# Multi-Objective Optimization of Aircraft Taxiing on the Airport Surface with Consideration to Taxiing Conflicts and the Airport Environment

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- Previous calculations of aircraft taxiway have excluded the waiting points on the taxiway from the multi-objective optimization of taxiing time and fuel emissions in order to avoid taxiing conflicts. Thus, this study improved the taxiing speed curve by including waiting points and by establishing a multi-objective optimization for aircraft taxiing. Accordingly, the calculation results are close to practical operating conditions.
- (2)
- Previous studies have rarely considered the taxiing multi-objective optimization problem under different airport environments. However, changes in air pressure and the environment at different airports affect the fuel combustion of aircraft engines. Hence, the fuel flows of different aircraft engines were modified in the present study. Moreover, a multi-objective optimization model of aircraft taxiing under different airport environments was constructed.
- (3)
- In this study, a multi-objective optimization for the taxiing time and fuel consumption of different aircraft modes was realized by acquiring their parameters and fuel consumption indexes. Through a multi-objective optimization of different aircraft models, the optimal values of the Pareto fronts were intuitively determined via a comparison of the calculation results, which provided references for the operational control of airport surfaces.

## 2. Literature Review

#### 2.1. Guiding Control Method of Aircraft Taxiing on the Airport Surface

#### 2.2. Multi-Objective Optimization Method of Taxiing Time, Fuel Consumption, and Pollutant Emission

_{x}, SO

_{2}, CO, unburnt hydrocarbons, CO

_{2}, carbon cigarette pellets (soot), particulate matter, and aviation-induced cloudiness [23]. Such emissions can influence the air quality and contribute to the greenhouse effect. At present, CO

_{2}emissions from air transport account for 2.0%–2.5% of total global CO

_{2}emissions by humans [24]. Damage assessment of carbon emissions in air transport, especially in the surface operating environments of airports, has attracted wide attention [25]. Aircraft taxiing on the airport’s surface also adopts a low speed and is in a fully-developed state. Taxiing optimization is of great significance to control fuel consumption and pollutant emissions in airports. Some scholars have carried out deep studies on the multi-objective optimization of taxiing time, fuel consumption, and pollutant emissions on airport surfaces in the past two decades. Smeltink [26] proposed an optimization model for the aircraft taxiing schedule on the airport’s surface and worked on aircraft taxiing via a hybrid integer programming model. An optimal schedule can reduce delays caused by taxiing conflicts as much as possible. In this study, only taxiing time was considered, while the balance between taxiing time, fuel consumption, and pollutant emissions was ignored. Herrero et al. [27] proposed an optimal taxiway planning method based on an improved spatiotemporal flow algorithm and the genetic algorithm; this approach minimized the total taxiing time. However, these authors ignored fuel consumption and pollutant emissions caused by taxiing on the airport’s surface. Simaiakis et al. [28] constructed a queuing theory prediction model to estimate the taxiing time of departing flights from the stand to the runway with consideration given to the mutual influences of different taxiways. Roling and Visser [29] studied the relationship between fuel consumption and taxiing time through surface taxiway optimization. These authors also improved the operational efficiency of the airport and reduced fuel consumption by shortening the total taxiing time. However, the authors did not consider pollutant emissions. Koeners et al. [30] implemented a real-time optimization of runway rankings through a dynamic planning of taxiways to increase runway facility utilization and reduce flight taxiing time.

_{x}, in airports to determine the conflict objective with a minimum quantity and generate an optimal speed curve. Their results demonstrated that NO

_{x}has a strong linear correlation with the combustion of fuels for all types of aircraft. In heavy aircraft, HC and CO emissions should be treated by separating them from taxiing time and fuel consumption. In medium-weight and light aircraft, HC and CO emissions are strongly correlated with taxiing time. This study did not analyze the operational results in plateau airports. Chen and Weiszer [7] introduced a systematic multi-objective speed profile generation framework to generate the optimal unimpeded taxiing speed profile on a given taxiway. This work aims to maintain the solvability of the complicated surface taxiing problem in airports with consideration given to many mutual conflicts. Brownleea et al. [35] proposed a method to estimate the uncertainty of aircraft surface taxiing time based on an adaptive Mamdani fuzzy rule. These authors also improved the time window algorithm for the existing fastest route problems to estimate the fuzzy taxiing time.

