Airport Field Path Optimization Method Based on Conflict Hotspot Avoidance Mechanism

Abstract

The state path optimization model, alongside strategies like slowing down and waiting, aims to identify optimal aircraft routes that minimize the total taxi time and prevent conflicts. Optimization reduces taxiing times for aircraft YZR7537, CES2558, and CSZ9806, while slightly increasing the times for CSN6310 and CSN3210 due to conflict hotspot avoidance measures. This approach also decreases the number of aircraft passing through key conflict hotspots, effectively reducing both conflicts and risk levels in these areas. Consequently, the total taxiing time for the optimized aircraft is cut by 53 s, enhancing airport operational efficiency. The proposed model serves as a theoretical foundation for developing an intelligent airport operation management system.

1. Introduction

According to the Civil Aviation Administration of China (CAAC), the aviation industry recorded 841,000 h of transport flights in January 2023, representing a sequential increase of 75.2% and a year-on-year rise of 11.0%. There were also 342,000 flights, reflecting increases of 78.2% sequentially and 10.4% year-on-year. Overall, the sector is experiencing a rapid recovery, with a transport turnover of 7.39 billion ton-kilometers, up 13.9% compared with the previous year. Passenger transport volume reached 39.775 million, marking an increase of 34.8%, while cargo and mail transport saw a decline of 25.1%, totaling 490,000 tons. This indicates a strong rebound toward pre-pandemic levels, although challenges remain in the cargo sector. As flight volumes increase, major airports serving over 10 million passengers are facing heightened operational pressures. To tackle these challenges, a study is being conducted to simulate the environments of busy airports and identify key conflict hotspots. By optimizing aircraft taxiing paths, this research aims to reduce conflicts and improve overall operational efficiency.

At present, domestic and international research on airport field aircraft path optimization is mainly divided into two aspects: static path planning and dynamic path planning. Static path planning generates one-time glide routes by calculating time-averaged costs or risks based on historical trajectories or predefined scenarios over a longer period of time, whereas dynamic path planning utilizes real-time radar/ADS-B data, or simulated forecasts, to update paths on a rolling basis and deconflict online, which is more responsive to the characteristics of traffic flow over time. With the expansion of airports and the increase in airport traffic, the field operation process becomes more and more complex, and the related studies on path optimization also consider more about the influence of field operation rules, field operation conflicts, and control transfer on the path optimization strategy. For static path planning, in 1998, Hesselink et al. used Dijkstra’s algorithm to optimize airport field aircraft paths based on airport network diagrams, but it lacked consideration of the possibility of dynamic taxi conflicts occurring during the aircraft taxiing process [1]. In 2015, Ghoniem et al. proposed an efficient branch delimitation algorithm for the problem of multi-runway aircraft sequencing to optimize the shortest path problem in the presence of time windows, as well as non-triangular separations [2]. In 2018, Adacher et al. implemented an aircraft field taxi path planning algorithm using a waitlist model to represent a path planning scheme, aiming to minimize the total taxi time and total waiting time [3]. In 2019, Yu used a genetic algorithm to analyze the taxi cost of a straight-line taxiway under specified weights and used a depth-first traversal algorithm to select and optimize aircraft ground taxi paths based on conflict resolution [4]. In 2020, Qianwen Huang established a computational model for fuel consumption and pollutant emissions of field taxiing to evaluate the fuel consumption and pollutant emissions during aircraft field taxiing and used it as the basis for path optimization [5]. In 2022, Zhaonin Zhang et al. used the aircraft field global operation time as the shortest, and proposed a taxiing path planning model based on situational awareness to optimize the aircraft taxiing path [6].

