# Transportation Structure Analysis Using SD-MOP in World Modern Garden City: A Case Study in China

Authors: Jiuping Xu; Jing Yang; Liming Yao
Journal: Discrete Dynamics in Nature and Society
 (2012)

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## Abstract

The idea of the “garden city” was developed theoretically to offer solutions to serious city development problems such as traffic congestion, population, and environmental pollution, among which the transportation is considered the most important. The question is how to develop balanced transportation in a garden city. Transportation is a complex system, particularly in a garden city. Therefore, we establish a new approach named the transportation multiobjective optimization system dynamics  (SD-MOP) model, which firstly calculates the optimal proportion of different transport means with an MOP approach and then applies them to the dynamic transportation system to analyze the results and analyze the influence on the whole system using different transportation means variation. In this paper, we take Chengdu as an example, one of the few cities in the world declared as building a garden city, and then develop some recommendations about world modern garden city transportation system development.


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## Body

## 1. Introduction

It is generally recognized that cities are experiencing huge change in terms of their development and mobility patterns, while transportation, and  will continue to plays, a critical role in city development [1–3]. Energy consumption is one of the most severe transportation problems. IEA [4] argues that transport plays an important role in addressing the challenges of climate change mitigation as it consumes nearly half of global oil and contributes 25% of total fossil fuel combustion-related CO2 emissions of the world, and road transport is responsible for about 75% of the emissions from the transport sector. Petri et al. [5] compare the development of transport and energy use with a focus on CO2 emissions and suggest a more sustainable passenger transport system. Dominic [6] examines recent temporal and spatial trends and forecasts in energy consumption, energy efficiency, and energy costs in the transport sector across Europe. Meanwhile, land use, health effects, employment, population growth, and transport alternatives are all considered as related to the transportation problems. Frank [7] focused on land use, noting that, with different land uses, traffic designs need to be different. Messenger and Ewing [8] think that employment, the balance of living space, ownership, and the public transport service level affect people’s transport choice. Martin [9] investigates the association between means of transportation to work and overweight and obesity. In this paper, transportation structure is our main concern to the research. Transportation structure is the proportion of traffic amount carried by different transport means in extent of time and space. As the transportation structure directly influences resource allocation, a reasonable urban transportation structure can contribute to the rational use of resources and ensure a well-functioning system [10]. Although these studies have contributed a lot to transportation, we feel that all of the studies had not analyzed the transportation in a systematic and dynamic way. Thus, this paper seeks to further research in solving transportation problem and differs from its predecessors and we hope to introduce completely and accurately new viewpoints and models and research.China is the largest developing country in the world. With rapid process of industrialization and urbanization, China has maintained an extensive growth in economic development while the deficiency of transportation began to emerge and became an urgent problem for us to deal with. Traffic congestion exists widely in metropolitan [11] capacity excess or overload caused by road passenger volume [12], which has already led to problems such as environmental pollution, lack of rational planning [13], economic intervention, and greenhouse gas emission excess [14]. Steps need to be taken to prevent the situation from deteriorating, otherwise, in return, this may hinder the development of the world modern garden city.The “garden city” was first proposed by Howard [15] in the late 19th century, which came into being with the overcrowded, pollution, and epidemic spreading problems. It focuses on the coalition of city and countryside in essence and, later, makes some city planning about city scale, layout and structure, population density, and green belt [16]. A garden city is designed for health, life, and industry; it contains both rural and urban areas and has a strictly controlled city scale. It is the farmlands and towns around the central cities that control the expanding of urban land without limit. The garden city can ensure every resident to be close to nature and surrounded by self-sufficient farmland; especially in an ideal garden city, the land belongs to the public and under the responsibility of a professional committee. Therefore, the world modern garden city has its own features that differ from the ordinary city. Firstly, the form and pattern of garden city are multicenter, networking, and clustered in development along with being humanized in urban spatial structure. Secondly, harmonious nature and society: there are two kinds of harmony which refer to the strengthening of ecology and environment, social welfare, and wellbeing. Thirdly, the development path: the city aims to modern service industry and headquarters economy as the core, for the direction of high-tech industry, based on the powerful modern manufacturing industry and agriculture, all of which projects to be an internationally regional hub and central city on the basis of to be western and national central city. Fourthly, land use layout and transportation: it is the decentralized layout that is put into use in garden city, while in ordinary city, the public buildings are always arranged in concentrated form.To realize the construction of world modern garden city, transportation should play its due role in it and act as a stimulus to promote it. As for the transportation in garden city, we think it is the traffic arteries that connect the central city with peripheral group city, with the agricultural land scattered around it, which finally realize the garden city. And the key way to build a world modern garden city is to promote the modernized and intellectualized transportation, that is, to make the linking of the urban and rural areas come true. In garden city, environmental and faster high-speed railway is the best choice to create the traffic circle in connecting between cities. In order to construct garden city, the transportation should match the development of garden city, and, in turn, the garden city will surely promote the transportation construction. Therefore, a strategy is needed to balance transportation system development and garden city construction, as transportation is an essential element of its success. Since regional transportation system is constantly changing, it is necessary to find a dynamic simulation method. System dynamics (SD) approaches as a modeling tool to provide a flexible way of building simulation models from causal loop or stock and flow diagrams. Therefore, to reflect the dynamic characteristics of garden city transportation system, the SD approach is the main methodology used in this paper, combined with multiobjective optimization (MOP) for its effectiveness.The aim of this paper is to propose a system dynamics and multiobjective programming integrated support model to predict and adjust transport structure for the modern garden city in the world. The remainder of this paper is structured as follows. Section2 describes the general system and solution approach problem. Section 3 develops a detailed garden city transportation system based on the SD-MOP model. In Section 4, Chengdu in China is discussed as a case study. Finally, we present some conclusions and proposals for the development of the transportation system in Chengdu and other garden cities in the world.


## 2. Problem Description

In this Section, a description of the problem is discussed, then a general framework to address the given problem is proposed. We give a basic background for our study.


### 2.1. System Description

It is of great significance to analyze logical urban transportation system in Chengdu, because it can assist in the development and management of the transportation plan and has a practical significance in helping relieving city traffic congestion [17]. Transport structure is an important factor in the whole system; a reasonable logic transport structure is a part of city planning and the adjustment of industrial structure, meanwhile, it guarantees minimum time waste, costs, and environment pollution.As has been mentioned, an urban transportation system is a complex system and is especially important in the development of the garden city. With population, transport means, transport congestion, transport demand, and vehicle travel time are emerging as concerns in transportation system analysis. These elements are highly interrelated, but they are not the only factors that affect the system, there is also social, economic, political, environmental, and technical factors [17]. From previous research [18, 19], we assume that the garden city transportation system consists of five subsystems: the economic subsystem, the environmental subsystem, the traffic congestion subsystem, the policy management subsystem, and the traffic mode subsystem. The whole system is constantly changing and has an interrelationship with each other. Figure 1 shows the relationships between them. With economic development, there are more travel demand and transport choices or modes, and if not managed properly, they will lead to traffic congestion, which can result in environmental pollution, and, in turn, impacts the economy. However, through manual intervention, policy management can be used to control these effects when necessary.Figure 1
The subsystems of garden city transportation system.


### 2.2. Method Design

System dynamics (SD) is a simulation technology that studies complex systems based on feedback control theory. It establishes synthetical models using system structures, the relation of consequent to antecedent and feedback loops, and, further, to find the solution to system performance using simulations. SD has been applied to a number of studies, not only the social sciences field, but also the agricultural practices [20], environmental issues [21], and economic controls [22] and has proven to be especially appropriate for modeling problems. Meanwhile, a number of system dynamics (SD) approaches have been used to do transportation modeling [23, 24], which give us successful examples for our research. SD can be used to forecast the trends in the next ten years by using certain parameters, but cannot be used to estimate exact levels reliably [25–27]. Therefore, while a system dynamics method is used as the main approach, we introduce multiobjective programming in the system dynamics model to develop an integrated model, which we call a system dynamics multiobjective programming model (SD-MOP), for the solution. The SD-MOP model not only provide better understanding of complex problems but also have considered the multiple objectives and also involve expert opinions in the decision. A general framework of the modeling process is shown in Figure 2. In a garden city transportation system decision process, a thorough analysis of the decision problem is conducted. Then, using the system dynamics (SD) approach, a causal loop diagram and detailed flow diagram are established. We run a series of MOPs to get the optimum value of those sensitive variables, and place these values into the SD model for simulation. Based on results of the SD-MOP integrated approach, different policy experiments are compared to choose the best route. If we are not satisfied with the result of the simulation, we can adjust the MOP models to yield better results; otherwise, the decision process is ended.Figure 2
The general framework of the modeling process.


