# Optimization of New Energy Public Transportation Network Based on Ant Colony Algorithm and Low-Carbon Concept

Authors: Jiaying Geng; Jichao Geng
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

In order to solve the optimization of new energy bus line network, a new energy bus line network based on ant colony algorithm and low-carbon concept is proposed. Firstly, the model of public transport network is established combined with OD matrix, and the improved ant colony algorithm is used to iteratively optimize the initial suboptimal route set, optimize the objective function, and finally obtain the optimal public transport route set. Secondly, the improved ant colony algorithm based on simulated annealing solves the design of public transport network, and the optimization scheme greatly reduces the number of passenger transfers and the total travel time of passengers. Finally, simulated annealing algorithm, basic ant colony algorithm, and simulated annealing improved ant colony algorithm are used to optimize the objective function. It is proved that the improved ant colony algorithm of simulated annealing can find the optimal solution of the three algorithms when solving the problem of public transport network design, which is better than the solution of basic ant colony and simulated annealing algorithm. The solution efficiency is 10.6 times that of simulated annealing algorithm and 3.5 times that of basic ant colony algorithm.


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## Body

## 1. Introduction

Since the 20th century, many scholars at home and abroad have actively invested in the research of new energy bus network optimization. The optimization of new energy public transport network is a multiobjective optimization problem; that is, within the spatial solution meeting the optimization constraints, we can find the optimal solution with satisfactory objective functions proposed in the optimization selection of public transport network. Specifically, after studying the law of passenger flow, organize the bus on the specified route, and formulate a rhythmic and repeated driving plan according to the number, direction, and time of passenger flow, so as to obtain the best economic and social benefits. This paper uses the method of establishing mathematical model to solve this combinatorial optimization problem [1].The research on the optimization of urban public transport network is mainly divided into two categories: one is simple theoretical research, that is, to solve the optimization problem of public transport network with simple quantitative model; the other is to give priority to qualitative and give consideration to quantitative. Part of the optimization process of online network is determined by quantitative model. As the urban public transport system is a complex, multifactor, multiobjective, and multifunctional random dynamic system, the new energy public transport network optimization model is the basis of the whole network optimization. The quality of the model directly affects the optimization effect. As a good optimization model, it should be clear, concise, and easy to implement. For the large-scale, complex, and diverse public transportation network optimization problem, there are many feasible schemes, and the traditional optimization algorithm is not easy to obtain a satisfactory approximate solution. According to the current characteristics of urban traffic development, on the basis of defining the three elements of bus line network optimization, and considering the four-dimensional consumption of time, space, environment, and energy, this paper establishes the bus line network optimization model and uses ant colony algorithm to solve the optimization model, as shown in Figure1.Figure 1
Ant group algorithm.


## 2. Literature Review

Under the background of rapid economic development and continuous optimization and upgrading of urban industrial structure, the office industry has formed a multicenter spatial agglomeration area. However, the suburbanization trend of urban housing is obviously faster than the expansion of office space to the suburbs. Therefore, there is still a serious dislocation of working and living space, which undoubtedly brings great urban traffic pressure. Giving priority to the development of public transport, it is recognized as the best strategy to solve the traffic problems of large- and medium-sized cities all over the world. It is also based on the implementation of the “four priorities” policy of “facility land, investment arrangement, right of way distribution, and fiscal and tax support” for public transport, so as to continuously improve the convenience of urban public transport network and make the proportion of office workers choosing public transport higher and higher. Moreover, the low fare system and bus card preference supported by the long-term and stable financial subsidy policy make passengers more concerned about the time and efficiency of bus travel.There are many researches on the optimization design theory and method of new energy bus network at home and abroad. Sun et al. studied the application of standard genetic algorithm (SGA) to the optimization design of public transit network [2]. Abdullah et al. studied the algorithm of using parallel genetic algorithm (PGA) to improve bus routes [3]. Li and Chen proposed the application of particle swarm optimization (PSO) to adjust and optimize the urban public transport network and proposed ant colony optimization (ACO) to optimize the public transport network [4]. Niu et al. proposed an algorithm of local search and tabu search strategy to optimize bus lines and vehicle allocation [5]. Pan et al., combined with genetic algorithm and domain search algorithm, established vehicle frequency and route design model [6]. Kim et al. proposed an ant colony algorithm to directly modify the line scheme [7]. Hossain et al. established a public transit network planning model aiming at minimizing passenger travel time and maximizing passenger comfort [8]. Furen and Yufang regarded the public transit network optimization model as a fixed demand model [9]. Kumar S. et al. optimize the public transportation network with the average transportation cost as the goal and use approximate algorithms to solve the public transportation network optimization model network and other algorithms [10]. Fang et al. proposed to use the hybrid algorithm combining the vehicle path search algorithm in artificial intelligence and the public transportation system analysis method in operation research to solve the problem of public transportation network optimization [11]. Ren and Long established an expert system for the layout and design of high-capacity bus stops by simulating the decision-making process of decision-makers and using combinatorial mathematics method [12].Based on the current research, an optimization method for new energy bus line network based on ant colony algorithm and low-carbon concept is proposed. The efficiency of the improved ant colony algorithm is 3.5 times that of the simulated annealing algorithm, which is better than that of the simulated annealing algorithm.


## 3. Optimization of New Energy Public Transportation Network Based on Ant Colony Algorithm and Low-Carbon Concept

### 3.1. Ant Colony Algorithm

#### 3.1.1. Basic Principle of Ant Colony Algorithm

According to the routing principle of “routing one by one and optimizing into a network,” combined with the basic principle of ant colony algorithm, an artificial ant is placed at the starting (ending) point of each existing bus, the transfer probability of the ant from the bus stop to its adjacent bus stop is determined according to the “taste” and “pheromone,” and the maximum value of the transfer probability is taken to move to the next bus stop and so on until all ants stop moving forward due to line length or degradation [13].


#### 3.1.2. Classification of Ant Colony Algorithm Model

The model of ant colony algorithm can be divided into three types according to different updating methods of pheromones:(1)
Ant density system: in this model, if antK passes through path (I,J), it releases pheromones with a concentration of Q units on the path per unit length. Otherwise, it releases 0 units of pheromones. In this system, the concentration of pheromone update is fixed, which is independent of the path length selected by ants. The update amount of pheromone concentration is shown in
(1)Δτijkt,t+1=Q,0(2)
Ant quantity system: in this model, if antK passes through path (I,J), it releases pheromones with a concentration of Q/DIJ units on the path per unit length. Otherwise, it releases 0 units of pheromones [14]. In this system, the concentration of pheromone update is inversely proportional to the length of the path. The shorter the path, the higher the concentration of pheromone update, and the greater the probability of subsequent ants choosing the shortest path. The update amount of pheromone concentration is shown in
(2)Δτijkt,t+1=Q,dij,0In ant density system and ant quantity system, ants update local pheromones while searching. This pheromone update strategy can easily lead to the algorithm not coordinating the whole situation and falling into local optimization when seeking the overall solution.(3)
Ant cycle system: in this model, ants need to search all paths and get a complete solution before updating the pheromone concentration on the path. In this system, the concentration of pheromone update is inversely proportional to the total length of the solution. The shorter the length, the higher the concentration of pheromone update. The update amount of pheromone concentration is shown in(3)Δτijkt,t+n=Q,Lk,0,where (T,t+n) means that the ant has to choose the path n times to complete a search. LK represents the total length of the path established by the k-th ant in this search. Δτijkt,t+n means updating pheromone concentration on the path traveled by the k-th ant