## 3. Multi-Objective Optimization Model of an Aircraft Taxiway

#### 3.1. Objective Functions

_{x}. Chen et al. [34] pointed out that a relationship curve between fuel flow and EIs can be fitted by the data when the thrust values are 7%, 30%, 85%, and 100%. Moreover, HC and CO were fitted into exponential functions, while NO

_{x}was fitted as a linear function. Therefore, NO

_{x}emissions can be overlooked in the multi-objective optimization.

_{x}.

#### 3.2. Constraints

- (1)
- The taxiing speed constraint: The maximum and minimum taxiing speeds (${v}_{max}$ and ${v}_{min}$) and the taxiing speed at the turning section (${v}_{\mathrm{turn}}$) were restricted to 25, 10, and 10 knots, respectively; this restriction was applied to ensure the safe and high-efficient surface taxiing of aircraft on airport surfaces, without considering the constraints of taxiway type over taxiing speeds [14];
- (2)
- Taxiing acceleration constraint: The acceleration ($a$) was restricted to <0.1 g to ensure the comfort of passengers during the accelerated taxiing of the aircraft [38].

#### 3.3. Modification of Fuel Consumption Coefficient

## 4. Taxiing Time and Fuel Consumption Models Based on the Optimized Speed Curve

#### 4.1. Optimized Speed Curve

#### 4.2. Taxiing Time, Fuel Consumption, and Pollutant Emission Model

## 5. Design of the Solving Algorithm

#### 5.1. Initialization of Population

_{1}, d

_{1}, d

_{2}, and d

_{4}. In the generation process of the various decision variables, the value ranges must be met. The value ranges of the different variables are equations: (8), (9), (10) and (12).

#### 5.2. Non-Dominant Ranking

_{1}, d

_{1}, d

_{2}, and d

_{4}were integrated into the formula. The fitness of the three objectives of the terminal operation optimization model was designed as (14), (17) and (18).

#### 5.3. Congestion Distance

#### 5.4. Selection, Crossing, and Variation

Algorithm 1: cyclical function of subjects |

1. The population size (pop) and the number of genetic iterations (GEN) are defined. The population at initialization moment t = 0 is P(0), and its dimension is (4,pop). Each column reflects one decision scheme; the first row to the fourth row are a_{1}, d_{1}, d_{2,} and d_{4}, respectively.2. Non-dominant ranking of initialized populations. 3. Let t = 0; 4. While t < GENAn offspring population Q(t) is generated by selection, crossing, and variation in the parent population P(t) through the binary bidding method; The integrated population: R(t)←P(t) + Q(t); Non-dominant ranking of R(t) is implemented to generate the ranked population F and N individuals are selected; P (t + 1) is set as an empty set; Let I = 0 While len (P (t + 1)) + len(F[i]) < = N when the new parent population is full (the number of the new parent population reaches N)Degree of congestion is estimated; P (t + 1)←P (t + 1) + F [i] selects from low to high in the ranked population F, and the selected individuals are added into the new parent population; i←i + 1 End whilei←I + 1; P (t + 1)←P (t + 1) + F [1:(N-len (P (t + 1))], the congestion distance is added into the population from large to small when the new parent population crosses the border; t←t + 1 End while |