### 2.3. Basic Assumption

The basic assumptions of a garden city transportation system are as follows.(1)
The main environmental pollution emissions we consider are CO2, excluding the exhausted gas from motorcycles.(2)
We consider private cars, buses, taxis, and rail as the four main transportation means that directly influence transportation congestion and ignore others such as bicycles, pedestrians, and others.(3)
The influence of employment is ignored in the whole system so the employment is ignored.(4)
We use gross domestic product (GDP) to measure the economic development.(5)
The purpose of this study is to promote coordinated economic development, environmental protection, policy management, and population through the optimization of transportation construction and structure.


### 2.4. Index System

The transportation system is one of the most complex systems in modern city. Similarly, the analysis of transportation has been a vital element in world modern garden city. Factors analysis is an effective way to understand the structure and function of a system well. According to the subsystems of garden city transportation system (Figure1) and the characteristic of world modern garden city, we analyze the subdivision of each subsystem by selecting variables and influential factors synthetically based on the relative theoretical basis and the existing and our own research foundation, in principle of integrality, objectivity, scientificity, nonlinearity, practicality, and availability. Here, we list the main variables and influential factors of this model in Table 1 (variables and symbols in garden city transportation system). In order to facilitate our research and establish a mathematical model, we sort them according to the symbol of the name.Table 1
Variables and symbols in garden city transportation system.
Sort
The meaning of variables
Variable units
Symbol
1
Road passenger capacity
Yuan
LE
V
CR
2
Railway passenger capacity
Yuan
LE
V
CRW
3
Exhaust emission
g
LE
V
EE
4
Emission intensity
g
LE
V
EI
5
Environmental pollution
L
LE
V
EP
6
Fuel consumption volume
L/100 km
LE
V
FC
7
Gross domestic product
Ten thousand
LE
V
GDP
8
Investment of bus
Yuan
LE
V
I
1
9
Investment of taxi
Yuan
LE
V
I
2
10
Investment of railway
Yuan
LE
V
I
3
11
Investment of infrastructure
Yuan
LE
V
II
12
Investment of public transportation
Km
LE
V
IPT
13
Investment of road
Yuan
LE
V
IR
14
Length of road
Km
LE
V
LR
15
Length of railway
Km
LE
V
LRW
16
Number of buses
Ten thousand
LE
V
N
1
17
Number of taxies
Ten thousand
LE
V
N
2
18
Number of railbus
Ten thousand
LE
V
N
3
19
Number of private cars
Ten thousand
LE
V
N
4
20
Private car increment
Ten thousand
LE
V
PC
21
Turnover of bus
Person/km
LE
V
T
1
22
Turnover of taxi
Person/km
LE
V
T
2
23
Turnover of railway
Person/km
LE
V
T
3
24
Turnover of private car
Person/km
LE
V
T
4
25
Traffic intensity
Person
LE
V
TI
26
Traffic load
Person/yuan
LE
V
TL
27
Total population
Ten thousand
LE
V
TP
28
Travel volume of bus
Person/day
LE
V
V
1
29
Travel volume of taxi
Person/day
LE
V
V
2
30
Travel volume of railway
Person/day
LE
V
V
3
31
Travel volume of private car
Person/day
LE
V
V
4
32
Travel volume of public transport
Person/day
LE
V
VPT
33
Travel volume of total trip
Person/day
LE
V
VT
34
Rate of average trip
%
RA
T
A
35
Transformation coefficient of bus
km/yuan
RA
T
C
1
36
Transformation coefficient of taxi
km/yuan
RA
T
C
2
37
Transformation coefficient of railway
km/yuan
RA
T
C
3
38
Transformation coefficient of private car
km/yuan
RA
T
C
4
39
Coefficient of discharge
g/L
RA
T
D
40
Coefficient of economic decrease
Yuan/g
RA
T
ED
41
Coefficient of emission factor
g/person
RA
T
EF
42
Coefficient of environmental influence
No  dimension
RA
T
EI
43
GDP growth rate
%
RA
T
GDP
44
Investment proportion of infrastructure
%
RA
T
II
45
Investment proportion of public transportation
%
RA
T
IPT
46
Investment proportion of road
%
RA
T
IR
47
Public transportation share rate
%
RA
T
S
R
1
48
Private car share rate
%
RA
T
S
R
2
49
Trip frequency of total average
Times
RA
T
TF
50
Net growth rate of population
%
RA
T
TP
51
Peak hour flow of bus
Person/times
PH
F
1
52
Peak hour flow of taxi
Person/times
PH
F
2
53
Peak hour flow of railway
Person/times
PH
F
3
54
Peak hour flow of private car
Person/times
PH
F
4
55
Travel distance of bus
km
T
D
1
56
Travel distance of taxi
km
T
D
2
57
Travel distance of railway
km
T
D
3
58
Travel distance of private car
km
T
D
4
59
Trip frequency of bus
Times
T
F
1
60
Trip frequency of taxi
Times
T
F
2
61
Trip frequency of railway
Times
T
F
3
62
Trip frequency of private car
Times
T
F
4
63
Investment proportion of bus
%
x
1
64
Investment proportion of taxi
%
x
2
65
Investment proportion of railway
%
x
3
66
Investment proportion of private car
%
x
4


## 2.1. System Description

It is of great significance to analyze logical urban transportation system in Chengdu, because it can assist in the development and management of the transportation plan and has a practical significance in helping relieving city traffic congestion [17]. Transport structure is an important factor in the whole system; a reasonable logic transport structure is a part of city planning and the adjustment of industrial structure, meanwhile, it guarantees minimum time waste, costs, and environment pollution.As has been mentioned, an urban transportation system is a complex system and is especially important in the development of the garden city. With population, transport means, transport congestion, transport demand, and vehicle travel time are emerging as concerns in transportation system analysis. These elements are highly interrelated, but they are not the only factors that affect the system, there is also social, economic, political, environmental, and technical factors [17]. From previous research [18, 19], we assume that the garden city transportation system consists of five subsystems: the economic subsystem, the environmental subsystem, the traffic congestion subsystem, the policy management subsystem, and the traffic mode subsystem. The whole system is constantly changing and has an interrelationship with each other. Figure 1 shows the relationships between them. With economic development, there are more travel demand and transport choices or modes, and if not managed properly, they will lead to traffic congestion, which can result in environmental pollution, and, in turn, impacts the economy. However, through manual intervention, policy management can be used to control these effects when necessary.Figure 1
The subsystems of garden city transportation system.


## 2.2. Method Design

System dynamics (SD) is a simulation technology that studies complex systems based on feedback control theory. It establishes synthetical models using system structures, the relation of consequent to antecedent and feedback loops, and, further, to find the solution to system performance using simulations. SD has been applied to a number of studies, not only the social sciences field, but also the agricultural practices [20], environmental issues [21], and economic controls [22] and has proven to be especially appropriate for modeling problems. Meanwhile, a number of system dynamics (SD) approaches have been used to do transportation modeling [23, 24], which give us successful examples for our research. SD can be used to forecast the trends in the next ten years by using certain parameters, but cannot be used to estimate exact levels reliably [25–27]. Therefore, while a system dynamics method is used as the main approach, we introduce multiobjective programming in the system dynamics model to develop an integrated model, which we call a system dynamics multiobjective programming model (SD-MOP), for the solution. The SD-MOP model not only provide better understanding of complex problems but also have considered the multiple objectives and also involve expert opinions in the decision. A general framework of the modeling process is shown in Figure 2. In a garden city transportation system decision process, a thorough analysis of the decision problem is conducted. Then, using the system dynamics (SD) approach, a causal loop diagram and detailed flow diagram are established. We run a series of MOPs to get the optimum value of those sensitive variables, and place these values into the SD model for simulation. Based on results of the SD-MOP integrated approach, different policy experiments are compared to choose the best route. If we are not satisfied with the result of the simulation, we can adjust the MOP models to yield better results; otherwise, the decision process is ended.Figure 2
The general framework of the modeling process.