#### 3.1.3. Characteristics of Mosquito Swarm Algorithm

Ant colony algorithm has achieved good results in some problems since it was proposed. The main advantages of ant colony algorithm are as follows.(1) Parallelism. Since the search process of each ant is independent of each other, they only search within their own scope and then exchange and exchange information through the information cable [15]. Therefore, ant colony algorithm can be designed as a parallel algorithm, and this parallel computing can greatly reduce the computing time of ant colony algorithm.(2) Good Robustness. Ant colony algorithm has strong adaptability. According to different problems, the basic ant colony algorithm can be adjusted accordingly to solve different problems.(3) Positive Feedback. An important feature of ant colony algorithm is positive feedback. In the process of searching the path, if the concentration of “pheromone” on a certain path is higher, more ants will choose this route, which will further increase the concentration of “pheromone” on this route, and the greater the concentration of “pheromone” will attract more ants. Thus, the concentration of “pheromone” on this route is much higher than that of other routes, and finally, all ants will choose this route, which will find the optimal route [16]. Therefore, the rapid convergence of ant colony algorithm is due to the existence of this positive feedback mechanism.(4) Good Combination. Ant colony algorithm can also be well combined with other heuristic algorithms (such as simulated annealing algorithm and genetic algorithm). This combination can effectively improve the performance of the algorithm and increase the search ability of the algorithm.However, ant colony algorithm also has the following disadvantages:(1)
The computation time of ant colony algorithm is longWhen the scale of the problem required to be solved is large, because the movement of ants in the ant colony algorithm is random at the beginning, it is difficult for ants to quickly find a better path from many paths, and the convergence speed will become relatively slow. Moreover, when the number of ant colony itself is large, the algorithm is also difficult to find the optimal path in a short time to reach the convergence state.(2)
It is easy to fall into local optimizationIn the ant colony algorithm, since the ant colony does not know the information about the path in the network at the beginning, the ant colony searches the path according to some local heuristic information [17]. Because ant colony algorithm is a positive feedback process, the interference of this local optimal information will gradually deepen with the continuous iteration of the algorithm, so that the “pheromone” concentration on the local optimal route is much higher than that of other paths, resulting in all ants choosing this local optimal path. It is impossible to jump out of the local optimum and continue to find other paths, resulting in premature convergence and falling into the local optimum.
(3)
Parameter setting and data initialization rely more on manual experienceThe performance of ant colony algorithm has a great relationship with the parameter setting of the algorithm. However, because the ant colony algorithm has no solid mathematical theoretical foundation and systematic parameter setting and analysis method, the parameter setting still mostly depends on continuous experiment and manual experience.


### 3.2. Low-Carbon Concept

#### 3.2.1. Concept

Although low-carbon concept is widely used by all parties, the specific definition of low-carbon concept is quite vague. On the contrary, the concretization of low-carbon concept in all aspects is quite clearly defined. For example, the definition of “low-carbon economy,” which was first used by the British government in official documents, is a state of harmony between energy, environment, and human economic development through scientific and technological innovation, system establishment and improvement, industrial structure change, and other ways. In order to clarify the concept of low-carbon concept, after summarizing the previous research results, the so-called low-carbon concept refers to the collection of a series of cognition and ideas with “low carbon” as the core [18]. “Low carbon” in the narrow sense means reducing the emission of greenhouse gases dominated by carbon dioxide; in the broad sense, it means various improvements including reducing energy consumption, improving energy efficiency, reducing greenhouse gas emissions, and changing development mode. With the low-carbon concept as the core, it has been embodied in various fields such as transportation, life, and economy, forming “low-carbon life,” “low-carbon travel,” and “low-carbon transportation.” For low-carbon transportation, domestic scholars have drawn many definitions, but they are similar. The vast majority believe that low-carbon transportation takes low-carbon economy as the core, aims to reduce carbon emissions and energy consumption, and takes measures to vigorously promote the transportation development of public transportation. After summarizing the previous research results, the interpretation of low-carbon transportation in this paper is as follows: low-carbon transportation refers to encouraging and supporting green and low-carbon travel modes and optimizing energy efficiency. Change the energy structure and develop and utilize new clean energy and other measures to realize the scientific transportation development of effectively reducing carbon emissions in the transportation field.


#### 3.2.2. Characteristics of Low-Carbon Transportation

(1)
Low carbon: low-carbon transportation is to pursue the low carbon of the transportation industry. Low carbon is both the goal and the means to reduce carbon emissions by optimizing the energy structure and developing new energy(2)
Measurability: through the statistics of energy consumption and combined with the carbon emission factor of each energy, the carbon emission of the transportation industry can be obtained [19]. Or calculate carbon emissions through “carbon footprint.” Its essence is the process of calculating and accumulating the carbon emissions of each mode of transportation or enterprises and individuals. With the help of the “carbon footprint” of each transportation mode, researchers can select low-carbon transportation from all transportation modes, which not only facilitates the realization of low-carbon transportation but also divides low-carbon transportation in detail(3)
Complexity: low-carbon transportation involves various modes of transportation, such as slow traffic, large volume transportation, and public transportation, and each mode of transportation has different impact on carbon emission and environment(4)
Comprehensive: low-carbon transportation involves not only transportation but also land use, intelligent system, energy development, infrastructure construction, and government macrocontrol. Low-carbon transportation formed by the combination of many aspects is the comprehensive product of modern science and technology and management


#### 3.2.3. Integration of Low-Carbon Concept and Conventional Bus Network Optimization Theory

For the low-carbon research of conventional public transport network, its external performance mainly focuses on the following aspects:(1)
Relevant carbon emission reduction measures of the operating company: public transport operation companies control the models of public transport vehicles and then control the carbon emissions of buses to a certain extent. Improving the energy structure of public transport vehicles to reduce carbon emissions or directly investing in new energy public transport vehicles can effectively control the carbon emissions of public transport network. For example, most cities now convert more original gasoline or diesel powered buses into oil-gas hybrid buses or the popular new energy buses introduced in China(2)
Initial planning and later optimization of public transportation network: the initial planning of public transport network is generally the reasonable layout of new lines and the best state of some indicators that can be achieved by the new line network, which needs to consider the station setting of new lines, the impact on the existing wired network, etc. The later optimization of public transport network is mostly applied when some problems existing in the front-line network need to be adjusted. It is the resource integration of the wired network to ensure that the line network reaches the best state of some indicators [20]. Both initial planning and later optimization are to ensure the travel quality of the line network as much as possible and reduce unnecessary detours. Reasonable route planning and optimization can make public transport vehicles meet the needs of travelers and reduce fuel consumption as much as possible, so as to reduce carbon emissions(3)
Layout of stations and other public transport facilities: the layout of stations can affect the direction of bus lines, the speed change of bus vehicles, and the full load rate of the whole bus line [21]. The overall direction of the bus line is directly determined by the initial and terminal stations and the larger hub stations in the line: the spacing between stations can affect the formal speed of buses. If the stations are too dense, buses cannot maintain a relatively uniform driving speed, which may also lead to a low bus load rate, which may lead to higher carbon emissions of the line: on the contrary, the stations are sparse. It is not conducive to the comprehensive dispatching of public transport and cannot attract more passengers to travel by public transport. It may also lead to the high load rate of public transport vehicles between local stations, resulting in high carbon emissions of public transport vehicles(4)
Other aspects, including the driving level of bus drivers: as we all know, the energy consumption of vehicles running at a relatively uniform speed is less than that of vehicles during braking and starting, while the service characteristics of conventional public transport determine that public transport vehicles have more starting and braking processes. Therefore, the excellent driving level of bus drivers can be reflected in how to ensure that the driving distance between the two stops is high and maintain a relatively stable speed [22]. A good bus driver can keep a relatively stable speed between the two stops, so that the bus can produce less carbon emissionsHowever, for the first aspect of the driving level of bus drivers, human factors are too heavy, which is related to the driver’s psychology, physiology, personal habits, and other factors. It is not suitable for quantification and calculation, and it is difficult to put forward quantifiable improvement suggestions when studying it. Second, the transformation and renewal of public transport equipment cannot be completed overnight. Moreover, combined with the current loss stage of conventional public transport in many cities, the transformation and renewal process of equipment is limited, which cannot meet the urgent needs of low-carbon optimization of conventional public transport network. Therefore, for the effective reduction of carbon emission of the current conventional bus network, we should start with the optimization and adjustment of the network, adjust the unreasonable lines in the network and improve the transportation efficiency, save energy consumption, and realize low-carbon optimization of conventional bus line network [23].


#### 3.2.4. Basic Principles of Low-Carbon Optimization of Conventional Bus Line Network

The low-carbon optimization of conventional bus line network, like the general optimization of bus line network, needs to follow certain principles, so as to make the optimization present the results consistent with the optimization objectives. The principles of low-carbon optimization of conventional public transport network are as follows:(1)
Travel convenience principle: the low-carbon optimization of conventional public transport is not a total negation of the yuan public transport network, nor does it conflict with the original travel convenience needs of the conventional public transport network, but to retain the original travel convenience principle here [24]. Equivalent to the conventional bus network after low-carbon optimization, it should also have the attributes of good accessibility, less transfer times, high network efficiency, short travel time, and so on(2)
The principle of effectively reducing carbon emissions: the purpose of low-carbon optimization of conventional public transport is to make the bus network meet the requirements of reducing carbon emissions through reasonable adjustment of conventional public transport network. It is equivalent to adding an item to the attribute of the original public transport network to reduce carbon emissions, making conventional public transport more competitive in public transport. Therefore, this is also one of the basic requirements for low-carbon optimization of conventional bus line network [25](3)
The principle of effective utilization: the purpose of optimization is to enable the existing network to meet the travel demand and have certain functions, that is, to reduce carbon emissions. Instead of the general abandonment of the existing conventional public transport network, the optimization is based on the original wired network, taking the essence to its dregs, that is, reasonable line reservation, abandoning the unreasonable ones, and adjusting the abandonment part by adding and adjusting the lines


### 3.3. Optimization of New Energy Bus Network

#### 3.3.1. Bus Line Network Optimization Theory

The optimization of public transport network optimization absorbs the essence of many disciplines such as operational research, system theory, and transportation planning theory. It aims to ease the pressure on city traffic and constantly study and develop the potential of public transport, so as to establish convenient and fast public transportation network. The optimization of public transportation network is based on the original public transportation lines, through the scientific allocation of public transportation vehicles, funds and other needs, and the reasonable adjustment of the layout of public transportation lines and stations, so as to reduce the operation cost of public transportation and make passengers travel with low cost and high efficiency. Public transport network optimization is mostly carried out from the aspects of public transport lines, the layout of public transport stations, and the scheduling of public transport vehicles. Through public transport network optimization, the total transportation capacity of the whole public transport network can be adjusted, and the convenience of conventional public transport can be improved, giving full play to the functions of safety, fairness, and quickness. It is of great significance to improve urban traffic efficiency and save social public travel resources. Therefore, public transport network optimization plays a very important role in the optimization of the whole public transport system.


