verify the hybrid PSO algorithm can produce high quality near-optimal solutions efficiently. • Show that the incorporation of passenger-route assignment optimization and transfer operation benefits customized bus network design. Customized bus (CB) is an increasingly popular mode of transportation in many cities around the world. However, studies on CB network design have mostly overlooked three options that may further improve system performance: passenger-route assignment, passenger transfer, and modular vehicles. To bridge this gap, this paper proposes to design a transfer-based CB network with a modular fleet while simultaneously optimizing the passenger-route assignment. To solve the optimal network structure with this new design paradigm, we formulate the network design problem into a nonlinear mixed integer optimization model. A linearization approach and a particle swarm optimization (PSO) algorithm are proposed to solve the exact and near-optimal solution(s) to the model, respectively. Numerical experiments are conducted on the Sioux Falls network and a large-scale network in Chengdu, China. Results show that the customized PSO algorithm efficiently provides high quality near-optimal solutions compared with CPLEX, the genetic algorithm, and the simulated annealing algorithm. Results also show that incorporating passenger-route assignment optimization and the transfer operation produces a more cost-effective CB operational network with less operational costs and higher service quality. The benefit increases as the passenger demand grows. [ABSTRACT FROM AUTHOR]