The flow corridor is a new type of flexible tube-shape airspace developed to better accommodate high levels of traffic for future air transportation systems. To take advantage of its prominent dynamic characteristic, exploring the flexibility deployment of flow corridors by considering favourable weather conditions is a prerequisite. This paper proposes an optimal design method to minimize the total flying cost within flow corridors with consideration of environmental impacts. We first specify the contrail and CO_{2} emissions as concerned environmental indicators for flexible deployment of flow corridors. Then, incorporating these two indicators into the objective function, an optimization model is presented to optimize the spatial location of flow corridors with consideration of the traffic demand, aircraft performance, and weather conditions. The genetic algorithm is selected for model resolution, and the proposed method is applied in Chinese airspace for case study with benefits assessment. Results show that the optimized 7 flow corridors cover 4.03% of flight demand in China, and the total flying cost with them could be further reduced by 3.19% with the proposed optimal design method.

#### 1. Introduction

With the continuous growth of air transportation around the world, the sustainable development in civil aviation has attracted many attentions from the public and authorities. The global Air Traffic Management (ATM) system is currently undergoing rapid change and evolution towards to the next generation air transportation system, including Performance Based Navigation (PBN), Trajectory-Based Operations (TBO), and Continuous Descent Operations (CDO). How to establish a new safety, efficiency and cost-effectiveness air transportation system with environmental sustainability has become an important research topic. [1–3].

The flow corridor is a new type of flexible tube-shape airspace developed to better accommodate high levels of traffic for future air transportation system [4]. It integrates a range of new airspace prototypes, including dynamic airspace super sectors (DASS) [5], high-volume tube-shaped sectors (HTS) [6], freeways [7], tubes [8, 9], self-separation corridor (SSC) [10], and dynamic multitrack airways (DMA) [11]. The prominent characteristics of flow corridors that would distinguish from the current airway system include allowance for multiple (parallel) lanes of traffic, aircraft self-separated flying within the lanes, and dynamic and flexible deployment.

Many design methods for flow corridor have been proposed to take good advantage of its new prominent characteristics, including city-pairs based methods, airport clustering methods, and traffic density-based methods. Yousefi started from the daily flights between city pairs and proposed a city-pair based idea to design flow corridors [6]. Wing et al. [11] presented a flow corridor deployment method according to the distance and traffic demand. Sridhar et al. [12] clustered the airports by Clustering by Region Growing (CRG) and Weighted-Proximity Classifier (WPC) and designed a flow corridor network with the cluster centers. Xue and Kopardekar [13] took the great circle trajectory of the aircraft as basis and proposed flow corridors based on Hough transform. Yousefi et al. [14] used the actual flight radar track to optimal design flow corridors on speed vectors. Kotecha and Hwang [15] studied the design and optimized the flow corridor network based on point to point operations data for the top 500 airports in USA. Han et al. [16] selected the analytic hierarchy process and adopted the planning method of MAKLINK diagram to design flow corridors. Gupta et al. [9] transformed the design of flow corridors into a multicommodity flow problem and solved it with a mixed integer programming model. Some other studies also refer to the operation rules within flow corridors [17–19].

Until now, the optimal design methods for flow corridors tend to focus on the demand and efficiency with the purpose of increasing capacity or alleviating traffic congestion. There is a lack of research and models that aim at optimal design of flow corridors with consideration of environmental impacts. Different from previous studies, we take advantage of flow corridors’ prominent dynamic characteristic, exploring the flexibility deployment of flow corridors to minimize the total flight cost with consideration of environmental impacts. The contrail and CO_{2} emissions are considered as concerned indicators, and an optimization model is presented to optimize the spatial location of flow corridors with consideration of the traffic demand, aircraft performance, and weather conditions (wind, temperature, humidity, etc.). The genetic algorithm is selected for model resolution, and the proposed method is applied in Chinese airspace for case study with benefits assessment.

The rest of the paper is organized as follows: Section 2 introduces the main environmental impacts that may be caused by flow corridors. Section 3 proposes an optimization model and solution algorithm for optimal design of flow corridors with consideration of environmental impacts. Section 4 employs a numerical case study with benefits assessment. Section 5 provides some conclusions and indicates the next research steps.