In terms of dynamic path planning, there is more research on optimizing aircraft taxiing paths by improving various path planning algorithms. Among them, some scholars improve the coding method of the genetic algorithm, integrate the glide conflict constraints, and consider the weight coefficients of waiting time to solve the glide optimization model to obtain the optimal glide path of aircraft and improve the efficiency of conflict resolution for field objectives [7,8]. Some scholars consider the maximum traversal time constraints, turn penalties, and other cost functions of the improved A* algorithm, solve the aircraft glide path optimization model based on the improved A* algorithm, and combine with the sliding time window to achieve intelligent conflict identification and relief, and obtain a conflict-free and smooth glide path [9,10,11,12]. In addition, in 2019, Zhou et al. proposed a dynamic taxi speed adjustment strategy for aircraft, using state space, action space, and reward function models to make speed adjustment decisions, to achieve path optimization with the goal of conflict-free and minimum taxiing time for aircraft [13]. In 2021, Xie Chunsheng et al. constructed an airport taxi time prediction model, combining a rolling time window and a fuzzy time window for taxi path optimization [14]. In the same year, Li Zhilong et al. analyzed the Q-learning path planning algorithm and A* path planning algorithm, and based on this, they made a plan for the field taxi path [15]. Liu Jinan et al. developed an aircraft taxi guidance system based on WORLD WIND and constructed an airport field structural model to achieve the path optimization of field taxi paths [16]. Jiang et al. constructed an airport field taxi optimization model based on two-layer planning and used an iterative heuristic algorithm to solve taxi conflicts, which significantly outperformed the first-come-first-served scheduling scheme under the premise of no conflicts and improved the overall operational efficiency [17]. In 2022, Huang Yiyi et al. evaluated the risk of airport field taxiways and divided the risk intervals by fusing the airport field Petri net model and the risk probability model of taxiing conflicts, and used an ant colony algorithm integrating the Stackelberg game idea to optimize the taxiing paths of aircraft to reduce the risk level of the airport taxiways [18]. That same year, Deng et al. used a new ant colony pheromone initialization method, pheromone allocation mechanism, and pheromone updating strategy based on the wolf predation principle, designing a multi-strategy particle swarm-ant colony hybrid optimization algorithm for solving the airport taxi planning model and a conflict adjustment strategy based on the speed-first and first-come-first-served principles, which effectively avoid taxiway conflicts and conflict propagation [19]. Then, Nöhren et al. used a multi-objective A* algorithm combined with a genetic algorithm to generate and optimize aircraft ground trajectories, solve the trajectory conflict problem, and adapt to environmental change conditions in real time [20]. In 2023, Xiang et al. improved the Q-Learning algorithm by optimizing Q-table exploration, resetting the initial Q-table values, introducing a dynamic exploration factor, and introducing a conflict avoidance strategy to plan taxi paths for aircraft in highly dynamic and stochastic airport environments [21]. In the same year, Gao Jiuzhou et al. proposed an improved A* algorithm, which applies an improved heuristic function to increase the search efficiency and improve path optimization [22]. The above studies mainly achieved conflict-free path planning for aircraft by improving the path planning algorithm, but they did not consider the limitations of the ground operation environment and the spatial and temporal distribution of aircraft taxiing. On this basis, in 2019, Tien et al. used the Markov decision process to model the field aircraft operation process and used a convolutional neural network to learn the airport ground operation environment and flight time constraints to achieve conflict-free flight path planning and conflict resolution [23]. In 2022, Zhang et al. established the three main conflicts of crossover, head-to-head, and tail-following in the taxiing process of the field aircraft in the airport dynamics model; determined the shortest path set using the Yen algorithm based on the topological network, conflict delays, and field taxi space distribution; and optimized aircraft taxi paths according to environmental parameters and aircraft type differences [24].

There are also some scholars who use different dynamic priority strategies to achieve conflict-free taxi path planning for aircraft. In 2015, Luo et al. proposed a Petri net model based on colored taxiways, which adjusts the taxi paths of aircraft in real time by lowering the priority of delayed aircraft entering the airport roadway under the condition of guaranteeing conflict-free taxiing, to avoid a long waiting time [25]. In 2020, Yassine et al. implemented a conflict detection and resolution algorithm by simulating the movement process of aircraft in the airport field through a first-come-first-served planner, using three priority strategies and comparing the number of delayed aircraft and the overall delay for conflict resolution [26]. In 2021, Jiang Yu et al. constructed a taxiway scheduling optimization model based on the control of time richness, which aimed to improve the punctuality of the arrival of aircraft at the endpoint and used a biogeography algorithm for validation, effectively reducing the number of aircraft taxiing conflicts and lowering the error of arriving at the taxiing terminal [27]. As the focus of research has shifted from standby conflict resolution to the improvement of overall operational efficiency, academics have begun to notice that conflict exhibits spatial clustering in run–slip networks. This space is known as a conflict hotspot. Therefore, the following definition can be derived: a conflict hotspot refers to a subregion of the running skidding system whose conflict probability or related risk index exceeds a certain threshold in a given time window and is spatially and continuously aggregated. Its formation is related to the coupling of traffic flow density, flow direction interweaving, control strategy, and machine-vehicle mixing, etc., which has significant spatial and temporal dynamics, and some scholars try to incorporate it into the study of path optimization in conflict avoidance. For example, in 2015, Pan Weijun et al. deeply analyzed the spatial and temporal distribution characteristics of airport hotspots, designed an aircraft taxi avoidance mechanism, and established an aircraft taxi path optimization model to optimize aircraft taxi paths to avoid potential taxi conflicts and effectively reduce the risk level of the hotspot areas [28]. In 2017, Wang et al. constructed an airport node–segment network topology model, established a taxi path optimization model to minimize aircraft taxiing time, and established a taxi avoidance mechanism based on airport ground hotspots to effectively avoid taxiing conflicts and reduce the total taxiing time [29]. In 2018, Dong Bing designed a selection avoidance mechanism based on the information on the conflict points, established a taxi path optimization model to minimize the aircraft taxiing time, and used a two-phase path planning algorithm to obtain the optimized path of the aircraft [30].