Algorithm 2: non-dominant ranking |

1. Two variables are set and initialized: the number of dominant np = 0; the dominated individual set (sp) is set as an empty set. 2. Determine the highest level of the non-dominant solution set. For p = 1:NFor q = 1:NIf the individual p dominates the individual q Thenthe individual q is added into sp Else if the individual p is dominated by the individual q Thennp←np + 1 End ifEnd for If np of the individual is 0 Thenthe Pareto level is p.rank = 1 End if End for3. Leveling of other individuals. i = 0 While F[i]For q = 1:len(sp)If the number of dominants of the individual (np) is 0 Thenthis individual is a non-dominant individual If i = 0 Thenthe Pareto level is added with 2 Else the Pareto level is added with 1End ifEnd fori←i + 1 End while |

Algorithm 3: estimation of degree of congestion |

1. Initialize the congestion distance in the population set P: P[p].distance = 0. 2. The first objective function is selected: g = 1. 3. While g < GIndividuals in the population are ranked from low to high according to the objective function g; The distance between the first and the last individuals in P is set as infinite. While p > 1 && p < len (p-1)Finding the crowding distance of the p-th individual p←p + 1 End whileg←g + 1 End while |

Algorithm 4: calculation of the objective function of individuals |

The taxi segment ld is defined.For ld = 1:NIf a segment is straight, it is optimized Thena1, d1, d2 and d4 are acquired according to encoding; t1, t2, t3, t4 and v1, v2, v3, v4 are calculated. If t1, t2, t3 or t4 have negatives or imaginary values ThenThe objective functions for this individual are set infinite ElseAll objective functions are calculated according to the formula ElseAll objective functions are calculated according to the formula for turns End ifEnd for |

## 6. Case Study

#### 6.1. Data Source

#### 6.1.1. Taxiway Data of the Aircraft

#### 6.1.2. Relevant Data of Aircraft

#### 6.2. Pareto Analysis among Different Optimization Objectives

#### 6.3. Analysis of the Taxiway Optimization Results for Different Aircraft Types

#### 6.4. Comparison of the Optimization Results with and without Taxiing Waiting Points

#### 6.5. Comparison of Optimization Results in Airports with Different Altitudes

## 7. Conclusions and Prospects

## Annotations

Variables | Meanings |

$i$ | Type of aircraft (i = 1, 2, 3, 4, which are types A, B, C, and D of the aircraft, respectively) |

$j$ | Taxiing state (j = 1, 2, 3, 4, which represents acceleration, uniform speed, idling, and turning) |

${y}_{i}$ | Speed curve of aircraft i |

${Y}_{i}$ | Set of speed curves of aircraft i |

${q}_{l}$ | Taxiway marked with l |

${g}_{1}$ | Taxiing time (s) |

${g}_{2}$ | Fuel consumption (kg) |

${g}_{3}$ | HC emissions (g) |

${g}_{4}$ | CO emissions (g) |

${w}_{i}$ | Aircraft i weight categories (light, medium-weight, and heavy aircraft) |

${v}_{max}$ | Maximum taxiing speed (knot) |

${v}_{min}$ | Minimum taxiing speed (knot) |

${v}_{\mathrm{turn}}$ | Taxiing speed at turning (knot) |

$a$ | Taxiing acceleration (m/s^{−2}) |

${f}_{ij}$ | Fuel flow of the aircraft $i$ in taxiing state j (kg/s) |

${f}_{ij0}$ | Fuel flow on seal level of aircraft $i$ in taxiing state j (kg/s) |

$\delta $ | Ratio between the environmental pressure on the airport surface and the sea-level pressure under international standard atmospheric (ISA) conditions |

$\theta $ | Ratio between the environmental temperature on the airport’s surface and at sea-level Temperature of the international standard atmosphere |

$T$ | Environmental temperature of the airport’s surface ($\mathbb{C}$) |

$p$ | Environmental pressure of the airport’s surface (hPa) |

$E{I}_{ijk}$ | Emission index of pollutant k of the aircraft $i$ at the taxiing state j |