#### 2. Concerned Environmental Indicators for Flow Corridors

One of the prominent characteristics of flow corridors that distinguish them from nowadays airways is the dynamic and flexible deployment, which allows flow corridors to be shifted to avoid severe weather and take advantage of favorable weather conditions [14]. Since the most natural home of flow corridors is in high-altitude airspace, contrail and carbon dioxide (CO_{2}) emissions are the main environmental impacts, which can lead to greenhouse effect [20, 21].

Thus, we took the contrail and CO_{2} emissions as concerned environmental indicators in this study and try to reduce these two indicators while designing flow corridors. Modeling details pertaining to contrail generation and CO_{2} emissions are presented below.

##### 2.1. Contrail Generation

Contrail is commonly referred to as aircraft smoke plume. It is a phenomenon of condensation of water vapor formed by the exhaust of aircraft engines cooling in the air and may eventually evolve into cirrus clouds, which can reflect a large amount of long-wave radiation on the ground surface and exacerbate the greenhouse effect.

According to the Schmidt–Appleman standard [22], if the relative humidity () of the environment is greater than or equal to some certain critical humidity () and the relative humidity of the ice surface () is greater than 100% at the same time, the continuous contrail will be generated. The formula for calculating can be expressed aswhere is the saturated water vapor pressure at atmospheric temperature (unit: pa), and is defined as the corresponding saturated water vapor pressure at 0°C. Equation (2) is Magnus saturated vapor pressure formula, in which [23], and is the critical temperature required for contrail formation (unit: °C). is water vapor emission index, and is specific heat capacity at constant air pressure (unit ). P is atmospheric pressure (unit: pa). In equation (4), is the ratio of the molecular weight of water to the average relative molecular weight of dry air. is fuel combustion value (unit ). is average efficiency of engine propulsion.

The formula for calculating on the ice surface can be given by

When is greater than 100%, the contrail can exist for a long time [24].

##### 2.2. CO_{2} Emissions

The CO_{2} emitted by aircraft comes from the combustion of aviation fuel and accounts for 70% of the emitted gas. CO_{2} emissions are not affected by the location of the aircraft but related to the emission index and fuel consumption. The emissions of CO_{2} can be expressed aswhere is the CO_{2} emission amount (unit: kg) and is the index of CO_{2} emission. The aviation fuel emission index refers to the mass of gas generated per unit mass of fuel consumption , which means that burning 1 kg of fuel generates 3.155 kg of CO_{2}. is the fuel consumption of aircraft *m* (unit: kg), which is related to aircraft type, fuel flow rate, and flying time. Usually, the short-term climate impact of CO_{2} emissions is less prominent than that of contrail [13, 14].

#### 3. Optimization Modeling for Design of Flow Corridors

In order to optimize flow corridors to alleviate environmental impact with consideration of en-route weather conditions, an optimization model is proposed for searching the best spatial deployment for flow corridors by considering air traffic demand, aircraft performance, and weather conditions.

Usually, weather conditions data are collected from different meteorological stations that are discrete and uneven distributed, so we discretized the airspace into 3-dimensional grid cells (*X*, *Y*, and *Z* axes) with discrete weather conditions, as shown in Figure 1. Flow corridors are supposed to be deployed within some of the grid cells, and a sequence of grid cells from the origin to the destination can represent an alternative flow corridor design.

Some basic design principles are presented as follows:(1)All flow corridors are supposed to be deployed at one of the alterative flight levels, which follows the proposed deployment rules for flow corridors [7].(2)Meteorological conditions within each grid are treated the same as the center of the grid and are supposed to be consistent with the weather prediction results.(3)Aircraft conflicts between different flow corridors are not considered in the model, since the potential conflicts at crossing parts can be supposed to be solved by the well design of crossing structure [8].(4)Aircraft conflicts within flow corridors are not considered in the model, since the potential conflicts can be supposed to be solved by aircraft self-separating algorithm for the flow corridors.(5)Only the reference Mass, the cruising Mach number, and fuel consumption are considered in the model, while the change of aerodynamics is not considered in the planning stage.