In summary, most of the current studies on airport field conflicts take aircraft as the main detection object to analyze microscopic conflicts and seldom include the impact of security vehicles in the scope of conflict risk analysis, and there are fewer studies on the comprehensive evaluation of airport conflict hotspots by integrating the activity targets of aircraft and security vehicles. The indicators for identifying the key conflict points are mainly centered on the probability of conflict, and seldom take into account the inherent complex network characteristics of the field taxi system and its impact on potential conflicts; airport hotspots are mainly identified as static hotspots based on historical trajectory data, and these hotspot areas are prone to conflict events only in some specific cases. The hotspots at airports are mainly identified as static hotspots based on historical trajectory data, and these hotspots are prone to conflicts only under certain specific circumstances, without considering the complexity of the dynamic traffic flow on the airport surface and the spatial and temporal distribution of hotspots. Therefore, this paper is oriented to the operation of large busy airports in China, considering the complex network characteristics of the airport surface running and taxiing system, the complexity of the traffic of the mixed operation of the aircraft vehicle, and the possible changes in the hotspots in the airport surface with space and time, combined with the complex network theory and the simulation of the traffic operation of the airport surface, to explore the potential hotspots of conflicts in the airport surface, and analyze and predict the temporal and spatial distribution of the potential hotspots of conflicts, identifying dynamics. The key conflict hotspots are identified, and the taxiing paths of aircraft are optimized for the key hotspot areas to reduce the conflict risk of the airport surface.

2. Modelling

2.1. Identification of Key Conflict Hotspot Areas

Currently, most hotspot identification in airport fields relies on static hotspots derived from historical data, which do not take into account the temporal and spatial variations in traffic flow. To address this limitation, this section utilizes findings from another study by the authors. It employs the Gated Recurrent Unit (GRU) model, along with a self-attention mechanism to develop a dynamic risk indicator prediction model for airport surfaces. This model aims to identify critical conflict hotspot areas more effectively.

The field dynamic risk indicator prediction model includes an input layer, a GRU layer, a self-attention mechanism layer, a fully connected layer, and an output layer. To prevent overfitting, the dropout layer is set after each GRU layer. Among them, the forward propagation formula [31] for the GRU layer is as follows:

(1)$r_t=\sigma \left(W_r{\left[h_{t-1},x_t\right]}_r\right)$

(2)$z_t=\sigma \left(W_z\left[h_{t-1},x_t\right]\right)$

(3)$h_t^{\prime }=\tanh \left(W_{h^{\prime }}\left[r_t\times h_{t-1},x_t\right]\right)$

(4)$h_t=\left(1-z_t\right)\times h_{t-1}+z_t\times h_t^{\prime }$

where $x_t$ is the input at the current moment $t$; $z_t$ is the update gate; $r_t$ is the reset gate; $h_t^{\prime }$ is the memory storage state; $h_t$ is the output at the current moment $t$; $h_{t-1}$ is the output at the previous moment; $W_r,W_z,W_{h^{\prime }}$ are the matrices of the weight coefficients to be learned; $\sigma$ is the sigmoid activation function; and tanh is the activation function.

The formula for the self-attention layer is as follows:

(5)$q_i=W^q{h}_i$

(6)$k_i=W^k{h}_i$

(7)$v_i=W^v{h}_i$

(8)$a_{t,i}={\displaystyle \frac{q_t•k_i^T}{\sqrt{d}}}$

(9)$a_{t,i}^{\prime }=soft\max (a_{t,i})$

(10)${\widehat{h}}_t={\displaystyle \sum _i{a}_{t,i}^{\prime }{v}_i}$

where $h_i$ denotes the implicit state feature of the $ith$ output time step of the output in the GRU layer;$q, k, v$ denote $Query, Key, Value$ in the attention mechanism, respectively; $W^q$, $W^k$, $W^v$ denote the matrices of the weight coefficients; $d$ denotes the variance of the elements of the $q\times k^T$ matrix for solving the gradient vanishing problem, where $q={\left(q_{t-T+1},\cdots q_t\right)}^T$, $k={\left(k_{t-T+1},\cdots k_t\right)}^T$; $a_{t,i}^{\prime }$ denotes the attention score, i.e., the weight of the time step $i$ on the time step $t$; and ${\widehat{h}}_t$ denotes the value of the time step $t$ weighted by the attention score. The $soft\max$ function is a normalized exponential mapping that takes any real vector scaled by exp(⋅) and normalizes it by the sum, outputting a set of probability weights between 0 and 1 and summing to 1, thus highlighting the relative advantage of high-scoring elements.