## 2.3. Basic Assumption

The basic assumptions of a garden city transportation system are as follows.(1)
The main environmental pollution emissions we consider are CO2, excluding the exhausted gas from motorcycles.(2)
We consider private cars, buses, taxis, and rail as the four main transportation means that directly influence transportation congestion and ignore others such as bicycles, pedestrians, and others.(3)
The influence of employment is ignored in the whole system so the employment is ignored.(4)
We use gross domestic product (GDP) to measure the economic development.(5)
The purpose of this study is to promote coordinated economic development, environmental protection, policy management, and population through the optimization of transportation construction and structure.


## 2.4. Index System

The transportation system is one of the most complex systems in modern city. Similarly, the analysis of transportation has been a vital element in world modern garden city. Factors analysis is an effective way to understand the structure and function of a system well. According to the subsystems of garden city transportation system (Figure1) and the characteristic of world modern garden city, we analyze the subdivision of each subsystem by selecting variables and influential factors synthetically based on the relative theoretical basis and the existing and our own research foundation, in principle of integrality, objectivity, scientificity, nonlinearity, practicality, and availability. Here, we list the main variables and influential factors of this model in Table 1 (variables and symbols in garden city transportation system). In order to facilitate our research and establish a mathematical model, we sort them according to the symbol of the name.Table 1
Variables and symbols in garden city transportation system.
Sort
The meaning of variables
Variable units
Symbol
1
Road passenger capacity
Yuan
LE
V
CR
2
Railway passenger capacity
Yuan
LE
V
CRW
3
Exhaust emission
g
LE
V
EE
4
Emission intensity
g
LE
V
EI
5
Environmental pollution
L
LE
V
EP
6
Fuel consumption volume
L/100 km
LE
V
FC
7
Gross domestic product
Ten thousand
LE
V
GDP
8
Investment of bus
Yuan
LE
V
I
1
9
Investment of taxi
Yuan
LE
V
I
2
10
Investment of railway
Yuan
LE
V
I
3
11
Investment of infrastructure
Yuan
LE
V
II
12
Investment of public transportation
Km
LE
V
IPT
13
Investment of road
Yuan
LE
V
IR
14
Length of road
Km
LE
V
LR
15
Length of railway
Km
LE
V
LRW
16
Number of buses
Ten thousand
LE
V
N
1
17
Number of taxies
Ten thousand
LE
V
N
2
18
Number of railbus
Ten thousand
LE
V
N
3
19
Number of private cars
Ten thousand
LE
V
N
4
20
Private car increment
Ten thousand
LE
V
PC
21
Turnover of bus
Person/km
LE
V
T
1
22
Turnover of taxi
Person/km
LE
V
T
2
23
Turnover of railway
Person/km
LE
V
T
3
24
Turnover of private car
Person/km
LE
V
T
4
25
Traffic intensity
Person
LE
V
TI
26
Traffic load
Person/yuan
LE
V
TL
27
Total population
Ten thousand
LE
V
TP
28
Travel volume of bus
Person/day
LE
V
V
1
29
Travel volume of taxi
Person/day
LE
V
V
2
30
Travel volume of railway
Person/day
LE
V
V
3
31
Travel volume of private car
Person/day
LE
V
V
4
32
Travel volume of public transport
Person/day
LE
V
VPT
33
Travel volume of total trip
Person/day
LE
V
VT
34
Rate of average trip
%
RA
T
A
35
Transformation coefficient of bus
km/yuan
RA
T
C
1
36
Transformation coefficient of taxi
km/yuan
RA
T
C
2
37
Transformation coefficient of railway
km/yuan
RA
T
C
3
38
Transformation coefficient of private car
km/yuan
RA
T
C
4
39
Coefficient of discharge
g/L
RA
T
D
40
Coefficient of economic decrease
Yuan/g
RA
T
ED
41
Coefficient of emission factor
g/person
RA
T
EF
42
Coefficient of environmental influence
No  dimension
RA
T
EI
43
GDP growth rate
%
RA
T
GDP
44
Investment proportion of infrastructure
%
RA
T
II
45
Investment proportion of public transportation
%
RA
T
IPT
46
Investment proportion of road
%
RA
T
IR
47
Public transportation share rate
%
RA
T
S
R
1
48
Private car share rate
%
RA
T
S
R
2
49
Trip frequency of total average
Times
RA
T
TF
50
Net growth rate of population
%
RA
T
TP
51
Peak hour flow of bus
Person/times
PH
F
1
52
Peak hour flow of taxi
Person/times
PH
F
2
53
Peak hour flow of railway
Person/times
PH
F
3
54
Peak hour flow of private car
Person/times
PH
F
4
55
Travel distance of bus
km
T
D
1
56
Travel distance of taxi
km
T
D
2
57
Travel distance of railway
km
T
D
3
58
Travel distance of private car
km
T
D
4
59
Trip frequency of bus
Times
T
F
1
60
Trip frequency of taxi
Times
T
F
2
61
Trip frequency of railway
Times
T
F
3
62
Trip frequency of private car
Times
T
F
4
63
Investment proportion of bus
%
x
1
64
Investment proportion of taxi
%
x
2
65
Investment proportion of railway
%
x
3
66
Investment proportion of private car
%
x
4


## 3. Modelling

Referring to the system description for garden city transportation structures, we construct a corresponding model. Firstly, the system dynamics general model is constructed. Secondly, a model is established, and the system dynamics model based on multiobjective optimization (SD-MOP) is developed. Finally, the model simulation method is analyzed.


### 3.1. System Dynamics Model

This Section is divided into two parts for a particular description of the modeling; firstly, the cause-effect relationship diagram, and, secondly, the stock and flow diagram, both of which are the two main steps when using system dynamics.


#### 3.1.1. Cause-Effect Relationship Diagram

The SD model for the present study is developed for a transportation system. There are many variables in the subsystems occupying important positions in the system; thus, we build the cause-effect relationship diagram (see Figure3) by incorporating the various features associated with the system. In this Figure, the arrows denote the cause-and-effect relationships and the plus and minus signs denote the positive and negative effects, respectively. The main feedback loops are given below:Figure 3
The cause-effect relationship diagram of garden city transportation system.(1)
economic development→+ total number of vehicles →+ transportation congestion →+ environmental pollution →- economic development;
(2)
population→+ trip demand →+ total trips →+ transportation congestion →- economic development →- urban population;
(3)
economic development→+ infrastructure investment →+ road investment →+ road capacity →- transportation congestion →- economic development;
(4)
policy management→+ economic development →+ environmental pollution →- policy intervention.


#### 3.1.2. Stock and Flow Diagram

The causal relationship diagram emphasizes the feedback structure of the system, which, however, can never be comprehensive. We need to convert the causal relationship diagram into the stock and flow diagram that emphasizes the physical structure of the model, which tends to be more detailed than the causal loop diagram [28], to force us to think more specifically about the system structure. Figure 4 gives a detailed description, with the main formula as follows.Figure 4
The stock and flow diagram of garden city transportation system.Through system dynamics modeling, we can get the first-order differential equations. The change rate of the turnover of bus, thed(LEVT1(t))/dt, is dependent on the stock of the turnover of bus LEVT1(t), and there exists the basic stock OT1, which is subject to factors of transport planning, demand volume, and so on; besides, it would be effected by functioning time OT, which regularly means one year:
(3.1)d(LEVT1(t))dt=LEVT1(t)-OT1OT.
Similarly, the differential equations of the turnover of the taxi, railway, and private car are
(3.2)d(LEVT2(t))dt=LEVT2(t)-OT2OT,d(LEVT3(t))dt=LEVT3(t)-OT3OT,d(LEVT4(t))dt=LEVT4(t)-OT4OT.
Through the previous analysis, we get the main part of the links in the garden city transport system:
(3.3)LEVGDP(t)=LEVGDP(t-1)×RATGDP(t),LEVII(t)=LEVGDP(t)×RATII(t),LEVIPT(t)=LEVII(t)×RATIPT(t),LEVI1(t)=x1·LEVIPT(t),LEVN1(t)=LEVI1(t)×RATC1(t),LEVV1(t)=PHF1×TF1×LEVN1(t),LEVT1(t)=TD1×LEVV1(t).Till now, we obtained the turnover of busLEVT1, similarly, the turnover of taxi, railway, and private car can be also described as LEVT2, LEVT3, and LEVT4, and the traffic intensity can be formulated as the following:
(3.4)LEVTI(t)=LEVT1(t)+LEVT2(t)+LEVT3(t)+LEVT4(t).
Further,
(3.5)LEVTL(t)=LEVTI(t)LEVCR(t),LEVEE(t)=LEVTL(t)×RATEF,LEVEP(t)=LEVEE(t)×RATEI,-LEVGDP(t)=-LEVEP(t)×RATED,
where it can indicated that the irrational structure of transportation can increase the environmental pollution and ultimately decrease the development of economy to a certain extent. Meanwhile,
(3.6)LEVTP(t)=LEVTP(t-1)+LEVTP(t-1)×RATTP(t),LEVVT(t)=LEVTP(t)×RATTF,RATSR1=LEVVPT(t)LEVVT(t),RATSR2=LEVV4(t)LEVVT(t).
Through this circulate series of formulation, each variable (the standard variable and rate variable) is defined, thus, building the foundation of our model.