#### 3.3.2. Principles for Optimization of New Energy Public Transport Network

Public transport network is the main bearer of urban public transport passenger flow. A reasonable public transport network layout can give full play to the advantages of public transport, improve operation efficiency, improve service level, alleviate the tension of public transport, facilitate residents’ travel, reduce the traffic pressure of urban road system, and give full play to the maximum efficiency of limited urban land. Therefore, the optimization of public transport network should follow the following principles:(1)
Minimum traffic demand: through scientific urban layout and network planning, the traffic volume required to maintain the operation and development of the city and society is minimized(2)
Best service level: urban public transport system can meet various traffic needs to the greatest extent. The whole public transport system operates in a safe, punctual, large volume, and high efficiency manner(3)
Minimum energy occupation: the traffic energy consumption per unit output value of the city is the lowest, and the construction, maintenance, use, and management of urban public transport system occupy the lowest land and human resources(4)
Minimum environmental impact: urban public transport has the least impact and interference on people’s living environment and activities


#### 3.3.3. Factors Affecting the Optimization of New Energy Public Transport Network

The optimization of new energy public transport network is a very complex process, involving many factors. Generally speaking, it mainly includes the following aspects.(1) Traffic Demand. Traffic demand is the most critical factor in the optimization of urban public transport network. Traffic demand mainly includes the number of passengers in the public transport network, the geographical distribution of passengers, and the choice of bus routes for passengers to travel. A good bus network should be able to meet the needs of the vast majority of passengers, make passengers reach their destination as far as possible, and reduce passengers’ travel time and waiting time as far as possible. In addition, in areas with large passenger flow demand, there should be a corresponding bus line network with large passenger carrying capacity to match it, while in areas with too small passenger flow demand, the opening of bus lines should be cancelled.(2) Road Conditions. Urban road network is an important basis for the design of public transport network. For urban public transport network planning, without the premise of urban road network, public transport network cannot exist alone. However, the layout of public transport network is only carried out on the roads that meet certain conditions (such as pavement conditions, geometric line shape, and capacity constraints). Therefore, when planning the public transportation network, we can combine the roads suitable for the layout of public transportation lines to form a “basic road network” and then plan the public transportation network on this “basic road network.”(3) Station Conditions. There are usually two ways to set the starting and ending points in bus line planning. One is to generate a bus line network and then determine the starting and ending points and the scale of starting and ending points according to the number of bus lines and the allocation of resources such as bus vehicles. The other is to plan the bus lines one by one according to the starting point and ending point of the bus lines set in advance and then form a complete urban bus line network.(4) Vehicle Condition. Vehicle conditions include physical characteristics (vehicle length, width, weight, etc.), operating performance and maximum passenger capacity of the vehicle.(5) Benefit Factors. Benefit refers to the income obtained from the investment of each unit (per shift, per kilometer, etc.) of the public transport network. The specific indicators reflecting the service income are as follows: income per train, income per kilometer, number of trips per month, number of passengers per train, operating cost-benefit ratio, number of passengers per kilometer, etc. These indicators can not only reflect the operation of each bus line but also reflect the passenger flow demand of bus lines and the service attraction of bus lines. Therefore, this factor needs to be considered when planning the public transportation network.(6) Policy Factors. In the planning process of urban public transport network, some relevant policies and regulations of the city need to be taken into account, such as land development policy, traffic management policy, and social equity security policy. In addition to the above factors, some other factors will also affect the planning of urban public transport network, mainly including the economic situation of the city, the culture of the city, and the travel habits of urban residents. In a word, the above factors need to be comprehensively considered in the process of urban public transport network planning.


#### 3.3.4. Common Modes of New Energy Public Transport Network Optimization

At present, there are two common modes of new energy bus network optimization: solution optimization method and certificate optimization method.(1) Worry Relief Method. The optimization method is also called the forward method. According to the given passenger flow OD data, urban road network, and other public transport data, the optimal public transport network is obtained by solving the optimal solution of the corresponding objective function and constraints. The flow chart is shown in Figure 2.Figure 2
Worry relief method.(2) Syndrome Excellence Method. The optimization method is also called test algorithm. Among several alternative bus line networks, the selected one is selected as the optimal bus line network according to the evaluation function. The flow chart is shown in Figure 3.Figure 3
Method of proving excellence.


## 3.1. Ant Colony Algorithm

### 3.1.1. Basic Principle of Ant Colony Algorithm

According to the routing principle of “routing one by one and optimizing into a network,” combined with the basic principle of ant colony algorithm, an artificial ant is placed at the starting (ending) point of each existing bus, the transfer probability of the ant from the bus stop to its adjacent bus stop is determined according to the “taste” and “pheromone,” and the maximum value of the transfer probability is taken to move to the next bus stop and so on until all ants stop moving forward due to line length or degradation [13].


### 3.1.2. Classification of Ant Colony Algorithm Model

The model of ant colony algorithm can be divided into three types according to different updating methods of pheromones:(1)
Ant density system: in this model, if antK passes through path (I,J), it releases pheromones with a concentration of Q units on the path per unit length. Otherwise, it releases 0 units of pheromones. In this system, the concentration of pheromone update is fixed, which is independent of the path length selected by ants. The update amount of pheromone concentration is shown in
(1)Δτijkt,t+1=Q,0(2)
Ant quantity system: in this model, if antK passes through path (I,J), it releases pheromones with a concentration of Q/DIJ units on the path per unit length. Otherwise, it releases 0 units of pheromones [14]. In this system, the concentration of pheromone update is inversely proportional to the length of the path. The shorter the path, the higher the concentration of pheromone update, and the greater the probability of subsequent ants choosing the shortest path. The update amount of pheromone concentration is shown in
(2)Δτijkt,t+1=Q,dij,0In ant density system and ant quantity system, ants update local pheromones while searching. This pheromone update strategy can easily lead to the algorithm not coordinating the whole situation and falling into local optimization when seeking the overall solution.(3)
Ant cycle system: in this model, ants need to search all paths and get a complete solution before updating the pheromone concentration on the path. In this system, the concentration of pheromone update is inversely proportional to the total length of the solution. The shorter the length, the higher the concentration of pheromone update. The update amount of pheromone concentration is shown in(3)Δτijkt,t+n=Q,Lk,0,where (T,t+n) means that the ant has to choose the path n times to complete a search. LK represents the total length of the path established by the k-th ant in this search. Δτijkt,t+n means updating pheromone concentration on the path traveled by the k-th ant


