# Considering the Optimization Design of Urban Bus Network Scheduling
## 1 Introduction  
With the acceleration of urbanization and rapid economic development in our country, the number of motor vehicles and the travel demands of residents are also rapidly increasing. Traffic congestion has become common and is becoming increasingly severe. To alleviate the current pressure on transportation, our country is vigorously promoting the development of public transportation, especially in large cities where public transportation is developing rapidly. For example, in Shenzhen, the length of operational rail transit lines exceeded 400 km in 2020, reaching 422.6 km, a year-on-year increase of 33.9%. The length of bus operating routes reached 21,310.53 km, a year-on-year decrease of 1.4%. Currently, in major cities across the country, transportation modes such as buses, subways, taxis, and trans together form a public transportation network, with overall passenger flow continually increasing. In 2019, the average daily passenger flow of public transportation in Shenzhen was 11.06 million passengers per day, an increase of 2.65 million passengers per day compared to 2011. In 2020, due to the impact of the COVID-19 pandemic, the average daily passenger volume for the entire year was 8.226 million passengers, a year-on-year decrease of 25.6%. As the pandemic situation improved and new subway lines opened, public transportation passenger flow in December rose to the highest level of the year, with an average daily passenger volume of 10.603 million passengers, recovering to 94.1% of the same period in 2019. To improve the transportation efficiency of buses and balance the supply and demand of the bus system, it is necessary to replan and redesign the bus network. This will help avoid significant overlap with rail transit lines, preventing redundant routes and resourcewaste. At the same time, it is crucial to ensure seamless connections and transfers between buses and rail transit, thereby meeting passengers' travel needs and reducing travel costs. After conducting domestic and international research and analysis on bus networks, it was found that existing studies overlook the impact of scheduling on bus network optimization. They also fail to consider passengers' waiting costs when calculating the total travel costs for passengers. Analysis of passenger card swiping data revealed a moderate correlation between passengers' route choices and the frequency of bus services. Therefore, this paper includes scheduling considerations in the optimization of bus networks. Scholars both domestically and internationally have conducted relatively mature research on the optimization of urban bus networks. The majority of research on network optimization focuses on three aspects: theory, model construction, and algorithm development. Theoretical Methods: [PERSON] et al. proposed a bus network optimization method based on multilayer complex networks [1]. [PERSON] et al. presented a multi-objective bus network optimization method [2]. [PERSON] et al. introduced a bus network design method based on aggregate networks and continuous approximation models [3]. [PERSON] et al. proposed a network optimization method for urban transportation networks and road networks [4]. [PERSON] developed a public transportation route network (PTRN) auxiliary optimization method based on link prediction [5]. [PERSON] introduced a novel optimization method for designing public transportation networks, maximizing the expected total number of public transportation passengers under budget constraints [6]. [PERSON] studied the coordinated train timetable optimization of urban rail transit networks and proposed a mathematical formula to generate the best-coordinated train timetable synchronously [7]. [PERSON] established a multi-objective model based on two conflicting objectives, and developed two populations to simultaneously optimize the network and frequency [8]. [PERSON] introduced a multi-level multi-mode network design method [9].