${E}_{ijk0}$ | Emission indexof sea-level pollutant type $k$ of the aircraft $i$ under taxiing state j under ISA conditions |

${v}_{i}$ | Taxiing speed of aircraft $i$ on the airport’s surface (knot) |

${t}_{j}$ | Taxiing time under taxiing state j (s) |

$s$ | Taxiing section s |

$T{T}_{s}$ | Taxiing time in taxiing section s (s) |

$\epsilon $ | Thrust level (%) |

$fue{l}_{s}$ | Fuel consumption for taxiing in section s (kg) |

$E{I}_{s}$ | Pollutant emission indices from taxiing in section s (g) |

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Table A1.**Fuel consumption and emission of the representative aircraft for taxiing at the speed of idling, uniform speed, and deceleration.

Aircraft Models | Fuel Consumption and Pollutant Emissions | Turning | Idling | Uniform Speed | Acceleration |
---|---|---|---|---|---|

35A | FUEL (kg/s) | 0.024 | 0.0184 | 0.0203 | 0.0277 |

HC (g/kg fuel) | 20.04 | 22.0983 | 21.4122 | 20.0871 | |

CO (g/kg fuel) | 58.6 | 63.3243 | 61.7496 | 55.4504 | |

NO_{X} (g/kg fuel) | 2.82 | 2.4183 | 2.5522 | 3.0878 | |

A320 | FUEL (kg/s) | 0.1011 | 0.0763 | 0.0846 | 0.1176 |

HC (g/kg fuel) | 1.4000 | 1.5304 | 1.4870 | 1.4030 | |

CO (g/kg fuel) | 17.6 | 19.5696 | 18.913 | 16.287 | |

NO_{X} (g/kg fuel) | 4 | 3.4783 | 3.6522 | 4.3478 | |

A333 | FUEL (kg/s) | 0.228 | 0.1633 | 0.1849 | 0.2711 |

HC (g/kg fuel) | 9.37 | 10.5739 | 10.1726 | 9.3976 | |

CO (g/kg fuel) | 42.67 | 48.0257 | 46.2404 | 39.0996 | |

NO_{X} (g/kg fuel) | 4.53 | 3.8283 | 4.0622 | 4.9978 |

Type | Model | Engine Type | Number of Engines |
---|---|---|---|

Narrow aircraft | B738 | CFM56-7B26 | 2 |

A320 | CFM56-5A1 | 2 | |

Wide aircraft | B777 | Trent892 | 2 |

A320 | CF6-80C2A2 | 2 | |

Ultra-wide aircraft | B747 | RB211-524D4 | 4 |

A340 | CFM56-5C4 | 4 |

Model | Fuel Flows (kg/s) | |||
---|---|---|---|---|

Turning | Idling | Uniform Speed | Acceleration | |

B738 | 0.113 | 0.0837 | 0.0934 | 0.1326 |

A320 | 0.1011 | 0.0763 | 0.0846 | 0.1176 |

B777 | 0.3 | 0.2087 | 0.239 | 0.361 |

A320 | 0.189 | 0.138 | 0.155 | 0.233 |

B747 | 0.3 | 0.2426 | 0.2617 | 0.3383 |

A340 | 0.124 | 0.0898 | 0.1012 | 0.1468 |

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**Figure 2.**Directed graph representation of the taxiway at the Shanghai Pudong International Airport.