##### 3.1. Objective Function

The objective function proposed in this model is to minimize the Total Flight Cost (TFC) for all aircraft flying within flow corridors with consideration of environmental impacts. The TFC consists of direct operating cost [25], including the cost of aircraft flying time, fuel consumptions, contrail generation, and CO_{2} emissions, and equations can be expressed as follows:

Equation (7) represents the objective function that aims to minimize TFC of aircraft flying within all flow corridors, where *c* represents one of the initial flow corridors, *S* is the initially designed flow corridors set, represents the time period within the deployment time (*W*) of flow corridors, *l* represents the flight level on which flow corridors can be deployed, and *L* is the alternative flight levels set. It implies that the designed flow corridors will be deployed on some alternative flight level with the minimum TFC. Equation (8) shows the major *TFC* components of flight *i* at flight level *l*, including the time cost (), the fuel cost (), the contrail generation cost (), and the CO_{2} emissions cost (), where *i* represents a flight, and *I* is the flight set that takes use of flow corridors. , and are Boolean variables indicating whether the flight *i* is using the flow corridor *c* at the flight level *l* at the time period . is set as 1 when both the departure and arrival time of flight *i* are within the deployment time of flow corridors, is set as 1 if flight *i* is using the flight level *l*, and is set as 1 if flight *i* is using the flow corridor *c*.

Equations (9)(13) present modeling details pertaining to the major components. *k* represents a grid, and *K*_{c} is an alternative grid set for flow corridor *c*. *P*_{T}*, P*_{F}*, P*_{CONT} and are cost indexes for components, represents flying time from grid *k*-1 to *k* at flight level *l* of flight *i,* represents flying distance of flight *i* from grid *k*-1 to grid *k* at flight level *l*, is the reference cruising airspeed (true airspeed) of flight *i* at flight level *l* relating to aircraft type, and and are the predicted wind speed and direction within the grid *k* at flight level *l* collected from meteorological stations. and represent the number of engines and fuel flow rate for flight *i* relating to aircraft type, represents the CO_{2} emission index, is a Boolean variable indicating whether contrail is generated in grid *k*, and value 1 means the weather conditions will generate contrail in the grid *k*.

The key point of the objective function is to find the optimal grid sets (*K*_{c}) for the initial designed flow corridors to minimize the Total Flight Cost (TFC). When searching the optimal grid sets, some constraints are presented as follows.

##### 3.2. Constraints

###### 3.2.1. Flow Corridor Set Size Constraints

Only when the daily flight frequency between city pairs () exceeds the threshold value (), a flow corridor can be constructed, which is given by

###### 3.2.2. Flight Level Boundary Constraint

The alternative flight level should not exceed the specified flight level boundary, the minimum flight level (), and the maximum flight level (), which is given by

###### 3.2.3. Total Length Constraint for Flow Corridors

The growth length of the optimized set should not exceed 10% of that of the length before the optimization (), which is given bywhere *L*_{0} represents the length before optimization.