### 3.1.3. Characteristics of Mosquito Swarm Algorithm

Ant colony algorithm has achieved good results in some problems since it was proposed. The main advantages of ant colony algorithm are as follows.(1) Parallelism. Since the search process of each ant is independent of each other, they only search within their own scope and then exchange and exchange information through the information cable [15]. Therefore, ant colony algorithm can be designed as a parallel algorithm, and this parallel computing can greatly reduce the computing time of ant colony algorithm.(2) Good Robustness. Ant colony algorithm has strong adaptability. According to different problems, the basic ant colony algorithm can be adjusted accordingly to solve different problems.(3) Positive Feedback. An important feature of ant colony algorithm is positive feedback. In the process of searching the path, if the concentration of “pheromone” on a certain path is higher, more ants will choose this route, which will further increase the concentration of “pheromone” on this route, and the greater the concentration of “pheromone” will attract more ants. Thus, the concentration of “pheromone” on this route is much higher than that of other routes, and finally, all ants will choose this route, which will find the optimal route [16]. Therefore, the rapid convergence of ant colony algorithm is due to the existence of this positive feedback mechanism.(4) Good Combination. Ant colony algorithm can also be well combined with other heuristic algorithms (such as simulated annealing algorithm and genetic algorithm). This combination can effectively improve the performance of the algorithm and increase the search ability of the algorithm.However, ant colony algorithm also has the following disadvantages:(1)
The computation time of ant colony algorithm is longWhen the scale of the problem required to be solved is large, because the movement of ants in the ant colony algorithm is random at the beginning, it is difficult for ants to quickly find a better path from many paths, and the convergence speed will become relatively slow. Moreover, when the number of ant colony itself is large, the algorithm is also difficult to find the optimal path in a short time to reach the convergence state.(2)
It is easy to fall into local optimizationIn the ant colony algorithm, since the ant colony does not know the information about the path in the network at the beginning, the ant colony searches the path according to some local heuristic information [17]. Because ant colony algorithm is a positive feedback process, the interference of this local optimal information will gradually deepen with the continuous iteration of the algorithm, so that the “pheromone” concentration on the local optimal route is much higher than that of other paths, resulting in all ants choosing this local optimal path. It is impossible to jump out of the local optimum and continue to find other paths, resulting in premature convergence and falling into the local optimum.
(3)
Parameter setting and data initialization rely more on manual experienceThe performance of ant colony algorithm has a great relationship with the parameter setting of the algorithm. However, because the ant colony algorithm has no solid mathematical theoretical foundation and systematic parameter setting and analysis method, the parameter setting still mostly depends on continuous experiment and manual experience.


## 3.1.1. Basic Principle of Ant Colony Algorithm

According to the routing principle of “routing one by one and optimizing into a network,” combined with the basic principle of ant colony algorithm, an artificial ant is placed at the starting (ending) point of each existing bus, the transfer probability of the ant from the bus stop to its adjacent bus stop is determined according to the “taste” and “pheromone,” and the maximum value of the transfer probability is taken to move to the next bus stop and so on until all ants stop moving forward due to line length or degradation [13].


## 3.1.2. Classification of Ant Colony Algorithm Model

The model of ant colony algorithm can be divided into three types according to different updating methods of pheromones:(1)
Ant density system: in this model, if antK passes through path (I,J), it releases pheromones with a concentration of Q units on the path per unit length. Otherwise, it releases 0 units of pheromones. In this system, the concentration of pheromone update is fixed, which is independent of the path length selected by ants. The update amount of pheromone concentration is shown in
(1)Δτijkt,t+1=Q,0(2)
Ant quantity system: in this model, if antK passes through path (I,J), it releases pheromones with a concentration of Q/DIJ units on the path per unit length. Otherwise, it releases 0 units of pheromones [14]. In this system, the concentration of pheromone update is inversely proportional to the length of the path. The shorter the path, the higher the concentration of pheromone update, and the greater the probability of subsequent ants choosing the shortest path. The update amount of pheromone concentration is shown in
(2)Δτijkt,t+1=Q,dij,0In ant density system and ant quantity system, ants update local pheromones while searching. This pheromone update strategy can easily lead to the algorithm not coordinating the whole situation and falling into local optimization when seeking the overall solution.(3)
Ant cycle system: in this model, ants need to search all paths and get a complete solution before updating the pheromone concentration on the path. In this system, the concentration of pheromone update is inversely proportional to the total length of the solution. The shorter the length, the higher the concentration of pheromone update. The update amount of pheromone concentration is shown in(3)Δτijkt,t+n=Q,Lk,0,where (T,t+n) means that the ant has to choose the path n times to complete a search. LK represents the total length of the path established by the k-th ant in this search. Δτijkt,t+n means updating pheromone concentration on the path traveled by the k-th ant


## 3.1.3. Characteristics of Mosquito Swarm Algorithm

Ant colony algorithm has achieved good results in some problems since it was proposed. The main advantages of ant colony algorithm are as follows.(1) Parallelism. Since the search process of each ant is independent of each other, they only search within their own scope and then exchange and exchange information through the information cable [15]. Therefore, ant colony algorithm can be designed as a parallel algorithm, and this parallel computing can greatly reduce the computing time of ant colony algorithm.(2) Good Robustness. Ant colony algorithm has strong adaptability. According to different problems, the basic ant colony algorithm can be adjusted accordingly to solve different problems.(3) Positive Feedback. An important feature of ant colony algorithm is positive feedback. In the process of searching the path, if the concentration of “pheromone” on a certain path is higher, more ants will choose this route, which will further increase the concentration of “pheromone” on this route, and the greater the concentration of “pheromone” will attract more ants. Thus, the concentration of “pheromone” on this route is much higher than that of other routes, and finally, all ants will choose this route, which will find the optimal route [16]. Therefore, the rapid convergence of ant colony algorithm is due to the existence of this positive feedback mechanism.(4) Good Combination. Ant colony algorithm can also be well combined with other heuristic algorithms (such as simulated annealing algorithm and genetic algorithm). This combination can effectively improve the performance of the algorithm and increase the search ability of the algorithm.However, ant colony algorithm also has the following disadvantages:(1)
The computation time of ant colony algorithm is longWhen the scale of the problem required to be solved is large, because the movement of ants in the ant colony algorithm is random at the beginning, it is difficult for ants to quickly find a better path from many paths, and the convergence speed will become relatively slow. Moreover, when the number of ant colony itself is large, the algorithm is also difficult to find the optimal path in a short time to reach the convergence state.(2)
It is easy to fall into local optimizationIn the ant colony algorithm, since the ant colony does not know the information about the path in the network at the beginning, the ant colony searches the path according to some local heuristic information [17]. Because ant colony algorithm is a positive feedback process, the interference of this local optimal information will gradually deepen with the continuous iteration of the algorithm, so that the “pheromone” concentration on the local optimal route is much higher than that of other paths, resulting in all ants choosing this local optimal path. It is impossible to jump out of the local optimum and continue to find other paths, resulting in premature convergence and falling into the local optimum.
(3)
Parameter setting and data initialization rely more on manual experienceThe performance of ant colony algorithm has a great relationship with the parameter setting of the algorithm. However, because the ant colony algorithm has no solid mathematical theoretical foundation and systematic parameter setting and analysis method, the parameter setting still mostly depends on continuous experiment and manual experience.


## 3.2. Low-Carbon Concept

### 3.2.1. Concept

Although low-carbon concept is widely used by all parties, the specific definition of low-carbon concept is quite vague. On the contrary, the concretization of low-carbon concept in all aspects is quite clearly defined. For example, the definition of “low-carbon economy,” which was first used by the British government in official documents, is a state of harmony between energy, environment, and human economic development through scientific and technological innovation, system establishment and improvement, industrial structure change, and other ways. In order to clarify the concept of low-carbon concept, after summarizing the previous research results, the so-called low-carbon concept refers to the collection of a series of cognition and ideas with “low carbon” as the core [18]. “Low carbon” in the narrow sense means reducing the emission of greenhouse gases dominated by carbon dioxide; in the broad sense, it means various improvements including reducing energy consumption, improving energy efficiency, reducing greenhouse gas emissions, and changing development mode. With the low-carbon concept as the core, it has been embodied in various fields such as transportation, life, and economy, forming “low-carbon life,” “low-carbon travel,” and “low-carbon transportation.” For low-carbon transportation, domestic scholars have drawn many definitions, but they are similar. The vast majority believe that low-carbon transportation takes low-carbon economy as the core, aims to reduce carbon emissions and energy consumption, and takes measures to vigorously promote the transportation development of public transportation. After summarizing the previous research results, the interpretation of low-carbon transportation in this paper is as follows: low-carbon transportation refers to encouraging and supporting green and low-carbon travel modes and optimizing energy efficiency. Change the energy structure and develop and utilize new clean energy and other measures to realize the scientific transportation development of effectively reducing carbon emissions in the transportation field.