### 3.2. Multiobjective Programming Model

The purpose of multiobjective programming (MOP) is to maximize (or minimize) different multiobjective functions under a set of constraints, which is suitable for decision making in systems which have two or more goals [29]. According to the analysis of the system above, the optimization of a garden city transportation structure needs to consider the economic, social, and environmental subsystems and the transportation structure together to maximize the final benefits. Therefore, a multiobjective method can be used to solve this problem. In this Section, we will apply a multiobjective optimization model into the stock and flow diagram to measure the most optimal transportation structure to invest.


#### 3.2.1. Objective Function

As usual, the objective is to pursue the maximal economic and, social benefit with minimal environmental pollution. Here we list our three main objective functions.(1) Maximal Gross Domestic Product  (GDP)
Economy is an important part involved in garden city transportation system, and, often, we use GDP to measure the level of it, the higher the GDP we produce, the better we operate our country and more investment on transportation be conducted and the system develops better:(3.7)maxf1=LEVGDP-M1∑i=14‍LEVEPi·RATEDi,
here, the LEVGDP represents the quantity of GDP, and LEVEPi·RATEDi is the economy decrease caused by environment pollution of each transportation means. Since LEVEPi represents the environment pollution, while GDP is dimensional, we add an M1 to the balance to make them under the same unit.(2) Less Environment Pollution
As the economy develops, the public consciousness of environmental protection is aroused. The automobile exhaust emission occupies most parts in air pollution, so the optimal the transportation structure combination, the minimal air pollution and environmental damage. To achieve this, we must guarantee the least exhaust emissions:(3.8)minf2=∑i=14‍LEVEEi-δ1f1,
where LEVEEi represents the level of exhaust emission, and δ1f1 represents the environment pollution reduction resulting from economy growth investment.(3) More Social Benefits
Social benefit is also an important aspect. Because transportation system can make people’s life more convenient; if the system is not operating well, there will not be sufficient supply for people to travel. Therefore, it needs more turnover of each transport means to bear people’s travel demand, which is a criterion to measure the transport capacity:(3.9)maxf3=∑i=14‍LEVTi-M2δ2f1-M3δ3f2.LEVTi is the turnover of each means of transportation and δ2f1 and δ3f2 represents the negative influence on turnover of transport means from the economy growth investment and environment pollution respectively. M2 and M3 are an equivalent used to balance different units.


#### 3.2.2. Constraints

(1) Total Transportation Structure Proportion Constraint
We assumed that there are only four means of transportation in the system, thus making the sum total 1:(3.10)∑i=14‍xi=1.(2) Investment Constraint
Because plans have been made in the government 5-year plans the transportation structures and therefore expenditures have already been determined. Thus, for each means of transport considered here there is a maximum and minimum ranges:(3.11)a11≤x1≤a12,a21≤x2≤a22,a31≤x3≤a32,a41≤x4≤a42,b1≤x1+x2+x3≤b2,x1, x2, x3, x4 represent each means of transportation, here, a11, a21, a31, a41 represent the lower limit of proportion, while the a12, a22, a32, a42, the upper limit. b1 is the lowest proportion of public transport, while b2 is the upper limit.(3) Ratio Constraint
There are two kinds of share rate in this system, the public transportation share rate and private car share rate, both of them are between0~1, and the sum of them is equal to 1:
(3.12)0<LEVVPTLEVVT<1,0<LEVV4LEVVT<1.(4) Intensity Constraint
Usually, the emission intensity index decreases along with technological progress and economic growth. The emission intensity of this year is expected to be smaller than that of the last year. Therefore, the emission intensity has an upper limit and decreases every year:(3.13)∑i=14LEVEEif1≤∑i=14‍LEVEIi(1-c1),
where LEVEEi(t-1) represent the exhaust emission and LEVEIi(t-1) represents emission intensity of last year, and c1 is the the average rate of decrease required.Similarly, the intensity of road occupation to economy also decreases:(3.14)f3f1≤∑i=14‍LEVTIi(1-c2),
where LEVTIi(t-1) represents road occupation intensity and c2 is the the average rate of decrease required.From this, we get (3.16) as follows:
(3.15)maxf1=LEVGDP-M1∑i=14‍LEVEPi·RATEDiminf2=∑i=14‍LEVEEi-δ1f1maxf3=∑i=14‍LEVTi-M2δ2f1-M3δ3f2(3.16)s.t.{∑i=14‍xi=1a11≤x1≤a12a21≤x2≤a22a31≤x3≤a32a41≤x4≤a42b1≤x1+x2+x3≤b20<LEVVPTLEVVT<10<LEVV4LEVVT<1∑i=14LEVEEif1≤∑i=14‍LEVEIi(1-c1)f3f1≤∑i=14‍LEVTIi(1-c2)e1≤δi≤e20≤a,b,c,e≤1,i=1,…,4.


### 3.3. Solution Method

In this Section, we make use of the ideal point method proposed by Yingming et al. [30]; Rakowska et al. [31]; and William [32] to resolve the multiobjective problem (3.16) with crisp parameters [33]. If the policy maker can firstly propose an estimated value F-i for each objective function fi(x) such that
(3.17)F-i≥maxx∈Xfi(x),i=1,2,3,
where X={x∣x∈X}, X is the collection range of constraints, and then F-i=(F-1,F-2,F-3)T is called the ideal point, especially if F-i≥maxx∈Xfi(x) for all i, we call F- the most ideal point.The basic theory of the ideal point method is to take an especial norm in the objective spaceRm and obtain feasible solution x so that the objective value approaches the ideal point F-=(F-1,F-2,F-3)T under the norm distance, that is, to seek the feasible solution x satisfying
(3.18)minx∈X′u(fi(x))=minx∈X′∥fi(x)-F-∥.Next, we take thep-mode function to describe the procedure for solving the problem (3.16).Step 1.
Find the ideal point. If the decision maker can give an ideal objective value satisfying condition (3.17), the value will be considered the ideal point. However, decision makers do not know how to estimate the objective value, so we can get the ideal point by solving the following programming problem:
(3.19)maxfi(x)s.t.x∈X.Then the ideal pointF-=(F-1,F-2,F-3)T can be fixed by F-i=fi(x*), where x* is the optimal solution of problem (3.19).Step 2.
Fix the weight. The method of selecting the weight is referred to in much research that interested readers can consult these. We usually use the following function to fix the weight:(3.20)ωi=F-i∑i=13F-i.Step 3.
Construct the minimal distance problem. Solve the following single-objective programming problem to obtain an efficient solution to problem (3.16):
(3.21)min[∑i=1m‍ωi|fi(x)-F-i|t]1/ts.t.
usually, we take t=2 to compute it.


## 3.1. System Dynamics Model

This Section is divided into two parts for a particular description of the modeling; firstly, the cause-effect relationship diagram, and, secondly, the stock and flow diagram, both of which are the two main steps when using system dynamics.


### 3.1.1. Cause-Effect Relationship Diagram

The SD model for the present study is developed for a transportation system. There are many variables in the subsystems occupying important positions in the system; thus, we build the cause-effect relationship diagram (see Figure3) by incorporating the various features associated with the system. In this Figure, the arrows denote the cause-and-effect relationships and the plus and minus signs denote the positive and negative effects, respectively. The main feedback loops are given below:Figure 3
The cause-effect relationship diagram of garden city transportation system.(1)
economic development→+ total number of vehicles →+ transportation congestion →+ environmental pollution →- economic development;
(2)
population→+ trip demand →+ total trips →+ transportation congestion →- economic development →- urban population;
(3)
economic development→+ infrastructure investment →+ road investment →+ road capacity →- transportation congestion →- economic development;
(4)
policy management→+ economic development →+ environmental pollution →- policy intervention.