##### 3.3. Solution Method for the Model

The model considers many flow corridors across the airspace between busy airports or city-pairs, serving a large number of flights with different aircraft, which can lead to a great calculating workload when we search the optimal solution. This is a complex search problem with fast request in response time. The genetic algorithm with elitist retention strategy [26, 27] is selected to solve the proposed model in this paper. Genetic algorithm is a variant of stochastic beam search algorithm, which is proved to be efficient when it is used to solve complex problems. Compared with the traditional optimization algorithm, genetic algorithm based on biological evolution has good convergence and robustness. The process of searching is simple, and the probability mechanism is used for iteration, which has randomness. It is this unique search method that makes genetic algorithm avoid the local minimum trap that other optimization algorithms often encounter. When genetic algorithm is used to solve practical problems, the optimal individuals that represent the best solution for the problem will be kept all the time, while the worse individuals will be abandoned during the searching process. It has the advantages of good convergence and computational efficiency, which meets the requirement of fast-time searching for this model. For the problem of flow corridors optimization to minimize environmental impact, the steps of the genetic algorithm are as follows:Step 1*Gene Coding*. Coding based on the grid number. Each flight path of the aircraft in the airspace is determined by the grid serial number method; take an individual; for example, {0, 1, 11, 21, 22, 23, 24, 35, 45, 55, 65, 66, 67, 72, 85, 88, 99} represents a path that is coded by a sequence of grid serial numbers.Step 2*Generation of Initial Population*. Set the population size and generate the initial path randomly according to the position and direction of the aircraft's starting and ending points.Step 3*Design Fitness Functions*. For the optimization problem in this study, the objective function is to minimize the total flight cost of traffic flow within flow corridors. Equation (17) is selected here to represent the individual fitness function:Step 4*Genetic Operator*. The key parameters of the genetic algorithm are set, including the population size, termination evolution algebra, crossover probability, mutation probability, and variation mode.Step 5*Elite Retention Strategy*. Determine whether the gene meets the constraint conditions; if not, discard the gene. Merge the processed child population with the parent population, calculate the fitness value of the gene, use the elite retention strategy to retain the gene corresponding to the better solution, and generate a new population as the new parent population. Elite individuals are the individuals with the highest fitness value searched by genetic algorithm so far, which have the best genetic structure and excellent characteristics. The elitist reservation is that the optimal individuals will not be lost and destroyed by selection, crossover, and mutation in the evolutionary process of genetic algorithm.Step 6*Comparison.* Compare the evolutionary algebra and termination evolutionary algebra in the genetic algorithm. If the two are equal, the iterative process will be ended and the optimal path will be obtained. Otherwise, return to Step 4 and continue.

#### 4. Numerical Case Study

This section employs the proposed optimal design method for flow corridors in Chinese airspace for case study with benefits assessment.

##### 4.1. Description of the Test Site

###### 4.1.1. Initial Design of Flow Corridors

For the initial design of flow corridors, the history operational data for all flights on July 3, 2017, were parsed to obtain the busy city pairs in China. Then, the city-pair based method [12] was used to construct the primary Chinese flow corridors. This is a reasonably good design method for flow corridors, since most flights have already flied between these city pairs.

The unidirectional flight frequency threshold () between city pairs is the key parameter determining the size of flow corridors set. The threshold value is set as 60 flights/day for case study in this research, which implies that the flow corridors will be deployed between the city pairs with more than 60 flight/day. Based on the statistic results, 7 city pairs in China satisfied the flight frequency requirements, which are Beijing-Shanghai, Shenzhen-Shanghai, Shenzhen-Beijing, Chengdu-Beijing, Shanghai-Guangzhou, Beijing-Guangzhou, and Hangzhou-Beijing as shown in Table 1. These 7 city pairs accommodate about 4.03% of flight demand in China.

Then, the related en-route entry and exit points were selected based on these city pairs, and 7 flow corridors were initially designed by using great circle routes. The entry and exit points with the length of flow corridors are shown in Table 2.

###### 4.1.2. Weather Data Collection and Preprocess

To optimize the flow corridors configuration, the airspaces were discretized into 3-dimensional grid cells based on the initial deployment. The basic grid size is set as 30 km 30 km, and the whole airspace is divided into 6271 grids with unique serial numbers. That is, the East-West length of the selected airspace is 6230 km, and that of the north-south direction is 7130 km. Five alternative flight levels (10100 m, 10400 m, 10700 m, 11000 m, and 11300 m) were considered for flow corridors deployment, and predicted weather conditions were collected from 42 adjacent meteorological stations with spatial interpolation method. For example, Figures 2 and 3 show the temperature and relative humidity distribution in the concerned airspace at the flight level 11300 m. Figure 4 shows the relative humidity (colored surface) and critical relative humidity (dark red surface) at the flight level 11300 m. Figure 5 shows the relative humidity of the ice at the flight level 11300 m. With these processes, each grid can be initialized with predicted weather conditions, and the generation of contrails in each grid can also be estimated according to the equations proposed in Section 2. Figure 6 shows the calculated distribution of contrails in grids at the flight level 11300 m, and the purple grids represent the airspace that can generate contrails.

###### 4.1.3. Experiment Parameters Initialization

The deployment time period of flow corridors is set between 08 : 00 and 14 : 00 in the experiment, and 58 flights with 9 different aircraft types are simulated to fly within the proposed flow corridors, including A320, A321, A332, A333, A388, B738, B763, B773, and B77 W. The related performance parameters for different aircraft types were obtained from the Base of Aircraft Data (BADA) published by EUROCONTRL [28], including the reference cruise speed (Mach number), number of engines, fuel flow rate in different flight level, and CO_{2} emission index etc.