### 3.2.2. Characteristics of Low-Carbon Transportation

(1)
Low carbon: low-carbon transportation is to pursue the low carbon of the transportation industry. Low carbon is both the goal and the means to reduce carbon emissions by optimizing the energy structure and developing new energy(2)
Measurability: through the statistics of energy consumption and combined with the carbon emission factor of each energy, the carbon emission of the transportation industry can be obtained [19]. Or calculate carbon emissions through “carbon footprint.” Its essence is the process of calculating and accumulating the carbon emissions of each mode of transportation or enterprises and individuals. With the help of the “carbon footprint” of each transportation mode, researchers can select low-carbon transportation from all transportation modes, which not only facilitates the realization of low-carbon transportation but also divides low-carbon transportation in detail(3)
Complexity: low-carbon transportation involves various modes of transportation, such as slow traffic, large volume transportation, and public transportation, and each mode of transportation has different impact on carbon emission and environment(4)
Comprehensive: low-carbon transportation involves not only transportation but also land use, intelligent system, energy development, infrastructure construction, and government macrocontrol. Low-carbon transportation formed by the combination of many aspects is the comprehensive product of modern science and technology and management


### 3.2.3. Integration of Low-Carbon Concept and Conventional Bus Network Optimization Theory

For the low-carbon research of conventional public transport network, its external performance mainly focuses on the following aspects:(1)
Relevant carbon emission reduction measures of the operating company: public transport operation companies control the models of public transport vehicles and then control the carbon emissions of buses to a certain extent. Improving the energy structure of public transport vehicles to reduce carbon emissions or directly investing in new energy public transport vehicles can effectively control the carbon emissions of public transport network. For example, most cities now convert more original gasoline or diesel powered buses into oil-gas hybrid buses or the popular new energy buses introduced in China(2)
Initial planning and later optimization of public transportation network: the initial planning of public transport network is generally the reasonable layout of new lines and the best state of some indicators that can be achieved by the new line network, which needs to consider the station setting of new lines, the impact on the existing wired network, etc. The later optimization of public transport network is mostly applied when some problems existing in the front-line network need to be adjusted. It is the resource integration of the wired network to ensure that the line network reaches the best state of some indicators [20]. Both initial planning and later optimization are to ensure the travel quality of the line network as much as possible and reduce unnecessary detours. Reasonable route planning and optimization can make public transport vehicles meet the needs of travelers and reduce fuel consumption as much as possible, so as to reduce carbon emissions(3)
Layout of stations and other public transport facilities: the layout of stations can affect the direction of bus lines, the speed change of bus vehicles, and the full load rate of the whole bus line [21]. The overall direction of the bus line is directly determined by the initial and terminal stations and the larger hub stations in the line: the spacing between stations can affect the formal speed of buses. If the stations are too dense, buses cannot maintain a relatively uniform driving speed, which may also lead to a low bus load rate, which may lead to higher carbon emissions of the line: on the contrary, the stations are sparse. It is not conducive to the comprehensive dispatching of public transport and cannot attract more passengers to travel by public transport. It may also lead to the high load rate of public transport vehicles between local stations, resulting in high carbon emissions of public transport vehicles(4)
Other aspects, including the driving level of bus drivers: as we all know, the energy consumption of vehicles running at a relatively uniform speed is less than that of vehicles during braking and starting, while the service characteristics of conventional public transport determine that public transport vehicles have more starting and braking processes. Therefore, the excellent driving level of bus drivers can be reflected in how to ensure that the driving distance between the two stops is high and maintain a relatively stable speed [22]. A good bus driver can keep a relatively stable speed between the two stops, so that the bus can produce less carbon emissionsHowever, for the first aspect of the driving level of bus drivers, human factors are too heavy, which is related to the driver’s psychology, physiology, personal habits, and other factors. It is not suitable for quantification and calculation, and it is difficult to put forward quantifiable improvement suggestions when studying it. Second, the transformation and renewal of public transport equipment cannot be completed overnight. Moreover, combined with the current loss stage of conventional public transport in many cities, the transformation and renewal process of equipment is limited, which cannot meet the urgent needs of low-carbon optimization of conventional public transport network. Therefore, for the effective reduction of carbon emission of the current conventional bus network, we should start with the optimization and adjustment of the network, adjust the unreasonable lines in the network and improve the transportation efficiency, save energy consumption, and realize low-carbon optimization of conventional bus line network [23].


### 3.2.4. Basic Principles of Low-Carbon Optimization of Conventional Bus Line Network

The low-carbon optimization of conventional bus line network, like the general optimization of bus line network, needs to follow certain principles, so as to make the optimization present the results consistent with the optimization objectives. The principles of low-carbon optimization of conventional public transport network are as follows:(1)
Travel convenience principle: the low-carbon optimization of conventional public transport is not a total negation of the yuan public transport network, nor does it conflict with the original travel convenience needs of the conventional public transport network, but to retain the original travel convenience principle here [24]. Equivalent to the conventional bus network after low-carbon optimization, it should also have the attributes of good accessibility, less transfer times, high network efficiency, short travel time, and so on(2)
The principle of effectively reducing carbon emissions: the purpose of low-carbon optimization of conventional public transport is to make the bus network meet the requirements of reducing carbon emissions through reasonable adjustment of conventional public transport network. It is equivalent to adding an item to the attribute of the original public transport network to reduce carbon emissions, making conventional public transport more competitive in public transport. Therefore, this is also one of the basic requirements for low-carbon optimization of conventional bus line network [25](3)
The principle of effective utilization: the purpose of optimization is to enable the existing network to meet the travel demand and have certain functions, that is, to reduce carbon emissions. Instead of the general abandonment of the existing conventional public transport network, the optimization is based on the original wired network, taking the essence to its dregs, that is, reasonable line reservation, abandoning the unreasonable ones, and adjusting the abandonment part by adding and adjusting the lines


## 3.2.1. Concept

Although low-carbon concept is widely used by all parties, the specific definition of low-carbon concept is quite vague. On the contrary, the concretization of low-carbon concept in all aspects is quite clearly defined. For example, the definition of “low-carbon economy,” which was first used by the British government in official documents, is a state of harmony between energy, environment, and human economic development through scientific and technological innovation, system establishment and improvement, industrial structure change, and other ways. In order to clarify the concept of low-carbon concept, after summarizing the previous research results, the so-called low-carbon concept refers to the collection of a series of cognition and ideas with “low carbon” as the core [18]. “Low carbon” in the narrow sense means reducing the emission of greenhouse gases dominated by carbon dioxide; in the broad sense, it means various improvements including reducing energy consumption, improving energy efficiency, reducing greenhouse gas emissions, and changing development mode. With the low-carbon concept as the core, it has been embodied in various fields such as transportation, life, and economy, forming “low-carbon life,” “low-carbon travel,” and “low-carbon transportation.” For low-carbon transportation, domestic scholars have drawn many definitions, but they are similar. The vast majority believe that low-carbon transportation takes low-carbon economy as the core, aims to reduce carbon emissions and energy consumption, and takes measures to vigorously promote the transportation development of public transportation. After summarizing the previous research results, the interpretation of low-carbon transportation in this paper is as follows: low-carbon transportation refers to encouraging and supporting green and low-carbon travel modes and optimizing energy efficiency. Change the energy structure and develop and utilize new clean energy and other measures to realize the scientific transportation development of effectively reducing carbon emissions in the transportation field.


## 3.2.2. Characteristics of Low-Carbon Transportation

(1)
Low carbon: low-carbon transportation is to pursue the low carbon of the transportation industry. Low carbon is both the goal and the means to reduce carbon emissions by optimizing the energy structure and developing new energy(2)
Measurability: through the statistics of energy consumption and combined with the carbon emission factor of each energy, the carbon emission of the transportation industry can be obtained [19]. Or calculate carbon emissions through “carbon footprint.” Its essence is the process of calculating and accumulating the carbon emissions of each mode of transportation or enterprises and individuals. With the help of the “carbon footprint” of each transportation mode, researchers can select low-carbon transportation from all transportation modes, which not only facilitates the realization of low-carbon transportation but also divides low-carbon transportation in detail(3)
Complexity: low-carbon transportation involves various modes of transportation, such as slow traffic, large volume transportation, and public transportation, and each mode of transportation has different impact on carbon emission and environment(4)
Comprehensive: low-carbon transportation involves not only transportation but also land use, intelligent system, energy development, infrastructure construction, and government macrocontrol. Low-carbon transportation formed by the combination of many aspects is the comprehensive product of modern science and technology and management