### 3.1.2. Stock and Flow Diagram

The causal relationship diagram emphasizes the feedback structure of the system, which, however, can never be comprehensive. We need to convert the causal relationship diagram into the stock and flow diagram that emphasizes the physical structure of the model, which tends to be more detailed than the causal loop diagram [28], to force us to think more specifically about the system structure. Figure 4 gives a detailed description, with the main formula as follows.Figure 4
The stock and flow diagram of garden city transportation system.Through system dynamics modeling, we can get the first-order differential equations. The change rate of the turnover of bus, thed(LEVT1(t))/dt, is dependent on the stock of the turnover of bus LEVT1(t), and there exists the basic stock OT1, which is subject to factors of transport planning, demand volume, and so on; besides, it would be effected by functioning time OT, which regularly means one year:
(3.1)d(LEVT1(t))dt=LEVT1(t)-OT1OT.
Similarly, the differential equations of the turnover of the taxi, railway, and private car are
(3.2)d(LEVT2(t))dt=LEVT2(t)-OT2OT,d(LEVT3(t))dt=LEVT3(t)-OT3OT,d(LEVT4(t))dt=LEVT4(t)-OT4OT.
Through the previous analysis, we get the main part of the links in the garden city transport system:
(3.3)LEVGDP(t)=LEVGDP(t-1)×RATGDP(t),LEVII(t)=LEVGDP(t)×RATII(t),LEVIPT(t)=LEVII(t)×RATIPT(t),LEVI1(t)=x1·LEVIPT(t),LEVN1(t)=LEVI1(t)×RATC1(t),LEVV1(t)=PHF1×TF1×LEVN1(t),LEVT1(t)=TD1×LEVV1(t).Till now, we obtained the turnover of busLEVT1, similarly, the turnover of taxi, railway, and private car can be also described as LEVT2, LEVT3, and LEVT4, and the traffic intensity can be formulated as the following:
(3.4)LEVTI(t)=LEVT1(t)+LEVT2(t)+LEVT3(t)+LEVT4(t).
Further,
(3.5)LEVTL(t)=LEVTI(t)LEVCR(t),LEVEE(t)=LEVTL(t)×RATEF,LEVEP(t)=LEVEE(t)×RATEI,-LEVGDP(t)=-LEVEP(t)×RATED,
where it can indicated that the irrational structure of transportation can increase the environmental pollution and ultimately decrease the development of economy to a certain extent. Meanwhile,
(3.6)LEVTP(t)=LEVTP(t-1)+LEVTP(t-1)×RATTP(t),LEVVT(t)=LEVTP(t)×RATTF,RATSR1=LEVVPT(t)LEVVT(t),RATSR2=LEVV4(t)LEVVT(t).
Through this circulate series of formulation, each variable (the standard variable and rate variable) is defined, thus, building the foundation of our model.


## 3.1.1. Cause-Effect Relationship Diagram

The SD model for the present study is developed for a transportation system. There are many variables in the subsystems occupying important positions in the system; thus, we build the cause-effect relationship diagram (see Figure3) by incorporating the various features associated with the system. In this Figure, the arrows denote the cause-and-effect relationships and the plus and minus signs denote the positive and negative effects, respectively. The main feedback loops are given below:Figure 3
The cause-effect relationship diagram of garden city transportation system.(1)
economic development→+ total number of vehicles →+ transportation congestion →+ environmental pollution →- economic development;
(2)
population→+ trip demand →+ total trips →+ transportation congestion →- economic development →- urban population;
(3)
economic development→+ infrastructure investment →+ road investment →+ road capacity →- transportation congestion →- economic development;
(4)
policy management→+ economic development →+ environmental pollution →- policy intervention.


## 3.1.2. Stock and Flow Diagram

The causal relationship diagram emphasizes the feedback structure of the system, which, however, can never be comprehensive. We need to convert the causal relationship diagram into the stock and flow diagram that emphasizes the physical structure of the model, which tends to be more detailed than the causal loop diagram [28], to force us to think more specifically about the system structure. Figure 4 gives a detailed description, with the main formula as follows.Figure 4
The stock and flow diagram of garden city transportation system.Through system dynamics modeling, we can get the first-order differential equations. The change rate of the turnover of bus, thed(LEVT1(t))/dt, is dependent on the stock of the turnover of bus LEVT1(t), and there exists the basic stock OT1, which is subject to factors of transport planning, demand volume, and so on; besides, it would be effected by functioning time OT, which regularly means one year:
(3.1)d(LEVT1(t))dt=LEVT1(t)-OT1OT.
Similarly, the differential equations of the turnover of the taxi, railway, and private car are
(3.2)d(LEVT2(t))dt=LEVT2(t)-OT2OT,d(LEVT3(t))dt=LEVT3(t)-OT3OT,d(LEVT4(t))dt=LEVT4(t)-OT4OT.
Through the previous analysis, we get the main part of the links in the garden city transport system:
(3.3)LEVGDP(t)=LEVGDP(t-1)×RATGDP(t),LEVII(t)=LEVGDP(t)×RATII(t),LEVIPT(t)=LEVII(t)×RATIPT(t),LEVI1(t)=x1·LEVIPT(t),LEVN1(t)=LEVI1(t)×RATC1(t),LEVV1(t)=PHF1×TF1×LEVN1(t),LEVT1(t)=TD1×LEVV1(t).Till now, we obtained the turnover of busLEVT1, similarly, the turnover of taxi, railway, and private car can be also described as LEVT2, LEVT3, and LEVT4, and the traffic intensity can be formulated as the following:
(3.4)LEVTI(t)=LEVT1(t)+LEVT2(t)+LEVT3(t)+LEVT4(t).
Further,
(3.5)LEVTL(t)=LEVTI(t)LEVCR(t),LEVEE(t)=LEVTL(t)×RATEF,LEVEP(t)=LEVEE(t)×RATEI,-LEVGDP(t)=-LEVEP(t)×RATED,
where it can indicated that the irrational structure of transportation can increase the environmental pollution and ultimately decrease the development of economy to a certain extent. Meanwhile,
(3.6)LEVTP(t)=LEVTP(t-1)+LEVTP(t-1)×RATTP(t),LEVVT(t)=LEVTP(t)×RATTF,RATSR1=LEVVPT(t)LEVVT(t),RATSR2=LEVV4(t)LEVVT(t).
Through this circulate series of formulation, each variable (the standard variable and rate variable) is defined, thus, building the foundation of our model.


## 3.2. Multiobjective Programming Model

The purpose of multiobjective programming (MOP) is to maximize (or minimize) different multiobjective functions under a set of constraints, which is suitable for decision making in systems which have two or more goals [29]. According to the analysis of the system above, the optimization of a garden city transportation structure needs to consider the economic, social, and environmental subsystems and the transportation structure together to maximize the final benefits. Therefore, a multiobjective method can be used to solve this problem. In this Section, we will apply a multiobjective optimization model into the stock and flow diagram to measure the most optimal transportation structure to invest.


### 3.2.1. Objective Function

As usual, the objective is to pursue the maximal economic and, social benefit with minimal environmental pollution. Here we list our three main objective functions.(1) Maximal Gross Domestic Product  (GDP)
Economy is an important part involved in garden city transportation system, and, often, we use GDP to measure the level of it, the higher the GDP we produce, the better we operate our country and more investment on transportation be conducted and the system develops better:(3.7)maxf1=LEVGDP-M1∑i=14‍LEVEPi·RATEDi,
here, the LEVGDP represents the quantity of GDP, and LEVEPi·RATEDi is the economy decrease caused by environment pollution of each transportation means. Since LEVEPi represents the environment pollution, while GDP is dimensional, we add an M1 to the balance to make them under the same unit.(2) Less Environment Pollution
As the economy develops, the public consciousness of environmental protection is aroused. The automobile exhaust emission occupies most parts in air pollution, so the optimal the transportation structure combination, the minimal air pollution and environmental damage. To achieve this, we must guarantee the least exhaust emissions:(3.8)minf2=∑i=14‍LEVEEi-δ1f1,
where LEVEEi represents the level of exhaust emission, and δ1f1 represents the environment pollution reduction resulting from economy growth investment.(3) More Social Benefits
Social benefit is also an important aspect. Because transportation system can make people’s life more convenient; if the system is not operating well, there will not be sufficient supply for people to travel. Therefore, it needs more turnover of each transport means to bear people’s travel demand, which is a criterion to measure the transport capacity:(3.9)maxf3=∑i=14‍LEVTi-M2δ2f1-M3δ3f2.LEVTi is the turnover of each means of transportation and δ2f1 and δ3f2 represents the negative influence on turnover of transport means from the economy growth investment and environment pollution respectively. M2 and M3 are an equivalent used to balance different units.