For the above neural network model, the loss function is defined as follows:

(11)$Los={\displaystyle \frac{{\displaystyle \sum _{n=1}^N{\displaystyle \sum _{t=1}^T{\left(y_{n,t}^{\prime }-y_{n,t}\right)}^2}}}{NT}}$

where $N$ is the number of potential conflict hotspot regions; $T$ is the total number of predicted time steps; $y_{n,t}^{\prime }$ is the predicted value of the $n th$ potential conflict hotspot region at the $t th$ time step; and $y_{n,t}$ is the labeled value of the $n th$ potential conflict hotspot region at the $t th$ time step.

2.2. Hotspot Avoidance Mechanisms

A hotspot avoidance mechanism is designed for critical conflict hotspot areas $HS=\{H{S}_1,H{S}_2,\cdots \}$, where the likelihood of conflict is high. The core of the mechanism is to determine the priority of aircraft in different operating environments, and then allow aircraft with a high priority to pass through the hotspot area first and continue taxiing on the pre-planned path, while aircraft with a low priority will use other resolution strategies. When a potential conflict occurs in a hotspot area, the following principles are used to determine the priority of aircraft:

(1) Priority judgment for inbound and outbound: In a certain period, if there are inbound and outbound aircraft occupying the hotspot area one after another and there is a potential taxiing conflict, the inbound aircraft will be allowed to continue taxiing in the hotspot area on the original taxiing path, and the outbound aircraft will either slow down and wait for it, or change to a suboptimal alternative taxiing path as shown in Figure 1a, to avoid the potential taxiing conflict.

(2) Taxiing time priority judgment: In a certain period, if there are inbound and outbound aircraft occupying the conflict hotspot area successively and there is a potential taxiing conflict, the aircraft with a longer taxiing time will be allowed to continue taxiing on the original taxiing path passing through the hotspot area, whereas the aircraft with shorter taxiing time will decelerate and wait for the alternative taxiing path or change to a suboptimal alternative taxiing path, as shown in Figure 1b, to optimize the field resource utilization.

(3) Aircraft priority judgement: In a certain period, there are more aircraft occupying the hotspot area one after another; therefore, the time is subdivided into several time slots, so that the aircraft in the first time slot will continue to taxi on the original taxiing path passing through the hotspot area, and the aircraft in the neighboring time slow down and wait for or choose the suboptimal alternative taxiing path, as shown in Figure 1c, to avoid the conflict of taxiing.

For the two options for conflict resolution—decelerate and wait, and replan the suboptimal alternative path—it is necessary to evaluate the waiting time for both and select the solution with the smaller waiting time. The time to decelerate and wait is $\Delta t$, and the time to replan the suboptimal alternative path over the original plan is $\Delta c/v$, where $\Delta c$ is the increased glide distance of the replanned path. To select the less costly solution to resolve the conflict, the conflict resolution process is shown in Figure 2. In the conflict resolution process, deadlocks or livelocks may occur. In order to avoid the phenomenon of a deadlock (waiting in a loop) or livelock (priority keeps changing but cannot be unlocked) that occur in the hotspot avoidance process, this paper introduces a waiting directed graph monitoring mechanism into the scheduling module. The system treats all the waiting aircrafts as vertices in real time, and constructs directed edges according to the relationship of letting them go first and then moving them later, and once the directed loop is detected, it is considered that a potential deadlock occurs. Firstly, the local unlocking strategy is executed, and the flight with the longest waiting time in the ring exchanges priority with its predecessor; if the ring is not broken by two consecutive local unlockings, the global unlocking is triggered, and a set of new alternative paths without the ring are generated to replace the original conflicting paths at one time [32] This is a detailed description of the Swap Aircraft Priority, Resolve Conflicts section of Figure 2.