## 3.2.3. Integration of Low-Carbon Concept and Conventional Bus Network Optimization Theory

For the low-carbon research of conventional public transport network, its external performance mainly focuses on the following aspects:(1)
Relevant carbon emission reduction measures of the operating company: public transport operation companies control the models of public transport vehicles and then control the carbon emissions of buses to a certain extent. Improving the energy structure of public transport vehicles to reduce carbon emissions or directly investing in new energy public transport vehicles can effectively control the carbon emissions of public transport network. For example, most cities now convert more original gasoline or diesel powered buses into oil-gas hybrid buses or the popular new energy buses introduced in China(2)
Initial planning and later optimization of public transportation network: the initial planning of public transport network is generally the reasonable layout of new lines and the best state of some indicators that can be achieved by the new line network, which needs to consider the station setting of new lines, the impact on the existing wired network, etc. The later optimization of public transport network is mostly applied when some problems existing in the front-line network need to be adjusted. It is the resource integration of the wired network to ensure that the line network reaches the best state of some indicators [20]. Both initial planning and later optimization are to ensure the travel quality of the line network as much as possible and reduce unnecessary detours. Reasonable route planning and optimization can make public transport vehicles meet the needs of travelers and reduce fuel consumption as much as possible, so as to reduce carbon emissions(3)
Layout of stations and other public transport facilities: the layout of stations can affect the direction of bus lines, the speed change of bus vehicles, and the full load rate of the whole bus line [21]. The overall direction of the bus line is directly determined by the initial and terminal stations and the larger hub stations in the line: the spacing between stations can affect the formal speed of buses. If the stations are too dense, buses cannot maintain a relatively uniform driving speed, which may also lead to a low bus load rate, which may lead to higher carbon emissions of the line: on the contrary, the stations are sparse. It is not conducive to the comprehensive dispatching of public transport and cannot attract more passengers to travel by public transport. It may also lead to the high load rate of public transport vehicles between local stations, resulting in high carbon emissions of public transport vehicles(4)
Other aspects, including the driving level of bus drivers: as we all know, the energy consumption of vehicles running at a relatively uniform speed is less than that of vehicles during braking and starting, while the service characteristics of conventional public transport determine that public transport vehicles have more starting and braking processes. Therefore, the excellent driving level of bus drivers can be reflected in how to ensure that the driving distance between the two stops is high and maintain a relatively stable speed [22]. A good bus driver can keep a relatively stable speed between the two stops, so that the bus can produce less carbon emissionsHowever, for the first aspect of the driving level of bus drivers, human factors are too heavy, which is related to the driver’s psychology, physiology, personal habits, and other factors. It is not suitable for quantification and calculation, and it is difficult to put forward quantifiable improvement suggestions when studying it. Second, the transformation and renewal of public transport equipment cannot be completed overnight. Moreover, combined with the current loss stage of conventional public transport in many cities, the transformation and renewal process of equipment is limited, which cannot meet the urgent needs of low-carbon optimization of conventional public transport network. Therefore, for the effective reduction of carbon emission of the current conventional bus network, we should start with the optimization and adjustment of the network, adjust the unreasonable lines in the network and improve the transportation efficiency, save energy consumption, and realize low-carbon optimization of conventional bus line network [23].


## 3.2.4. Basic Principles of Low-Carbon Optimization of Conventional Bus Line Network

The low-carbon optimization of conventional bus line network, like the general optimization of bus line network, needs to follow certain principles, so as to make the optimization present the results consistent with the optimization objectives. The principles of low-carbon optimization of conventional public transport network are as follows:(1)
Travel convenience principle: the low-carbon optimization of conventional public transport is not a total negation of the yuan public transport network, nor does it conflict with the original travel convenience needs of the conventional public transport network, but to retain the original travel convenience principle here [24]. Equivalent to the conventional bus network after low-carbon optimization, it should also have the attributes of good accessibility, less transfer times, high network efficiency, short travel time, and so on(2)
The principle of effectively reducing carbon emissions: the purpose of low-carbon optimization of conventional public transport is to make the bus network meet the requirements of reducing carbon emissions through reasonable adjustment of conventional public transport network. It is equivalent to adding an item to the attribute of the original public transport network to reduce carbon emissions, making conventional public transport more competitive in public transport. Therefore, this is also one of the basic requirements for low-carbon optimization of conventional bus line network [25](3)
The principle of effective utilization: the purpose of optimization is to enable the existing network to meet the travel demand and have certain functions, that is, to reduce carbon emissions. Instead of the general abandonment of the existing conventional public transport network, the optimization is based on the original wired network, taking the essence to its dregs, that is, reasonable line reservation, abandoning the unreasonable ones, and adjusting the abandonment part by adding and adjusting the lines


## 3.3. Optimization of New Energy Bus Network

### 3.3.1. Bus Line Network Optimization Theory

The optimization of public transport network optimization absorbs the essence of many disciplines such as operational research, system theory, and transportation planning theory. It aims to ease the pressure on city traffic and constantly study and develop the potential of public transport, so as to establish convenient and fast public transportation network. The optimization of public transportation network is based on the original public transportation lines, through the scientific allocation of public transportation vehicles, funds and other needs, and the reasonable adjustment of the layout of public transportation lines and stations, so as to reduce the operation cost of public transportation and make passengers travel with low cost and high efficiency. Public transport network optimization is mostly carried out from the aspects of public transport lines, the layout of public transport stations, and the scheduling of public transport vehicles. Through public transport network optimization, the total transportation capacity of the whole public transport network can be adjusted, and the convenience of conventional public transport can be improved, giving full play to the functions of safety, fairness, and quickness. It is of great significance to improve urban traffic efficiency and save social public travel resources. Therefore, public transport network optimization plays a very important role in the optimization of the whole public transport system.


### 3.3.2. Principles for Optimization of New Energy Public Transport Network

Public transport network is the main bearer of urban public transport passenger flow. A reasonable public transport network layout can give full play to the advantages of public transport, improve operation efficiency, improve service level, alleviate the tension of public transport, facilitate residents’ travel, reduce the traffic pressure of urban road system, and give full play to the maximum efficiency of limited urban land. Therefore, the optimization of public transport network should follow the following principles:(1)
Minimum traffic demand: through scientific urban layout and network planning, the traffic volume required to maintain the operation and development of the city and society is minimized(2)
Best service level: urban public transport system can meet various traffic needs to the greatest extent. The whole public transport system operates in a safe, punctual, large volume, and high efficiency manner(3)
Minimum energy occupation: the traffic energy consumption per unit output value of the city is the lowest, and the construction, maintenance, use, and management of urban public transport system occupy the lowest land and human resources(4)
Minimum environmental impact: urban public transport has the least impact and interference on people’s living environment and activities


### 3.3.3. Factors Affecting the Optimization of New Energy Public Transport Network

The optimization of new energy public transport network is a very complex process, involving many factors. Generally speaking, it mainly includes the following aspects.(1) Traffic Demand. Traffic demand is the most critical factor in the optimization of urban public transport network. Traffic demand mainly includes the number of passengers in the public transport network, the geographical distribution of passengers, and the choice of bus routes for passengers to travel. A good bus network should be able to meet the needs of the vast majority of passengers, make passengers reach their destination as far as possible, and reduce passengers’ travel time and waiting time as far as possible. In addition, in areas with large passenger flow demand, there should be a corresponding bus line network with large passenger carrying capacity to match it, while in areas with too small passenger flow demand, the opening of bus lines should be cancelled.(2) Road Conditions. Urban road network is an important basis for the design of public transport network. For urban public transport network planning, without the premise of urban road network, public transport network cannot exist alone. However, the layout of public transport network is only carried out on the roads that meet certain conditions (such as pavement conditions, geometric line shape, and capacity constraints). Therefore, when planning the public transportation network, we can combine the roads suitable for the layout of public transportation lines to form a “basic road network” and then plan the public transportation network on this “basic road network.”(3) Station Conditions. There are usually two ways to set the starting and ending points in bus line planning. One is to generate a bus line network and then determine the starting and ending points and the scale of starting and ending points according to the number of bus lines and the allocation of resources such as bus vehicles. The other is to plan the bus lines one by one according to the starting point and ending point of the bus lines set in advance and then form a complete urban bus line network.(4) Vehicle Condition. Vehicle conditions include physical characteristics (vehicle length, width, weight, etc.), operating performance and maximum passenger capacity of the vehicle.(5) Benefit Factors. Benefit refers to the income obtained from the investment of each unit (per shift, per kilometer, etc.) of the public transport network. The specific indicators reflecting the service income are as follows: income per train, income per kilometer, number of trips per month, number of passengers per train, operating cost-benefit ratio, number of passengers per kilometer, etc. These indicators can not only reflect the operation of each bus line but also reflect the passenger flow demand of bus lines and the service attraction of bus lines. Therefore, this factor needs to be considered when planning the public transportation network.(6) Policy Factors. In the planning process of urban public transport network, some relevant policies and regulations of the city need to be taken into account, such as land development policy, traffic management policy, and social equity security policy. In addition to the above factors, some other factors will also affect the planning of urban public transport network, mainly including the economic situation of the city, the culture of the city, and the travel habits of urban residents. In a word, the above factors need to be comprehensively considered in the process of urban public transport network planning.


### 3.3.4. Common Modes of New Energy Public Transport Network Optimization

At present, there are two common modes of new energy bus network optimization: solution optimization method and certificate optimization method.(1) Worry Relief Method. The optimization method is also called the forward method. According to the given passenger flow OD data, urban road network, and other public transport data, the optimal public transport network is obtained by solving the optimal solution of the corresponding objective function and constraints. The flow chart is shown in Figure 2.Figure 2
Worry relief method.(2) Syndrome Excellence Method. The optimization method is also called test algorithm. Among several alternative bus line networks, the selected one is selected as the optimal bus line network according to the evaluation function. The flow chart is shown in Figure 3.Figure 3
Method of proving excellence.