### 3.2.2. Constraints

(1) Total Transportation Structure Proportion Constraint
We assumed that there are only four means of transportation in the system, thus making the sum total 1:(3.10)∑i=14‍xi=1.(2) Investment Constraint
Because plans have been made in the government 5-year plans the transportation structures and therefore expenditures have already been determined. Thus, for each means of transport considered here there is a maximum and minimum ranges:(3.11)a11≤x1≤a12,a21≤x2≤a22,a31≤x3≤a32,a41≤x4≤a42,b1≤x1+x2+x3≤b2,x1, x2, x3, x4 represent each means of transportation, here, a11, a21, a31, a41 represent the lower limit of proportion, while the a12, a22, a32, a42, the upper limit. b1 is the lowest proportion of public transport, while b2 is the upper limit.(3) Ratio Constraint
There are two kinds of share rate in this system, the public transportation share rate and private car share rate, both of them are between0~1, and the sum of them is equal to 1:
(3.12)0<LEVVPTLEVVT<1,0<LEVV4LEVVT<1.(4) Intensity Constraint
Usually, the emission intensity index decreases along with technological progress and economic growth. The emission intensity of this year is expected to be smaller than that of the last year. Therefore, the emission intensity has an upper limit and decreases every year:(3.13)∑i=14LEVEEif1≤∑i=14‍LEVEIi(1-c1),
where LEVEEi(t-1) represent the exhaust emission and LEVEIi(t-1) represents emission intensity of last year, and c1 is the the average rate of decrease required.Similarly, the intensity of road occupation to economy also decreases:(3.14)f3f1≤∑i=14‍LEVTIi(1-c2),
where LEVTIi(t-1) represents road occupation intensity and c2 is the the average rate of decrease required.From this, we get (3.16) as follows:
(3.15)maxf1=LEVGDP-M1∑i=14‍LEVEPi·RATEDiminf2=∑i=14‍LEVEEi-δ1f1maxf3=∑i=14‍LEVTi-M2δ2f1-M3δ3f2(3.16)s.t.{∑i=14‍xi=1a11≤x1≤a12a21≤x2≤a22a31≤x3≤a32a41≤x4≤a42b1≤x1+x2+x3≤b20<LEVVPTLEVVT<10<LEVV4LEVVT<1∑i=14LEVEEif1≤∑i=14‍LEVEIi(1-c1)f3f1≤∑i=14‍LEVTIi(1-c2)e1≤δi≤e20≤a,b,c,e≤1,i=1,…,4.


## 3.2.1. Objective Function

As usual, the objective is to pursue the maximal economic and, social benefit with minimal environmental pollution. Here we list our three main objective functions.(1) Maximal Gross Domestic Product  (GDP)
Economy is an important part involved in garden city transportation system, and, often, we use GDP to measure the level of it, the higher the GDP we produce, the better we operate our country and more investment on transportation be conducted and the system develops better:(3.7)maxf1=LEVGDP-M1∑i=14‍LEVEPi·RATEDi,
here, the LEVGDP represents the quantity of GDP, and LEVEPi·RATEDi is the economy decrease caused by environment pollution of each transportation means. Since LEVEPi represents the environment pollution, while GDP is dimensional, we add an M1 to the balance to make them under the same unit.(2) Less Environment Pollution
As the economy develops, the public consciousness of environmental protection is aroused. The automobile exhaust emission occupies most parts in air pollution, so the optimal the transportation structure combination, the minimal air pollution and environmental damage. To achieve this, we must guarantee the least exhaust emissions:(3.8)minf2=∑i=14‍LEVEEi-δ1f1,
where LEVEEi represents the level of exhaust emission, and δ1f1 represents the environment pollution reduction resulting from economy growth investment.(3) More Social Benefits
Social benefit is also an important aspect. Because transportation system can make people’s life more convenient; if the system is not operating well, there will not be sufficient supply for people to travel. Therefore, it needs more turnover of each transport means to bear people’s travel demand, which is a criterion to measure the transport capacity:(3.9)maxf3=∑i=14‍LEVTi-M2δ2f1-M3δ3f2.LEVTi is the turnover of each means of transportation and δ2f1 and δ3f2 represents the negative influence on turnover of transport means from the economy growth investment and environment pollution respectively. M2 and M3 are an equivalent used to balance different units.


## 3.2.2. Constraints

(1) Total Transportation Structure Proportion Constraint
We assumed that there are only four means of transportation in the system, thus making the sum total 1:(3.10)∑i=14‍xi=1.(2) Investment Constraint
Because plans have been made in the government 5-year plans the transportation structures and therefore expenditures have already been determined. Thus, for each means of transport considered here there is a maximum and minimum ranges:(3.11)a11≤x1≤a12,a21≤x2≤a22,a31≤x3≤a32,a41≤x4≤a42,b1≤x1+x2+x3≤b2,x1, x2, x3, x4 represent each means of transportation, here, a11, a21, a31, a41 represent the lower limit of proportion, while the a12, a22, a32, a42, the upper limit. b1 is the lowest proportion of public transport, while b2 is the upper limit.(3) Ratio Constraint
There are two kinds of share rate in this system, the public transportation share rate and private car share rate, both of them are between0~1, and the sum of them is equal to 1:
(3.12)0<LEVVPTLEVVT<1,0<LEVV4LEVVT<1.(4) Intensity Constraint
Usually, the emission intensity index decreases along with technological progress and economic growth. The emission intensity of this year is expected to be smaller than that of the last year. Therefore, the emission intensity has an upper limit and decreases every year:(3.13)∑i=14LEVEEif1≤∑i=14‍LEVEIi(1-c1),
where LEVEEi(t-1) represent the exhaust emission and LEVEIi(t-1) represents emission intensity of last year, and c1 is the the average rate of decrease required.Similarly, the intensity of road occupation to economy also decreases:(3.14)f3f1≤∑i=14‍LEVTIi(1-c2),
where LEVTIi(t-1) represents road occupation intensity and c2 is the the average rate of decrease required.From this, we get (3.16) as follows:
(3.15)maxf1=LEVGDP-M1∑i=14‍LEVEPi·RATEDiminf2=∑i=14‍LEVEEi-δ1f1maxf3=∑i=14‍LEVTi-M2δ2f1-M3δ3f2(3.16)s.t.{∑i=14‍xi=1a11≤x1≤a12a21≤x2≤a22a31≤x3≤a32a41≤x4≤a42b1≤x1+x2+x3≤b20<LEVVPTLEVVT<10<LEVV4LEVVT<1∑i=14LEVEEif1≤∑i=14‍LEVEIi(1-c1)f3f1≤∑i=14‍LEVTIi(1-c2)e1≤δi≤e20≤a,b,c,e≤1,i=1,…,4.


## 3.3. Solution Method

In this Section, we make use of the ideal point method proposed by Yingming et al. [30]; Rakowska et al. [31]; and William [32] to resolve the multiobjective problem (3.16) with crisp parameters [33]. If the policy maker can firstly propose an estimated value F-i for each objective function fi(x) such that
(3.17)F-i≥maxx∈Xfi(x),i=1,2,3,
where X={x∣x∈X}, X is the collection range of constraints, and then F-i=(F-1,F-2,F-3)T is called the ideal point, especially if F-i≥maxx∈Xfi(x) for all i, we call F- the most ideal point.The basic theory of the ideal point method is to take an especial norm in the objective spaceRm and obtain feasible solution x so that the objective value approaches the ideal point F-=(F-1,F-2,F-3)T under the norm distance, that is, to seek the feasible solution x satisfying
(3.18)minx∈X′u(fi(x))=minx∈X′∥fi(x)-F-∥.Next, we take thep-mode function to describe the procedure for solving the problem (3.16).Step 1.
Find the ideal point. If the decision maker can give an ideal objective value satisfying condition (3.17), the value will be considered the ideal point. However, decision makers do not know how to estimate the objective value, so we can get the ideal point by solving the following programming problem:
(3.19)maxfi(x)s.t.x∈X.Then the ideal pointF-=(F-1,F-2,F-3)T can be fixed by F-i=fi(x*), where x* is the optimal solution of problem (3.19).Step 2.
Fix the weight. The method of selecting the weight is referred to in much research that interested readers can consult these. We usually use the following function to fix the weight:(3.20)ωi=F-i∑i=13F-i.Step 3.
Construct the minimal distance problem. Solve the following single-objective programming problem to obtain an efficient solution to problem (3.16):
(3.21)min[∑i=1m‍ωi|fi(x)-F-i|t]1/ts.t.
usually, we take t=2 to compute it.