In the algorithm, the genetic algorithm parameters are set as follows: population size is 300, the termination generation is 150, crossover probability is 0.8, mutation probability is 0.01, the elite strategy keeps 4 best chromosomes for each generation, and the linear recombination and stochastic factor mutation are used in the experiment. According to previous research [29], the cost indexes PT, PF, PCONT, and PCO2 are set as 0.0026 ($/min), 11.0626 ($/kg), 0.0021 ($/km), and 0.5414 ($/kg).

##### 4.2. Analysis of Results

Figure 7 shows the variation of the total flight cost with the increase of population generation. The total flight cost reduced from 389,000$ to 383,000$ quickly within 50 generations by the proposed algorithm. From 50 to 150 generations, the total flight cost decreases slowly at first and then stays at 382,367 after 75 generations, implying that the approximate optimized results are obtained.

Figure 8 shows the initial total flight cost and optimized results from flight levels aspect. The initial total flight cost for deploying flow corridors at different flight levels is displayed by black bars, while the optimized results are displayed by red ones. It can be seen that the total flight cost at different flight levels is different than that before optimization, implying that flight level could be an important factor for flow corridors deployment. Potential reasons may include weather conditions and aircraft performance differences. For example, the weather elements (wind and temperature) are usually different at different altitudes, then the True Air Speed (TAS) and fuel flow rate for the same type of aircraft at different altitudes will be different. The weather factors considered in this paper include wind, temperature, and humidity. From the analysis in Chapter 2 and the objective function in Section 3.1, it can be seen that they not only affect the generation of carbon dioxide emissions and condensation, but also affect the flight time and fuel emissions of aircraft.

After optimization, the results show that the total flight cost at all flight levels can be decreased, and when the flow corridors are deployed at the flight level 11300 m, the minimum total flight cost is obtained.

Table 3 also shows the minimum total flight cost with the major components, including time cost, fuel cost, CO_{2} emissions cost, and contrail generation cost. In general, the reduction rate for total flight cost is 3.19% after optimization with the time cost (2.74%), fuel cost (3.21%), CO_{2} emissions cost (2.74%), and contrail generation cost (7.60%). A noticeable point is that although the reduction rate for contrails generation is the maximum, fuel cost reduction is the dominant component for the total flight cost reduction. In addition, although both the fuel cost and CO_{2} emissions should be calculated in practice, these two indexes are linearly dependent, which leads to the same reduction rate for fuel cost and CO_{2} emissions.

Figure 9 shows the optimal results for designed Chinese flow corridors deployed at the flight level 11300 m. Although the shape of the flow corridors is no longer great circle routes, with the dynamic and flexible deployment of flow corridors, the total flight cost with environmental impact could be reduced with consideration of the en-route weather conditions.

#### 5. Conclusions

This paper presented an optimal design method for flow corridors to minimize the total flying cost with consideration of environmental impacts. The proposed optimization model integrated the cost of aircraft flying time, fuel consumptions, contrail generation, and CO_{2} emissions together and optimized the spatial location of flow corridors by using genetic algorithm with consideration of the traffic demand, aircraft performance, and weather conditions.

The proposed optimal design method for flow corridor is applied in Chinese airspace for numerical case study with benefits assessment. The results obtained show that the designed 7 flow corridors cover 4.03% of flight demand in China, and the total flight cost could be reduced by 3.19% with the proposed optimization model. Although flow corridors can be deployed on one flight level, the deployed flight level should be considered carefully since the total flight cost is usually differently caused by the inconformity of weather conditions and aircraft performance. Although the reduction rate for contrails generation is the maximum in the numerical case, fuel cost reduction is the dominant component for the total flight cost reduction.

The optimal design method presented in this paper could be applied in flexible deployment of flow corridors, which is in alignment with flow contingency management and trajectory management in the future air transportation systems. Future works include extending the model to flow corridors network design as well as incorporating some spatial-temporal factors.

#### Data Availability

The mat data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

This work was supported by the National Natural Science Foundation of China (nos. U1933119 and 61671237).