**Figure 3.**Pareto fronts of the multi-objective optimization of different aircraft types. (

**a**) Learjet35A Pareto front of taxiing time, fuel consumption, and HC emissions; (

**b**) Learjet35A Pareto front of taxiing time, fuel consumption, and CO emissions; (

**c**) A320 Pareto front of taxiing time, fuel consumption, and HC emissions; (

**d**) A320 Pareto front of taxiing time, fuel consumption, and CO emissions; (

**e**) A333 Pareto front of taxiing time, fuel consumption, and HC emissions; and (

**f**) A333 Pareto front of taxiing time, fuel consumption, and CO emissions.

**Figure 4.**Pareto fronts on the optimization of taxiing time and fuel consumption of different aircraft types (

**a**) B738; (

**b**) A320; (

**c**) B777; (

**d**) A310; (

**e**) B747; and (

**f**) A340.

**Figure 5.**Speed curves of the aircraft under the most time-saving and fuel-saving taxiing schemes: (

**a**) the most time-saving taxi speed curve; and (

**b**) the fuel economy taxi speed curve.

**Figure 6.**Comparison of the Pareto fronts of the different aircraft with and without taxiing waiting points. (

**a**) B738; (

**b**) A320; (

**c**) B777; (

**d**) A310; (

**e**) B747; and (

**f**) A340.

**Figure 7.**Comparison of the speed curves of A320 under the most time-saving taxiing schemes with or without waiting points being present.

**Figure 8.**Comparison of the thrust/braking curves of A320 in the most time-saving taxiing schemes with or without waiting points.

**Figure 9.**Comparison of Pareto fronts for the optimization goals of different aircraft in various airports: (

**a**) B738; (

**b**) A320; (

**c**) B777; (

**d**) A310; (

**e**) B747; and (

**f**) A340.

A-SMGCS | Variables | Optimization |
---|---|---|

1st generation | assigned routes and time slots | conventional taxiing |

2nd generation | speed profiles, time slots, assigned routes | high-precision taxiing |

3rd generation | potential routs, speed profiles, 4D trajectory generation, assigned routes, and speed profiles | cost-effective and environmentally friendly taxiing |

Number of Sections | Type of Sections | ${\mathit{v}}_{0}\left(\mathbf{knot}\right)$ | ${\mathit{v}}_{4}\left(\mathbf{knot}\right)$ | $\mathbf{d}\left(\mathbf{m}\right)$ |
---|---|---|---|---|