## 4. A Case Study

In this section, we choose Chengdu, first city that advocates to “being a world modern garden city,” in China as our application to verify the approach in the previous section. we apply the data and parameter values of Chengdu into the system dynamics model. A system simulation was performed using the simulation software VENSIM and the data from 2010 as initial conditions, time  =  0. Our simulation spans 11 years, from 1 to 11, and results in data analysis for the years 2010 to 2020 and we depict the main pattern in figures.


### 4.1. Regional Situation

As a general transportation hub for western China, Chengdu is an important nexus city linking up China to mid-Asia, south Asia, west Asia, and Europe. Located in the middle of Sichuan province in southwest China, Chengdu covers a total land area of 12121 square kilometers, with its central downtown area extending for approximately 350 square kilometers. With its name and location kept unchanged for more than 2300 years, the city’s history traces back far and the culture reaches wide. As the main hub for western transportation and the most developed city in the southwest China, with the nature advantages, the proposition of the objective of a “world modern garden city” is necessary and surely no accident. Chengdu is blessed with unsurpassed resources, and the nature, humanity, and history of Chengdu make it well qualified for garden city construction. In late 2009, the city committee and government made the development of a “world modern garden city” its historic positioning and long-term target based on in-depth research, sufficient analysis, and extensive public participation in the notion. It presents an attempt to capitalize on the historic opportunities generated by the prosperity of China to further the urban-rural integration and push along the strategic transformation of growth models so that the city can better contribute to the new round of opening-up and development activities in western China and to the province’s strategic move to become the top driving force in the development of western China. However, in the way of garden city construction, the transport problems have become increasingly severe. We have to deal with the traffic problems as an ordinary city and as a particular problem emerged in the construction of world modern garden city, which is brand new for us.


### 4.2. Simulation Results and Analysis

We collect the parameter statistics by studying the garden city transportation system and analyzing the flows of processing technique and show the results in Table2. The settled values for the substance transforming rates, and some settled parameters in the system dynamic model, are mainly based on the administration annual report for the region: and National Statistical Bureau [34, 35], Ministry of Transport and Communication [36], Chengdu Bureau of Statistics and the planning reports: Chengdu Twelfth Five Years of planning [37], and National Twelfth Five Years of planning [38] on correlative industries and the present market situation. The settled values were obtained via equilibration, linearity regression, index smoothness, and other related mathematical models based on the principles like relativity, comparability, scientificity, and comprehensiveness. We define the parameters used to describe and analyze the system, and the parameters of the transportation system are presented in Table 2.Table 2
The value of parameters.
Symbol
Value
Units
RA
T
A
82
%
RA
T
C
1
96.94
%
RA
T
C
2
94.40
%
RA
T
C
3
92.30
%
RA
T
C
4
90.50
%
RA
T
D
3.9175
g/L
RA
T
ED
-
0.29
Yuan/g
RA
T
EF
1.5
g/person
RA
T
EI
0.6
No dimension
RA
T
GDP
14.70
%
RA
T
II
12
%
RA
T
IPT
40
%
RA
T
IR
60
%
PH
F
1
0.3242
Person/times
PH
F
2
0.2260
Person/times
PH
F
3
0.3065
Person/times
PH
F
4
0.4006
Person/times
T
D
1
10.545
km/time
T
D
2
9.413
km/time
T
D
3
12.413
km/time
T
D
4
10.517
km/time
T
F
1
11.37
Times
T
F
2
10.5
Times
T
F
3
12.28
Times
T
F
4
4.16
TimesIn order to achieve the government’s goal, a multiobjective optimization problem incorporating the decision makers’ preferences is formulated. The multiobjective model is based on Model (3.16). There are some parameters which are determined by the decision maker of local government. In the current case, parameters such asa, b, c, d have to be given according to the preferences of decision maker. The decision maker can provide different values and decide which solutions are adopted by comparing the solutions. The decision maker is encouraged to give probable numbers to express their preference. With this method, we obtained three different solutions as shown in Table 3 (control variables) for different weights considered for the objective functions, among which the current program presents the current situation of transport proportion. In this table, the different proportions of transport means show that from the current program to optimization program 3, the proportion of public transport is increasing, especially the bus and railway, while the private car decreases dramatically, and the number of taxi decreases slightly. Finally, these numbers and cases will be used as control variables in transportation system dynamics modeling to operate along with the initial data. We use the four groups of figures (Table 3) to predict the coming 10 years, and, in turn, suggest actions to improve the present situation.Table 3
Control variables.
Current  program
Optimization program 1
Optimization program 2
Optimization  program 3
x
1
0.3830
0.3000
0.3600
0.1750
x
2
0.1036
0.2000
0.1375
0.2096
x
3
0.4080
0.2750
0.3400
0.2658
x
4
0.1054
0.2250
0.1625
0.3496The results after the system dynamics modeling are shown from Figure5 to Figure 10. As the system is simulated, six variables are selected for observation which are classified in three groups: the transport structure represented by the public transport share rate and railway passenger capacity (Figures 5 and 6), the road use situation represented by the traffic intensity and public transport volume (Figures 7 and 8), and the environmental circumstances represented by the exhaust emissions and environment pollution (Figures 9 and 10). From Figure 5, the public transport share rate is increasing, if no changes had taken place, the public transport share rate will remain the same as the current situation. And we can see that optimization 3 is the highest in the coming 10 years, and optimization 2 is higher than optimization 1 in the first several years, and all the three optimizations show significant improvement than continuing with the current situation. Figure 6 describes that the railway passenger capacity will be greatly strengthened if optimization cases are adopted. In terms of the road use situation, Figure 7, traffic intensity means the higher the intensity, the more utilization of the road, and Figure 8 presents travel volume of public transport is always increasing, and indicates the demand of transport. Both of them show that optimization 3 is the best choice. Lastly, in terms of the environmental circumstance, both Figures 9 and 10 are critical factor in assessing environment contamination. Most of the exhaust emission contributes to the environment pollution, and there is a linear relationship between them. Generally speaking, from analysis of these 6 graphs we observe that the most suitable case is optimization 3, which in all cases offers better progress towards the goal of a garden city than the current situation.Figure 5
Public transport share rate.Figure 6
Railway passenger capacity.Figure 7
Traffic intensity.Figure 8
Travel volume of public transport.Figure 9
Exhaust emission.Figure 10
Environment pollution.


## 4.1. Regional Situation

As a general transportation hub for western China, Chengdu is an important nexus city linking up China to mid-Asia, south Asia, west Asia, and Europe. Located in the middle of Sichuan province in southwest China, Chengdu covers a total land area of 12121 square kilometers, with its central downtown area extending for approximately 350 square kilometers. With its name and location kept unchanged for more than 2300 years, the city’s history traces back far and the culture reaches wide. As the main hub for western transportation and the most developed city in the southwest China, with the nature advantages, the proposition of the objective of a “world modern garden city” is necessary and surely no accident. Chengdu is blessed with unsurpassed resources, and the nature, humanity, and history of Chengdu make it well qualified for garden city construction. In late 2009, the city committee and government made the development of a “world modern garden city” its historic positioning and long-term target based on in-depth research, sufficient analysis, and extensive public participation in the notion. It presents an attempt to capitalize on the historic opportunities generated by the prosperity of China to further the urban-rural integration and push along the strategic transformation of growth models so that the city can better contribute to the new round of opening-up and development activities in western China and to the province’s strategic move to become the top driving force in the development of western China. However, in the way of garden city construction, the transport problems have become increasingly severe. We have to deal with the traffic problems as an ordinary city and as a particular problem emerged in the construction of world modern garden city, which is brand new for us.