2.3. Path Optimization Model

To establish a path optimization model for the conflict hotspot area of the airport field, the model parameters are defined as follows:

$F$: denotes the set of all aircraft in the specified time, $F=\left\{f_1,f_2,\cdots ,f_k\right\}$;

$N$: denotes the set of nodes of the airport field topology network;

$L_{ab}$: denotes the length of the glide path from node $a$ to node $b$, where $a,b\in N$;

$T_{ia}$: denotes the actual time at which the aircraft $f_i$ needs to avoid the hotspot area to reach the node $a$ or $T_{ia}=0$ if aircraft $f_i$ does not reach the node $a$;

$t_{ia}$: denotes the time when the aircraft $f_i$ reaches the node $a$ without avoiding the hotspot area, or $t_{ia}=0$ if the aircraft $f_i$ does not reach the node $a$;

$t_{ij}^a$: denotes the minimum safe interval, $t_{ij}^e=40 \mathrm{s}$;

$v_i$: denotes the glide speed of the aircraft, taking $v_i=50 \mathrm{k}\mathrm{m}/\mathrm{h}$;

$C_{ab}$: indicates whether there is a feasible glide path from node $a$ to node $b$. $C_{ab}=1$ indicates that there is a feasible glide path from node $a$ to node $b$, otherwise $C_{ab}=0$;

$R_{iab}$: indicates the glide direction of the aircraft, $R_{iab}=1$ indicates that the aircraft $f_i$ glides from node $a$ to node $b$, otherwise $R_{iab}=0$;

$Z_{ija}$: denotes the order in which two aircraft arrive at a node, $Z_{ija}=1$ denotes that aircraft $f_i$ arrives at the node $a$ before the aircraft, otherwise $Z_{ija}=0$;

$N^i$:denotes the glide path of an aircraft $f_i$, consisting of a series of field network nodes, $N^i=\left\{o^i,n_1^i,n_2^i,\cdots ,n_{k_i}^i,d^i\right\}$;

$M^i$: denotes the set of field network nodes that aircraft $f_i$ has passed through: $M^i=\left\{o^i,n_1^i,n_2^i,\cdots ,n_{k_i}^i,d^i\right\}$, $o^i$ is the starting point, and $d^i$ is the endpoint.

In this paper, the shortest taxiing time for all aircraft to taxi to the endpoint within the specified time is taken as the objective, and the objective function is constructed as follows:

(12)$\min T={\displaystyle \sum _{f_i\in F}{\displaystyle \sum _{a,b\in N}\frac{R_{iab}{L}_{ab}}{v_i}}}+\left(T_{ia}-t_{ia}\right)$

Aircraft taxiing needs to satisfy taxi path constraints, safety interval constraints, head-to-head constraints, and overrun constraints.

(1). Glide path constraints

(13) $R_{iab}\le C_{ab},\forall f_i\in F,\forall a,b\in N$

(14) ${\displaystyle \sum _{a\in N}{R}_{iab}}-{\displaystyle \sum _{s\in N}{R}_{ibs}}=\left\{\begin{array}{l}1,b=d^i\\ -1,b=o^i\\ 0,otherwize\end{array}\right.,\forall f_i\in F,\forall a,b,s\in N$

Equation (13) indicates that the aircraft glide path must be feasible and Equation (14) indicates that the aircraft glide path must be continuous.

(2). Safety interval constraints

(15) $T_{ja}-T_{ia}\ge t_{ij}^e,\forall f_i,f_j\in F,\forall a\in N$

Equation (15) indicates that the distance between any two aircraft passing through the unity node must satisfy the minimum safe separation.

(3). Head-to-head constraints

(16) $\left\{\begin{array}{l}{Z}_{ija}-Z_{ijb}\le 2-\left(R_{iab}+R_{jba}\right)\\ Z_{ija}-Z_{ijb}\ge -2+\left(R_{iab}+R_{jba}\right)\end{array}\right.,\forall f_i,f_j\in F\wedge i\ne j,\forall a,b\in N$

Equation (16) indicates that head-to-head conflict is not permitted between any two aircraft.

(4). Beyond constraints

(17) $\left\{\begin{array}{l}{Z}_{ija}-Z_{ijb}\le 2-\left(R_{iab}+R_{jab}\right)\\ Z_{ija}-Z_{ijb}\le -2+\left(R_{iab}+R_{jab}\right)\end{array}\right.,\forall f_i,f_j\in F\wedge i\ne j,\forall a,b\in N$

Equation (17) indicates that a tailgating conflict between any two aircraft is not permitted.

In summary, a path optimization model can be constructed for the hotspot area of the airport field with the objective of minimizing the total taxiing time of the aircraft by taking into account the constraints of the aircraft’s taxiing path, the safety interval, and the conflicts during the taxiing process.