1 | Straight | 10 | 10 | 429 |

2 | Turn | 10 | 10 | 82 |

3 | Straight | 10 | 10 | 199 |

4 | Turn | 10 | 10 | 197 |

5 | Straight | 10 | 10 | 38 |

6 | Turn | 10 | 10 | 90 |

7 | Straight | 10 | 10 | 270 |

8 | Turn | 10 | 10 | 57 |

9 | Straight | 10 | 10 | 146 |

10 | Turn | 10 | 10 | 127 |

11 | Straight | 10 | 10 | 237 |

12 | Turn | 10 | 10 | 147 |

13 | Straight | 10 | 10 | 464 |

14 | Straight stopping | 10 | 0 | 76 |

Weight Type | Light | Medium-Weighted | Heavy |
---|---|---|---|

Representative aircraft | Learjet35A | A320 | A333 |

Maximum take-off weight | 8300 kg | 78,000 kg | 230,000 kg |

Engine type | TFE731–2–2B | CMF56–5–A1 | CF6–80E1A2 |

Number of engines | 2 | 2 | 2 |

Fuel flow under a 7% thrust level (kg/s) | 0.024 | 0.101 | 0.228 |

Fuel flow under a 30% thrust level (kg/s) | 0.067 | 0.291 | 0.724 |

EI of HC under a 7% thrust level (g/kg) | 20.04 | 1.4 | 9.37 |

EI of HC under a 30% thrust level (g/kg) | 4.26 | 0.4 | 0.14 |

EI of CO under a 7% thrust level (g/kg) | 58.6 | 17.6 | 42.67 |

EI of CO under a 30% thrust level (g/kg) | 22.38 | 2.5 | 1.61 |

EI of NO_{x} under a 7% thrust level (g/kg) | 2.82 | 4 | 4.53 |

EI of NO_{x} under a 30% thrust level (g/kg) | 5.9 | 8 | 9.91 |

Taxiing Time | Fuel Consumption | EI of HC | EI of CO | |
---|---|---|---|---|

Taxiing time | 1 | −0.8768 | 0.994 | 0.9893 |

Fuel consumption | 1 | −0.9146 | −0.8216 | |

EI of HC | 1 | 0.9786 | ||

EI of CO | 1 |

Taxiing Time | Fuel Consumption | EI of HC | EI of CO | |
---|---|---|---|---|

Taxiing time | 1 | −0.8753 | 0.9951 | 0.9826 |

Fuel consumption | 1 | −0.9014 | −0.9368 | |

EI of HC | 1 | 0.9875 | ||

EI of CO | 1 |

Taxiing Time | Fuel Consumption | EI of HC | EI of CO | |
---|---|---|---|---|

Taxiing time | 1 | −0.819 | 0.8542 | 0.8974 |

Fuel consumption | 1 | −0.9316 | −0.9417 | |

EI of HC | 1 | 0.9907 | ||

EI of CO | 1 |

Taxiing Time (s) | Fuel Consumption (kg) | |||||
---|---|---|---|---|---|---|

B738 | A320 | B777 | A310 | B747 | A340 | |

285 | 116.70 | 103.93 | 314.05 | 195.77 | 606.75 | 257.34 |

407 | 84.44 | 75.04 | 226.21 | 141.51 | 442.12 | 185.22 |

Section Number | Section Type | ${\mathit{v}}_{0}\left(\mathbf{knot}\right)$ | ${\mathit{v}}_{4}\left(\mathbf{knot}\right)$ | $\mathbf{d}\left(\mathbf{m}\right)$ |
---|---|---|---|---|

1 | Straight | 10 | 10 | 429 |

2 | Turn | 10 | 10 | 82 |

3 | Straight | 10 | 10 | 199 |

4 | Turn | 10 | 10 | 197 |

5 | Straight | 10 | 10 | 38 |

6 | Turn | 10 | 10 | 90 |

7 | Straight | 10 | 0 | 170 |

8 | Straight | 0 | 10 | 100 |

9 | Turn | 10 | 10 | 57 |

10 | Straight | 10 | 10 | 146 |

11 | Turn | 10 | 10 | 127 |

12 | Straight | 10 | 10 | 237 |

13 | Turn | 10 | 10 | 147 |

14 | Straight | 10 | 10 | 464 |

15 | Straight stopping | 10 | 0 | 76 |

Aircraft Model | Taxiing Schemes | Unimpeded Taxiing | Taxiing with Waiting Points | ||
---|---|---|---|---|---|

Taxiing Time (s) | Fuel Consumption (kg) | Taxiing Time (s) | Fuel Consumption (kg) | ||

B738 | Shortest taxiing time | 285 | 116.70 | 302 | 120.84 |

Least fuel consumption | 407 | 84.44 | 422 | 88.86 | |

A320 | Shortest taxiing time | 285 | 103.93 | 302 | 107.59 |

Least fuel consumption | 407 | 75.04 | 422 | 79.24 | |

B777 | Shortest taxiing time | 285 | 314.05 | 302 | 325.30 |

Least fuel consumption | 407 | 226.21 | 422 | 238.25 | |

A310 | Shortest taxiing time | 285 | 195.77 | 302 | 202.72 |

Least fuel consumption | 407 | 141.51 | 422 | 148.95 | |

B747 | Shortest taxiing time | 285 | 606.75 | 302 | 627.84 |

Least fuel consumption | 407 | 442.12 | 422 | 464.69 | |

A340 | Shortest taxiing time | 285 | 257.34 | 302 | 266.49 |

Least fuel consumption | 407 | 185.22 | 422 | 195.70 |

Airports | Altitude (m) | Local Atmospheric Pressure (kPa) | $\mathbf{Annual}\text{}\mathbf{Average}\text{}\mathbf{Temperature}\text{}(\xb0\mathrm{C})$ |
---|---|---|---|