## 3.3.1. Bus Line Network Optimization Theory

The optimization of public transport network optimization absorbs the essence of many disciplines such as operational research, system theory, and transportation planning theory. It aims to ease the pressure on city traffic and constantly study and develop the potential of public transport, so as to establish convenient and fast public transportation network. The optimization of public transportation network is based on the original public transportation lines, through the scientific allocation of public transportation vehicles, funds and other needs, and the reasonable adjustment of the layout of public transportation lines and stations, so as to reduce the operation cost of public transportation and make passengers travel with low cost and high efficiency. Public transport network optimization is mostly carried out from the aspects of public transport lines, the layout of public transport stations, and the scheduling of public transport vehicles. Through public transport network optimization, the total transportation capacity of the whole public transport network can be adjusted, and the convenience of conventional public transport can be improved, giving full play to the functions of safety, fairness, and quickness. It is of great significance to improve urban traffic efficiency and save social public travel resources. Therefore, public transport network optimization plays a very important role in the optimization of the whole public transport system.


## 3.3.2. Principles for Optimization of New Energy Public Transport Network

Public transport network is the main bearer of urban public transport passenger flow. A reasonable public transport network layout can give full play to the advantages of public transport, improve operation efficiency, improve service level, alleviate the tension of public transport, facilitate residents’ travel, reduce the traffic pressure of urban road system, and give full play to the maximum efficiency of limited urban land. Therefore, the optimization of public transport network should follow the following principles:(1)
Minimum traffic demand: through scientific urban layout and network planning, the traffic volume required to maintain the operation and development of the city and society is minimized(2)
Best service level: urban public transport system can meet various traffic needs to the greatest extent. The whole public transport system operates in a safe, punctual, large volume, and high efficiency manner(3)
Minimum energy occupation: the traffic energy consumption per unit output value of the city is the lowest, and the construction, maintenance, use, and management of urban public transport system occupy the lowest land and human resources(4)
Minimum environmental impact: urban public transport has the least impact and interference on people’s living environment and activities


## 3.3.3. Factors Affecting the Optimization of New Energy Public Transport Network

The optimization of new energy public transport network is a very complex process, involving many factors. Generally speaking, it mainly includes the following aspects.(1) Traffic Demand. Traffic demand is the most critical factor in the optimization of urban public transport network. Traffic demand mainly includes the number of passengers in the public transport network, the geographical distribution of passengers, and the choice of bus routes for passengers to travel. A good bus network should be able to meet the needs of the vast majority of passengers, make passengers reach their destination as far as possible, and reduce passengers’ travel time and waiting time as far as possible. In addition, in areas with large passenger flow demand, there should be a corresponding bus line network with large passenger carrying capacity to match it, while in areas with too small passenger flow demand, the opening of bus lines should be cancelled.(2) Road Conditions. Urban road network is an important basis for the design of public transport network. For urban public transport network planning, without the premise of urban road network, public transport network cannot exist alone. However, the layout of public transport network is only carried out on the roads that meet certain conditions (such as pavement conditions, geometric line shape, and capacity constraints). Therefore, when planning the public transportation network, we can combine the roads suitable for the layout of public transportation lines to form a “basic road network” and then plan the public transportation network on this “basic road network.”(3) Station Conditions. There are usually two ways to set the starting and ending points in bus line planning. One is to generate a bus line network and then determine the starting and ending points and the scale of starting and ending points according to the number of bus lines and the allocation of resources such as bus vehicles. The other is to plan the bus lines one by one according to the starting point and ending point of the bus lines set in advance and then form a complete urban bus line network.(4) Vehicle Condition. Vehicle conditions include physical characteristics (vehicle length, width, weight, etc.), operating performance and maximum passenger capacity of the vehicle.(5) Benefit Factors. Benefit refers to the income obtained from the investment of each unit (per shift, per kilometer, etc.) of the public transport network. The specific indicators reflecting the service income are as follows: income per train, income per kilometer, number of trips per month, number of passengers per train, operating cost-benefit ratio, number of passengers per kilometer, etc. These indicators can not only reflect the operation of each bus line but also reflect the passenger flow demand of bus lines and the service attraction of bus lines. Therefore, this factor needs to be considered when planning the public transportation network.(6) Policy Factors. In the planning process of urban public transport network, some relevant policies and regulations of the city need to be taken into account, such as land development policy, traffic management policy, and social equity security policy. In addition to the above factors, some other factors will also affect the planning of urban public transport network, mainly including the economic situation of the city, the culture of the city, and the travel habits of urban residents. In a word, the above factors need to be comprehensively considered in the process of urban public transport network planning.


## 3.3.4. Common Modes of New Energy Public Transport Network Optimization

At present, there are two common modes of new energy bus network optimization: solution optimization method and certificate optimization method.(1) Worry Relief Method. The optimization method is also called the forward method. According to the given passenger flow OD data, urban road network, and other public transport data, the optimal public transport network is obtained by solving the optimal solution of the corresponding objective function and constraints. The flow chart is shown in Figure 2.Figure 2
Worry relief method.(2) Syndrome Excellence Method. The optimization method is also called test algorithm. Among several alternative bus line networks, the selected one is selected as the optimal bus line network according to the evaluation function. The flow chart is shown in Figure 3.Figure 3
Method of proving excellence.


## 4. Application Examples

### 4.1. Site Demand Matrix

In order to verify the superiority of the algorithm, the bus network diagram is provided, as shown in Figure4. The bus network consists of 15 stations, including three starting stations s=1,2,3 and five terminal stations P=21,22,23,24,25 and seven intermediate stations. Among them, the connecting line between stations represents the feasible path of each station, and the number on the connecting line of each station is the ideal driving time of public transport between stations.Figure 4
Bus network.


### 4.2. Results and Analysis

Comprehensively considering the OD demand matrix, take the total number of bus linesC=6, the weight of total passenger travel time γ1=1.5, the weight of total passenger transfer times γ2=2.5, and the average transfer time t0=1.5. Optimize the objective function with simulated annealing algorithm, basic ant colony algorithm, and improved simulated annealing ant colony algorithm, respectively, and program with MATLAB. The operating environment CPU is Intel Core 13 processor and 4G memory.


#### 4.2.1. Solution of Simulated Annealing Algorithm

After many tests, take the initial temperatureθ=20000°C, the termination temperature θ1=1°C, and the annealing speed α=0.95, and test 20 times to obtain the optimal objective function value curve, as shown in Figure 5. The corresponding optimal lines are {1 6 5 11 10 9 8 16 17 21}, {2 4 1 7 8 16 18 20 17 22}, {3 11 10 9 13 14 15 16 18 19 23}, {2 5 6 11 10 9 8 16 19 24}, {3 11 10 9 13 15 19 25}, and {3 11 10 12 14 15 19 25}.Figure 5
Optimization process of simulated annealing algorithm.


#### 4.2.2. Solution of Basic Ant Colony Algorithm

The initial pheromone quantityQ=200, the maximum number of iterations nmax=30 (when nmax>30, the ant colony search is slow and prone to stagnation), and the pheromone persistence coefficient ρ=0.85. Test 20 times to obtain the optimal objective function value curve, as shown in Figure 6. The corresponding optimal routes are {1 6 7 9 13 14 19 18 17 21}, {2 4 1 6 7 8 16 18 17 22}, {3 12 10 9 13 15 19 23}, {2 5 6 7 9 13 14 19 24}, {2 5 6 7 9 13 14 19 25}, and {3 11 6 7 8 16 18 20 17 22}.Figure 6
Optimization process of basic ant colony algorithm.


#### 4.2.3. Solution of Simulated Annealing Improved Ant Colony Algorithm

The initial temperatureB=20000°C, the termination temperature θ1=1°C, the annealing speed α=0.6, the initial pheromone quantity Q=200, the maximum number of iterations nmax=50, the pheromone persistence coefficient ρ=0.85, τmin=0.05, τmin=0.1, and the optimal objective function value curve is obtained after 20 tests, as shown in Figure 7. The corresponding optimal routes are {3 11 6 7 8 16 18 20 17 21}, {3 12 14 13 9 8 16 17 22}, {1 6 11 10 13 15 14 19 23}, {2 5 6 11 10 13 14 19 24}, {3 11 5 6 1 7 8 16 18 19 25}, and {2 4 1 6 11 10 13 14 19 24}.Figure 7
Optimization process of simulated annealing improved mosquito swarm algorithm.