3. Algorithm Design

Combining the hotspot area path optimization model of the airport field, as well as the hotspot area avoidance mechanism and conflict resolution strategy described above, the genetic algorithm is selected to solve the optimal taxiing scheme considering the unsmoothness of the objective function in the model. In this chapter, based on a traditional genetic algorithm, the heuristic search algorithm is introduced to generate the initial feasible solution, which effectively reduces the number of iterations of the algorithm, and at the same time, the hotspot area avoidance mechanism and conflict resolution strategy are added, which can achieve the restoration of the individual and enhance its adaptability by evaluating the strengths and weaknesses of the individual and resolving the conflict.

3.1. Operator Design

(1). Coding

The conventional binary coding method may produce more non-feasible solutions, which makes the search time increase greatly and makes it easy to fall into the local optimum. Therefore, based on the field hotspot area path optimization model established above, this section adopts the real number coding method to encode the aircraft taxi paths, using real numbers as chromosomes to reduce the complexity of the correspondence between the solution space and the coding space. The gene segment of the chromosome consists of the numerical numbering of the nodes of the airport field network topology model, and the order of the nodes reflects the sequence of the taxi paths of the aircraft from the start point to the endpoint. The chromosome shown in Figure 3 represents the sequence of the taxi paths for Aircraft $f_i$ as it rolls out of the parking position (node number 174) and taxis to the runway entrance (node number 10) using runway 33.

(2). Population Initialization

It is known that the starting node of the aircraft is $o$ and the target node is $d$. Use a heuristic search algorithm to obtain $N$ initial feasible solutions (i.e., $N$ initial glide paths) to form the first generation of the population, The specific process is shown in Figure 4 and the specific steps are as follows:

Step 1: Initialize the sequence of the starting nodes, and set the initial $N=1$. When running to the $N$ th time, determine whether $N$ satisfies the cyclic condition; if not go to Step 2, if so, go to Step 6.

Step 2: Search the neighboring node $n_1,n_2,n_3\cdots$ of the starting node $o$, sort the distance cost of the neighboring node sequence, and calculate the sum.

Step 3: Calculate the cumulative probability $p$ of the costs of all neighboring nodes and generate $(0,1)$ random number $random$.

Step 4: Compare $random$ and $p$, select the node $p$ corresponding to the probability interval, add the node $n_1$ to the path sequence, and store the $N$ th cycle path sequence.

Step 5: Determine whether the selected node a is the target node of the aircraft; if not, take the node as the current node and go to Step 2, if it is the target node then go to Step 1.

Step 6: Output the initial pre-gliding path set of all aircraft.

(3). Selection

In this section, the combination of the elite preservation method and sorting selection method is used to carry out the selection operation. Firstly, the fitness values of individuals are calculated and sorted to eliminate the individuals with poor fitness values in the population; then, the individuals with superior fitness values are selected according to a certain proportion to evolve to the next generation.

(4). Crossovers and Variations

To ensure that the encoding does not affect the global optimal solution in the crossover and mutation process, an adaptive genetic algorithm is used so that the crossover operator and mutation operator can carry out the corresponding genetic operation according to the change of the fitness, which helps to improve the convergence speed and global search ability of the algorithm. The crossover probability and mutation probability are calculated as follows:

(18)$P_c=\left\{\begin{array}{cc}{\displaystyle \frac{k_1(f_{\max }-f^{\prime })}{f_{\max }-\overline{f}}}& , f\ge \overline{f}\\ k_3& , f<\overline{f}\end{array}\right.$

(19)$P_v=\left\{\begin{array}{cc}{\displaystyle \frac{k_2(f_{\max }-f^{\prime })}{f_{\max }-\overline{f}}}& , f\ge \overline{f}\\ k_4& , f<\overline{f}\end{array}\right.$

where $f_{\max }$ denotes the maximum value of the fitness value of all individuals in the aircraft population, $\overline{f}$ denotes the average value of the fitness value of all individuals in the aircraft population, $f^{\prime }$ denotes the value of the larger fitness among the two aircraft that need to be subjected to the variation and crossover operations, $f$ denotes the fitness value of the individual that needs to be subjected to the variation operation, and $k_1,k_2,k_3,k_4$ is a constant, with the value of $k_1=k_3=1, k_2=k_4=0.5$ taken by reference [33].

3.2. Adaptation Function Setting

Since the established optimization model minimizes the total aircraft taxi time as the objective, a smaller objective corresponds to a more optimal aircraft taxi path. Therefore, in this section, the objective function is transformed into a problem of seeking the maximum value of fitness, and the fitness function is set as:

(20)$f(x)=\left\{\begin{array}{l}{\displaystyle \frac{1}{1+\ln (F(X))}} , Satisfies all constraints\\ 0, If not\end{array}\right.$

where $F(x)=\min T$ represents the total glide time minimized. When the adaptation values of all the output paths are calculated, the glide paths with larger adaptation values are selected to enter the next generation, and those with smaller adaptation values are eliminated, and the optimal glide paths are gradually approximated according to this method.

