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urban public transportation system is an important part of urban transportation, and the rationality of public transportation routes layout plays a vital role in the transportation of the city. Improving the efficiency of public transportation can have a positive impact on the operation of the public transportation system. This paper uses complex network theory and the symmetry of the up and down bus routes and stations to establish an urban public transit network model and calculates the probability of passengers choosing different routes in the public transit network according to passenger travel impedance. Based on passenger travel impedance, travel path probability and passenger travel demand, the links are weighed, and the network efficiency calculation method is improved. Finally, the urban public transportation network optimization model was established with network efficiency as the objective function and solved by the ant colony algorithm. In order to verify the effectiveness of the model and the solution method, this paper selects areas in Uyo Capital City for example analysis. The result shows that the efficiency of the optimized network is 8.5% higher than that of the original network, which proves the feasibility of the optimized model and solution method.

CHAPTER ONE Introduction

The development of urban public transportation in Nigeria lags in the development of urban economy. Therefore, a series of traffic problems has appeared in the process of urbanization, such as serious traffic congestion during peak travel times, frequent traffic accidents, significant difficulty in parking, etc. In the urban transportation system, urban public transportation has become one of the main travel modes of residents due to the advantages of large passenger capacity, low travel cost and wide coverage. At the same time, the development of the public transportation system has effectively alleviated traffic congestion and other traffic problems; thus, the development of urban public transportation and the encouragement of green public transportation have become the main development goals of urban transportation [2]. Urban rail transit and conventional transit are important components of the urban public transportation system, and the rationality of the layout plays a vital role in the transportation of the city. Due to the late beginning of the construction of urban rail transit in Nigeria and the relatively short development time, the city failed to form a reasonable urban public transportation system. There are many problems in the network layout, and one of the most important problem is that public transportation routes cannot complement each other’s advantages, and there is vicious competition, which renders the overall urban public transportation system inefficient.

With the rapid development of computer technology, complex network theory can be applied to all fields of life [3,4]. When road conditions permit, the driving routes and stations of the up and down bus routes are symmetrical; thus, urban public transportation can be abstracted as an upline transit network and a downline transit network. According to complex network theory, the overall level of the public transportation network can be described scientifically and comprehensively, and it can also objectively reflect the connection of various routes and stations in the bus route network [5]. As early as 2000, some scholars have carried out research on the application of complex networks to transportation networks. In the literature [6], the study modeled the world aviation network and analyzed network topology. Finally, this study found that network topology has a scale-free characteristic. A typical research study on the application of complex network theory to urban public transportation systems is Ref. [7]; the study used the Space L method and Space P method separately to model the public transit network of 22 cities in Poland and systematically analyzed the statistical characteristics of network topology.

Background of the study

Finally, the author used the impedance and the transit time of the station as weights. Cats O et al. [11] took passenger flow in the route as the weight of the link. So far, most of the existing research studies considered single factors such as cross-section passenger flow, travel time or impedance in order to provide weight to the network but only considering that single factors cannot reflect the true network operation status. These factors need to be considered comprehensively to weight the network. In terms of urban public transportation network optimization, Ding J et al. [12] established an optimization model of the urban public transportation network for the dual goals of bus station optimization and bus routes optimization based on the direct accessibility of the stations and optimized the urban public transportation network by using the K shortest path algorithm. Lu H et al. [13] considered the influence of travel behavior in route layout and built a double-layer optimization model based on the spatial topological structure of rail transit routes and bus routes, while optimizing bus routes and departure intervals. Wang F [14] constructed a bus–subway  weighted composite network based on card swiping data of the bus and subway and optimized the bus route network. Network efficiency was improved based on the traffic efficiency of the link.
Finally, the author took the improved urban public transportation network efficiency as the optimization goal and used the addition and deletion of stations as the optimization method. Hao Y [15] put forward the idea of hierarchical optimization of multi-mode public transit network. The optimization goal of the main route network was to reduce the negative effect of travel, and the optimization goal of the branch route network was to increase the coverage of the route network. The ant colony algorithm was used to achieve route network optimization. Some classic studies are provided in Table 1. The existing research studies lack consideration of the overall network in the selection of the optimization goal of the urban public transportation network, such as [12,13,15], or achieves the optimization of the overall efficiency of the network but ignores the influence of the direction of the bus routes, such as [14]. The overall efficiency of the public transit network should be optimized while considering changes in bus routes.

Statement of the problem

Due to the fact that the urban public transportation system is complex, the powerless network cannot show a real urban public transportation system. Many scholars have carried out research on the empowerment of the urban public transportation network. Yang J et al. [8] weighted the urban public transportation network with cross-sectional passenger flow, and they found that the weighted invulnerability measurement index can better describe the robustness of the network. Lu Q et al. [9] used passenger travel time and passenger flow as weights for the rail transit network. The research results show that the failure of stations with high time weighting and passenger flow centrality in the weighted rail transit network can cause a greater loss of average travel time for users. Zhou Y [10] used the PTEW weighting method to assign weights to the urban public transportation network. The study introduced the BPR function in order to reflect public travel time cost and used PTEW weighting to calculate traffic impedance of each section.


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