## 4.2. Simulation Results and Analysis

We collect the parameter statistics by studying the garden city transportation system and analyzing the flows of processing technique and show the results in Table2. The settled values for the substance transforming rates, and some settled parameters in the system dynamic model, are mainly based on the administration annual report for the region: and National Statistical Bureau [34, 35], Ministry of Transport and Communication [36], Chengdu Bureau of Statistics and the planning reports: Chengdu Twelfth Five Years of planning [37], and National Twelfth Five Years of planning [38] on correlative industries and the present market situation. The settled values were obtained via equilibration, linearity regression, index smoothness, and other related mathematical models based on the principles like relativity, comparability, scientificity, and comprehensiveness. We define the parameters used to describe and analyze the system, and the parameters of the transportation system are presented in Table 2.Table 2
The value of parameters.
Symbol
Value
Units
RA
T
A
82
%
RA
T
C
1
96.94
%
RA
T
C
2
94.40
%
RA
T
C
3
92.30
%
RA
T
C
4
90.50
%
RA
T
D
3.9175
g/L
RA
T
ED
-
0.29
Yuan/g
RA
T
EF
1.5
g/person
RA
T
EI
0.6
No dimension
RA
T
GDP
14.70
%
RA
T
II
12
%
RA
T
IPT
40
%
RA
T
IR
60
%
PH
F
1
0.3242
Person/times
PH
F
2
0.2260
Person/times
PH
F
3
0.3065
Person/times
PH
F
4
0.4006
Person/times
T
D
1
10.545
km/time
T
D
2
9.413
km/time
T
D
3
12.413
km/time
T
D
4
10.517
km/time
T
F
1
11.37
Times
T
F
2
10.5
Times
T
F
3
12.28
Times
T
F
4
4.16
TimesIn order to achieve the government’s goal, a multiobjective optimization problem incorporating the decision makers’ preferences is formulated. The multiobjective model is based on Model (3.16). There are some parameters which are determined by the decision maker of local government. In the current case, parameters such asa, b, c, d have to be given according to the preferences of decision maker. The decision maker can provide different values and decide which solutions are adopted by comparing the solutions. The decision maker is encouraged to give probable numbers to express their preference. With this method, we obtained three different solutions as shown in Table 3 (control variables) for different weights considered for the objective functions, among which the current program presents the current situation of transport proportion. In this table, the different proportions of transport means show that from the current program to optimization program 3, the proportion of public transport is increasing, especially the bus and railway, while the private car decreases dramatically, and the number of taxi decreases slightly. Finally, these numbers and cases will be used as control variables in transportation system dynamics modeling to operate along with the initial data. We use the four groups of figures (Table 3) to predict the coming 10 years, and, in turn, suggest actions to improve the present situation.Table 3
Control variables.
Current  program
Optimization program 1
Optimization program 2
Optimization  program 3
x
1
0.3830
0.3000
0.3600
0.1750
x
2
0.1036
0.2000
0.1375
0.2096
x
3
0.4080
0.2750
0.3400
0.2658
x
4
0.1054
0.2250
0.1625
0.3496The results after the system dynamics modeling are shown from Figure5 to Figure 10. As the system is simulated, six variables are selected for observation which are classified in three groups: the transport structure represented by the public transport share rate and railway passenger capacity (Figures 5 and 6), the road use situation represented by the traffic intensity and public transport volume (Figures 7 and 8), and the environmental circumstances represented by the exhaust emissions and environment pollution (Figures 9 and 10). From Figure 5, the public transport share rate is increasing, if no changes had taken place, the public transport share rate will remain the same as the current situation. And we can see that optimization 3 is the highest in the coming 10 years, and optimization 2 is higher than optimization 1 in the first several years, and all the three optimizations show significant improvement than continuing with the current situation. Figure 6 describes that the railway passenger capacity will be greatly strengthened if optimization cases are adopted. In terms of the road use situation, Figure 7, traffic intensity means the higher the intensity, the more utilization of the road, and Figure 8 presents travel volume of public transport is always increasing, and indicates the demand of transport. Both of them show that optimization 3 is the best choice. Lastly, in terms of the environmental circumstance, both Figures 9 and 10 are critical factor in assessing environment contamination. Most of the exhaust emission contributes to the environment pollution, and there is a linear relationship between them. Generally speaking, from analysis of these 6 graphs we observe that the most suitable case is optimization 3, which in all cases offers better progress towards the goal of a garden city than the current situation.Figure 5
Public transport share rate.Figure 6
Railway passenger capacity.Figure 7
Traffic intensity.Figure 8
Travel volume of public transport.Figure 9
Exhaust emission.Figure 10
Environment pollution.


## 5. Proposals

From an analysis of the results and in consideration of local conditions, suggestions are made to find a feasible solution to the transportation development in garden city. To achieve a continual optimization of the transportation structure, low-carbon transportation development needs to be promoted through the formulation of relevant policy by the local government.(1) Transportation Structure Optimization
The adjustment of the transportation structure is a long complicated process which cannot be achieved through a single policy. A previous simulation confirms that if the government ensures the preferential development of the public transport, the situation can get better. Firstly, develop the loop line. The loop line and radiation transport route can associate the central city with the countryside areas, which takes a great advantage of the plain landscape, as well as, the standard model of garden city transportation. Secondly, the subway construction. It is convinced that the railway transport is the context to open garden city construction. With the 1st line of Chengdu Metro operating well and its notable benefit, new subways should be constructed to spread further and ultimately to the whole city. Thirdly, construct the bus rapid transit (BRT), which is an important part in mass rapid public transit. Here, the mass rapid public transit is an resources saving and socially beneficial which includes BRT, subway, light railway, and others. The bus rapid transit (BRT) integrates the bus technology, intelligent traffic system with rail transit operations management mode into a relatively low-cost mass transit mode, which is regarded as a revolutionized solution of public transport by International Energy Agency. Fourthly, restrict development of private cars. As the private cars are at an absolute disadvantage in transport area possession, energy consuming, and exhaust emissions, measures should be taken to restrict it such as purchase limiting, levying a tax based on the emissions to the environment, and reducing the supply of oil.(2) Promoting the Land Use Mode
There is a close relationship between land use planning and transport construction. Land use planning is crucial to the whole transportation system. As our simulation model shows, land use influences the transport infrastructure such as road length, road capacity, and the investment proportion of road. According to the actual land situation of Chengdu, firstly, emphasis on the mixed use of land and the various functional complement with each other is applied in order to improve the overall efficiency of central district. Secondly, newly developed areas should conduct preliminary transport planning before the land use plan. Thirdly, the public transport guide land use mode needs to be developed to shorten the travel distance between bus stops and increase the operating speed. Fourthly, controlling the diversity of land use intensity along the road lines to maintain traveling speed and raise land use intensity and efficiency. Fifthly, attention should be paid to the ecological construction of land. The government should transfer the distant and relatively large land parcels to farmland to develop urban agriculture which can improve the environmental quality, and suppress the unlimited extension of city construction land use scale, for example, the Shahe, Sansheng, and Shiling park. Lastly, free up the original lane space to provide for the new bus station and parking place, at the same time, set up new bicycle squares in the city center.(3) Strengthening the Low-Carbon Consciousness
Because there is a high value put on environmental protection in our model, it is necessary to examine and weigh the optimization using environmental indexes. A green travel consciousness needs to be developed which would focus on the sustainable development of the urban inhabitable environment. Thus, both the walking and alternative means need to be promoted along with the low-carbon, safe, comfortable, and low-pollution public transport. It is an effective way to introduce the low-carbon consciousness into primary school classroom education, which cannot only guide the students to establish the right consumption concept, but also to foster their socially responsible manner and has a profound effect on low-carbon transportation construction. This promotion of green transportation will lower the dependence on motor vehicles and encourage people to use hybrid or clean fueled vehicles which would also satisfy one of the measures proposed by the State Council for reducing greenhouse gas emissions and conserving energy.


## 6. Conclusion

Great many cities are experiencing traffic problems in the process of city development, including the garden city. Many researchers did not conclude all the factors in the transport system when estimating it. Therefore, to address the problems, a methodology for the analysis of the whole transportation system by adjustment of transport structure was outlined. Particularly, we develop a system dynamics and multiobjective programming integrated model (SD-MOP) to simulate different results with different proportions of transport means. The system dynamics model describes the relationships between the economy, environment, traffic mode traffic congestion, and the policy management. A multiobjective programming model helps policy makers to make choices according to their preferences. In the case study, a representative city, Chengdu, a world modern garden city was chosen. Various scenarios and different optimization cases were simulated to show the future trends of the transportation system. According to the simulation results, we propose the reasonable pieces of advice on transportation structure and transportation development mode in world modern garden city.It is of great significance to study transportation system by system dynamics integrated with multiobjective optimization model. There is much scope to expand this field of research into the future. There may exist some omissions in this system, future research will focus on establishing a more complex transportation system which considers more factors and deals with other optimizations.



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*Source: 710854-2012-11-22.xml*