3.3. Algorithm Flow

The overall algorithm flow of path optimization for the hotspot region of field conflict is shown in Figure 5, and the specific steps are as follows:

Step 1: Design the chromosome coding rules and generate the initial feasible solution population according to the heuristic path search algorithm.

Step 2: Sort the fitness values of individuals, determine whether the iteration conditions satisfy the conflict constraints; if the conditions are not satisfied, go to Step 3, otherwise, go to Step 6.

Step 3: Perform crossover and mutation operations on individuals that do not satisfy the convergence conditions and conflict constraints.

Step 4: A conflict resolution strategy is used to deconflict the individuals in the population, including those after crossover and mutation.

Step 5: Calculate and sort the fitness values of all individuals in the population, select the individuals with higher fitness values to evolve according to a certain proportion, retain them to the next generation, and go to Step 2.

Step 6: Output the optimal glide path of the aircraft.

The time-consuming iterative process of the improved adaptive genetic algorithm in this paper focuses on constraint repair and fitness assessment for P-bar chromosomes, and the complexity is about $O(P•\overline{L})$, where $\overline{L}$ is the average number of path nodes. While the hash-based hotspot local checking used for conflict detection has a complexity of $O(P•\left|F\right|)$, where $\left|F\right|$ is the number of conflict candidate aircraft pairs.

4. Example Analysis

Shenzhen Bao’an International Airport is selected for the validation analysis, and the airport field topology structure map is shown in Figure 6. Combined with the historical data, the potential conflict hotspot areas are numbered 20, 23, 27, 40, 43, 58–59, 61–65, 69–70, 72, 78, 98, 106, 108–109, 111, 124, 135, 143, and 194, with the historical flight data of January 2022 at Shenzhen Bao’an Airport as the basis for the subsequent validation analysis. Obtain 1 month of traffic data of the potential conflict hotspot area, and take 15 min as the step segment. Take the average 15 min traffic data $V_1$, use the principal component analysis method, combined with the degree centrality $V_2$, median centrality $V_3$, proximity centrality $V_4$, eigenvector centrality $V_5$, the loss of network efficiency $V_6$, the loss of the largest subgraphs $V_7$, the number of conflicts than the number of $V_8$, and other indicators, to find out the risk index. The specific methods of calculation are shown in Equations (21)–(28), where $N$ is the number of nodes, $D_i$ is the degree of nodes $i$, $l_{jk}(i)$ is the number of shortest paths from node $j$ to node $k$ through node $i$, and $l_{jk}$ is the total number of shortest paths from node $j$ to node $k$. $d_{ij}$ is the shortest distance from node i to node $j$, ${\lambda }_{\max }$ is the maximal eigenvalue of the network adjacency matrix $A$, and its corresponding maximal eigenvector is $\mathrm{x}={\left[x_1,x_2,\cdots ,x_n\right]}^{{\rm T}}$, $E$ is the network efficiency, and $E_i$ is the new network efficiency after the deletion of node $i$ and its connected edges. $N^{\prime }$ is the number of nodes contained in the maximum connected subgraph of the original network, $N_i^{\prime }$ and is the number of nodes contained in the maximum connected subgraph after the deletion of node $i$. $C_i$ is the number of abnormal active targets passed by a node $i$ in a given period, $\stackrel{⏜}{N}$ is the total number of active targets in the field topology network in a given period, and $CI$ is the risk index [34].

The flow and risk index are used as input features. The output feature is the predicted value of the risk index, which is used to train the model and output the results. The results are obtained as shown in Figure 7, which are divided into four intervals of [0.1–0.6], [0.6–0.9], [0.9–1.2], and [1.2–1.5] according to the risk index, which indicates the four risk levels—the low likelihood of conflict, the average likelihood of conflict, the high likelihood of conflict, and the very high likelihood of conflict—which are represented by labels of different colors. From Figure 7, it can be seen that hotspot 23 maintains a high conflict risk over a long period, and hotspots 62 and 64 maintain a high conflict risk during certain hours of the day, so hotspots 23, 62, and 64 can be considered as critical conflict hotspot areas, while hotspots 108 and 109 have conflicts occurring during some periods, but they maintain them for a short period and have a low risk level, so they cannot be recognized as critical hotspot areas.