ZULS | 3570 | 65.91 | 9 |

ZPPP | 2104 | 77.41 | 14 |

ZSPD | 3.8 | 101.64 | 15.5 |

Aircraft | Fuel Flow | Airport | ||
---|---|---|---|---|

ZULS | ZPPP | ZSPD | ||

B738 | Turning | 0.160 | 0.146 | 0.113 |

Idling | 0.119 | 0.108 | 0.084 | |

Uniform speed | 0.133 | 0.120 | 0.093 | |

Acceleration | 0.188 | 0.171 | 0.133 | |

A320 | Turning | 0.144 | 0.130 | 0.101 |

Idling | 0.108 | 0.098 | 0.076 | |

Uniform speed | 0.120 | 0.109 | 0.085 | |

Acceleration | 0.167 | 0.152 | 0.118 | |

B777 | Turning | 0.426 | 0.387 | 0.300 |

Idling | 0.296 | 0.269 | 0.209 | |

Uniform speed | 0.339 | 0.308 | 0.239 | |

Acceleration | 0.513 | 0.465 | 0.361 | |

A310 | Turning | 0.268 | 0.244 | 0.189 |

Idling | 0.196 | 0.178 | 0.138 | |

Uniform speed | 0.220 | 0.200 | 0.155 | |

Acceleration | 0.331 | 0.300 | 0.233 | |

B747 | Turning | 0.426 | 0.387 | 0.300 |

Idling | 0.344 | 0.313 | 0.243 | |

Uniform speed | 0.372 | 0.337 | 0.262 | |

Acceleration | 0.480 | 0.436 | 0.338 | |

A340 | Turning | 0.176 | 0.160 | 0.124 |

Idling | 0.128 | 0.116 | 0.090 | |

Uniform speed | 0.144 | 0.130 | 0.101 | |

Acceleration | 0.208 | 0.189 | 0.147 |

Aircraft | Taxiing Scheme | Fuel Consumption | ||
---|---|---|---|---|

ZULS | ZPPP | ZSPD | ||

B738 | Most time-saving | 165.36 | 150.63 | 116.89 |

Most fuel-saving | 119.52 | 109.03 | 84.46 | |

A320 | Most time-saving | 147.79 | 134.00 | 104.07 |

Most fuel-saving | 107.16 | 97.02 | 75.48 | |

B777 | Most time-saving | 446.12 | 404.80 | 314.05 |

Most fuel-saving | 321.30 | 291.65 | 226.21 | |

A310 | Most time-saving | 284.55 | 258.43 | 200.47 |

Most fuel-saving | 203.23 | 185.43 | 143.77 | |

B747 | Most time-saving | 861.22 | 782.33 | 606.47 |

Most fuel-saving | 627.64 | 570.15 | 441.98 | |

A340 | Most time-saving | 364.92 | 331.66 | 257.53 |

Most fuel-saving | 263.70 | 239.69 | 186.00 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhang, M.; Huang, Q.; Liu, S.; Li, H.
Multi-Objective Optimization of Aircraft Taxiing on the Airport Surface with Consideration to Taxiing Conflicts and the Airport Environment. *Sustainability* **2019**, *11*, 6728.
https://doi.org/10.3390/su11236728

**AMA Style**

Zhang M, Huang Q, Liu S, Li H.
Multi-Objective Optimization of Aircraft Taxiing on the Airport Surface with Consideration to Taxiing Conflicts and the Airport Environment. *Sustainability*. 2019; 11(23):6728.
https://doi.org/10.3390/su11236728

**Chicago/Turabian Style**

Zhang, Ming, Qianwen Huang, Sihan Liu, and Huiying Li.
2019. "Multi-Objective Optimization of Aircraft Taxiing on the Airport Surface with Consideration to Taxiing Conflicts and the Airport Environment" *Sustainability* 11, no. 23: 6728.
https://doi.org/10.3390/su11236728