# Optimization Method of Customized Shuttle Bus Lines under Random Condition
## 1 Introduction
The objective function of the first level was defined with the aim of reducing the user and agency costs. In the second level, the performance of users was addressed. Furthermore, a local search method based on the Tabu search algorithm was carried out to guide the exploration in the solution domain [9]. [PERSON] et al. (2012) presented a model and an algorithm for the design of a home-to-work bus service in a metropolitan area. A multiobjective model was introduced, among other aspects, equity was considered by time windows on the arrival time of a bus at a stop. In addition, a cluster routing approach was proposed to model both the bus stop location and routing in urban road networks where turn restrictions exist. The resulting multi-objective location-routing model was solved by a Tabu search algorithm [10]. [PERSON] et al. (2014) based on the analysis of seasonal transit demand variations, studied the design of the bus network. In order to solve this NP hard problem, a genetic algorithm-based method was proposed. The optimization was realized by a defined objective function [11]. [PERSON] et al. (2017) compared solution methods for different location-routing problems and the optimal route between 300-700 bus stops allocated by the K-means clustering analysis was determined with the ant colony optimization [12]. A methodological framework was formulated by [PERSON] et al. (2014), and heterogeneous route configurations generated by this framework can reduce the cost of bus users and operating agency [13]. [PERSON] and [PERSON] (2005) proposed a linear mathematical model on the bus line network, and passengers' travel time, public transit network density, as well as operator's benefit were considered [14]. [PERSON] and [PERSON] (2003) designed the transit route network in a two-phase solution process: A large set of the candidate route is generated in the first phase and a solution route set is selected from the candidate route set in the second phase, while the bus operating cost and passenger total travel time were minimized [15]. [PERSON] and [PERSON] (2006, 2012) considered the user cost,operator cost, and unsatisfied demand cost [16; 17]. [PERSON] et al. (2015) considered the interests of passengers and bus companies and established a bi-level programming model of public transit network planning, while the equilibrium analysis of the passenger travelling choice behavior was made based on the strategy equilibrium transit assignment [18]. [PERSON] and [PERSON] (2016) established an integer nonlinear programming model for designing the optimal bus transit network to minimize the total cost of the bus operation and passenger travel time [19]. A network optimization model was developed by [PERSON] et al. (2008), and benefits maximization, costs minimization, and sustainable development were considered [20]. [PERSON] et al. (2012) built a direct traveler density model and extended it to design the transit network, aiming to minimize the number of transfer times and maximize the demand density of the route [21]. [PERSON] and [PERSON] (2007) presented a methodology for optimizing transit networks based on both passenger and operator costs [22]. [PERSON] and [PERSON] (2014) proposed a bi-level transit network design problem and the objective of upper-level was to minimize the number of passenger transfers, while the lower-level problem was a transit assignment problem [23]. We can conclude that the objectives of works on the bus network optimization are mainly minimal travel time, cost or transfer times, while residents' travel behavior is less considered. Among the factors affecting the optimization of customized bus routes, the most important are the travel cost and time, in which travel time often has a certain randomness. Given that stops of the customized shuttle bus are set up according to demands, this paper optimizes the customized shuttle bus network from the point of residents' travel behavior.