#### 4.2.4. Algorithm Comparison

The author uses simulated annealing algorithm, basic ant colony algorithm, and improved simulated annealing ant colony algorithm to optimize the objective function for 20 times and sets the average solution time ast. The comparison results are shown in Table 1.Table 1
Comparison of results of different algorithms.
AlgorithmOptimal solutionWorst solutionMean solutiont/sSimulated annealing204122347821694.3166.674Basic ant colony204782359822874.956.952Simulated annealing improved ant colony200652235821472.214.215It can be seen from Table1 that the improved ant colony algorithm of simulated annealing is better than the basic ant colony algorithm and simulated annealing algorithm in solving the design of public transport network and has the characteristics of fast solution speed and more accurate optimization results.


## 4.1. Site Demand Matrix

In order to verify the superiority of the algorithm, the bus network diagram is provided, as shown in Figure4. The bus network consists of 15 stations, including three starting stations s=1,2,3 and five terminal stations P=21,22,23,24,25 and seven intermediate stations. Among them, the connecting line between stations represents the feasible path of each station, and the number on the connecting line of each station is the ideal driving time of public transport between stations.Figure 4
Bus network.


## 4.2. Results and Analysis

Comprehensively considering the OD demand matrix, take the total number of bus linesC=6, the weight of total passenger travel time γ1=1.5, the weight of total passenger transfer times γ2=2.5, and the average transfer time t0=1.5. Optimize the objective function with simulated annealing algorithm, basic ant colony algorithm, and improved simulated annealing ant colony algorithm, respectively, and program with MATLAB. The operating environment CPU is Intel Core 13 processor and 4G memory.


### 4.2.1. Solution of Simulated Annealing Algorithm

After many tests, take the initial temperatureθ=20000°C, the termination temperature θ1=1°C, and the annealing speed α=0.95, and test 20 times to obtain the optimal objective function value curve, as shown in Figure 5. The corresponding optimal lines are {1 6 5 11 10 9 8 16 17 21}, {2 4 1 7 8 16 18 20 17 22}, {3 11 10 9 13 14 15 16 18 19 23}, {2 5 6 11 10 9 8 16 19 24}, {3 11 10 9 13 15 19 25}, and {3 11 10 12 14 15 19 25}.Figure 5
Optimization process of simulated annealing algorithm.


### 4.2.2. Solution of Basic Ant Colony Algorithm

The initial pheromone quantityQ=200, the maximum number of iterations nmax=30 (when nmax>30, the ant colony search is slow and prone to stagnation), and the pheromone persistence coefficient ρ=0.85. Test 20 times to obtain the optimal objective function value curve, as shown in Figure 6. The corresponding optimal routes are {1 6 7 9 13 14 19 18 17 21}, {2 4 1 6 7 8 16 18 17 22}, {3 12 10 9 13 15 19 23}, {2 5 6 7 9 13 14 19 24}, {2 5 6 7 9 13 14 19 25}, and {3 11 6 7 8 16 18 20 17 22}.Figure 6
Optimization process of basic ant colony algorithm.


### 4.2.3. Solution of Simulated Annealing Improved Ant Colony Algorithm

The initial temperatureB=20000°C, the termination temperature θ1=1°C, the annealing speed α=0.6, the initial pheromone quantity Q=200, the maximum number of iterations nmax=50, the pheromone persistence coefficient ρ=0.85, τmin=0.05, τmin=0.1, and the optimal objective function value curve is obtained after 20 tests, as shown in Figure 7. The corresponding optimal routes are {3 11 6 7 8 16 18 20 17 21}, {3 12 14 13 9 8 16 17 22}, {1 6 11 10 13 15 14 19 23}, {2 5 6 11 10 13 14 19 24}, {3 11 5 6 1 7 8 16 18 19 25}, and {2 4 1 6 11 10 13 14 19 24}.Figure 7
Optimization process of simulated annealing improved mosquito swarm algorithm.


### 4.2.4. Algorithm Comparison

The author uses simulated annealing algorithm, basic ant colony algorithm, and improved simulated annealing ant colony algorithm to optimize the objective function for 20 times and sets the average solution time ast. The comparison results are shown in Table 1.Table 1
Comparison of results of different algorithms.
AlgorithmOptimal solutionWorst solutionMean solutiont/sSimulated annealing204122347821694.3166.674Basic ant colony204782359822874.956.952Simulated annealing improved ant colony200652235821472.214.215It can be seen from Table1 that the improved ant colony algorithm of simulated annealing is better than the basic ant colony algorithm and simulated annealing algorithm in solving the design of public transport network and has the characteristics of fast solution speed and more accurate optimization results.


## 4.2.1. Solution of Simulated Annealing Algorithm

After many tests, take the initial temperatureθ=20000°C, the termination temperature θ1=1°C, and the annealing speed α=0.95, and test 20 times to obtain the optimal objective function value curve, as shown in Figure 5. The corresponding optimal lines are {1 6 5 11 10 9 8 16 17 21}, {2 4 1 7 8 16 18 20 17 22}, {3 11 10 9 13 14 15 16 18 19 23}, {2 5 6 11 10 9 8 16 19 24}, {3 11 10 9 13 15 19 25}, and {3 11 10 12 14 15 19 25}.Figure 5
Optimization process of simulated annealing algorithm.


## 4.2.2. Solution of Basic Ant Colony Algorithm

The initial pheromone quantityQ=200, the maximum number of iterations nmax=30 (when nmax>30, the ant colony search is slow and prone to stagnation), and the pheromone persistence coefficient ρ=0.85. Test 20 times to obtain the optimal objective function value curve, as shown in Figure 6. The corresponding optimal routes are {1 6 7 9 13 14 19 18 17 21}, {2 4 1 6 7 8 16 18 17 22}, {3 12 10 9 13 15 19 23}, {2 5 6 7 9 13 14 19 24}, {2 5 6 7 9 13 14 19 25}, and {3 11 6 7 8 16 18 20 17 22}.Figure 6
Optimization process of basic ant colony algorithm.


## 4.2.3. Solution of Simulated Annealing Improved Ant Colony Algorithm

The initial temperatureB=20000°C, the termination temperature θ1=1°C, the annealing speed α=0.6, the initial pheromone quantity Q=200, the maximum number of iterations nmax=50, the pheromone persistence coefficient ρ=0.85, τmin=0.05, τmin=0.1, and the optimal objective function value curve is obtained after 20 tests, as shown in Figure 7. The corresponding optimal routes are {3 11 6 7 8 16 18 20 17 21}, {3 12 14 13 9 8 16 17 22}, {1 6 11 10 13 15 14 19 23}, {2 5 6 11 10 13 14 19 24}, {3 11 5 6 1 7 8 16 18 19 25}, and {2 4 1 6 11 10 13 14 19 24}.Figure 7
Optimization process of simulated annealing improved mosquito swarm algorithm.


## 4.2.4. Algorithm Comparison

The author uses simulated annealing algorithm, basic ant colony algorithm, and improved simulated annealing ant colony algorithm to optimize the objective function for 20 times and sets the average solution time ast. The comparison results are shown in Table 1.Table 1
Comparison of results of different algorithms.
AlgorithmOptimal solutionWorst solutionMean solutiont/sSimulated annealing204122347821694.3166.674Basic ant colony204782359822874.956.952Simulated annealing improved ant colony200652235821472.214.215It can be seen from Table1 that the improved ant colony algorithm of simulated annealing is better than the basic ant colony algorithm and simulated annealing algorithm in solving the design of public transport network and has the characteristics of fast solution speed and more accurate optimization results.


## 5. Conclusion

(1)
Considering the total travel time and the total transfer times of passengers, the model of public transport network is established combined with OD matrix. The initial suboptimal public transport route set is generated by simulated annealing algorithm. The initial suboptimal route set is iteratively optimized by improved ant colony algorithm, and the optimal public transport route set is finally obtained by optimizing the objective function(2)
Compared with the existing research, the improved ant colony algorithm based on simulated annealing effectively solves the design of public transport network. The optimization scheme can greatly reduce the number of passenger transfers and the total travel time of passengers and has good applicability(3)
The improved ant colony algorithm of simulated annealing can find the optimal solutions of the three algorithms when solving the problem of public transport network design. The worst solution and average solution are better than the solutions of basic ant colony and simulated annealing algorithm. The solution efficiency is 10.6 times that of simulated annealing algorithm and 3.5 times that of basic ant colony algorithm(4)
Based on the solution of the model by ant colony algorithm, the practical application of the model is analyzed. The results show that through the restriction of point, line, and surface, not only the reliability and calculation accuracy of the algorithm are improved, but also the number of feasible line networks is reduced, unnecessary calculation is eliminated in the optimization stage, and the obtained bus line network is more reasonable and scientific



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*Source: 1528211-2022-05-05.xml*