(21)$V_2={\displaystyle \frac{D_i}{N-1}}$

(22)$V_3={\displaystyle \sum _{i\ne j\ne k}\frac{l_{jk}(i)}{l_{jk}}}$

(23)$V_4={\displaystyle \frac{N-1}{{\displaystyle \sum _{j\ne 1}^N{d}_{ij}}}}$

(24)$V_5=x_i={\displaystyle \frac{1}{{\lambda }_{\max }}}{\displaystyle \sum _{j=1}^n{A}_{ij}{x}_j}$

(25)$\left\{\begin{array}{l}E={\displaystyle \frac{1}{N(N-1)}}{\displaystyle \sum _{i\ne j}\frac{1}{d_{ij}}}\\ V_6={\displaystyle \frac{E-E_i}{E}}\end{array}\right.$

(26)$V_7={\displaystyle \frac{N^{\prime }-N_i^{\prime }}{N^{\prime }}}$

(27)$V_8={\displaystyle \frac{C_i}{\stackrel{⏜}{N}}}$

(28)$CI=0.159V_1+0.118V_2+0.139V_3+0.088V_4+0.147V_5+0.128V_6+0.068V_7+0.153V_8$

According to the above experimental results, the key hotspot areas 23, 62, and 64 are obtained. The actual operation data of Shenzhen Airport on 17 January 2022, are used for the simulation experiments, and the inbound and outbound flight data of the airport flight area from 17:00 to 18:00 for one hour are selected, including the flight number, the aircraft type, the inbound and outbound, the use of the runway, and the stopping position, as well as the corresponding node number of the field network and the start of the taxiing time, as shown in Table 1.

According to the field aircraft operation specification, set the field taxiing speed of the aircraft as 50 km/h and the field taxiing interval as 40 s. According to the flight base data, set the population size as 100, the maximum number of iterations as 150, the crossover probability constant $k_1=k_3=1.0$, and the variance probability constant $k_2=k_4=0.5$. To validate the effectiveness of the algorithm, the change of the fitness value in the process of algorithm evolution is analyzed, and the change of the fitness value is shown in Figure 8. From the figure, it can be seen that after evolution to 30 generations, the adaptation degree begins to increase; after evolution to 80 generations, the range of variation of the adaptation degree value begins to narrow; after evolution to 120 generations, the adaptation degree value is close to convergence and tends to stabilize.

Without considering the conflicts between aircraft and the influence of critical conflict hotspot areas, a static path planning algorithm is used to plan a pre-gliding path for each aircraft and determine whether there are any potential conflicts in the subsequent gliding process. Under the condition of no conflict resolution, some of the aircraft taxi paths and path sequence crossing moments are shown in Table 2, where the aircraft crossing moments are recorded using seconds.

According to the data in the table, it can be found that:

(1) Aircraft CES2558, CES5348, and CSN6310 occupy the critical hotspot area HS64 successively, the taxiing time of inbound aircraft CES2558 is 293 s, the taxiing time of departing aircraft CES5348 is 315 s, and the taxiing time of departing aircraft CSN6310 is 276 s. Therefore, the aircraft CES5348 has the longest taxiing time, so the aircraft is given the priority to pass the hotspot area; the inbound aircraft CES2558 occupies the hotspot area first, and the cost of its deceleration and waiting strategy is much larger than that of the alternative path, so the aircraft CES2558 needs to choose the suboptimal alternative path to avoid the hotspot area HS64.

(2) Aircraft CES5348 occupies the critical conflict hotspot area HS64 at the passing moment 2764, while aircraft CSN6310 also occupies the hotspot area at the passing moment 2791, and does not satisfy the field glide interval of the 40 s, so there is a risk of tailgating conflict between these two aircraft at the hotspot area HS64.

(3) Aircraft CSN3210 occupies the critical conflict hotspot area HS23 at the passing moment 3676, while aircraft CCA4314 will also pass through the hotspot area at the passing moment 3696, and both of them do not meet the field taxi interval of 40 s, so there is a risk of tailgating conflict.

Aiming at the above-mentioned aircrafts that may have conflicts in the hotspot area, the hotspot area avoidance mechanism is used to judge the priority between the aircraft and calculate the waiting time cost of the two solution strategies of decelerating and waiting, and choosing the suboptimal taxiing path, to select the solution strategy for the aircraft and optimize the taxiing path. Some of the optimized paths and crossing point moments for aircraft are shown in Table 3.

According to the data in the table, it can be found that:

(1) Aircraft CES2558, CES5348, and CSN6310 occupy the critical hotspot area HS64 successively, the taxiing time of inbound aircraft CES2558 is 293 s, the taxiing time of departing aircraft CES5348 is 315 s, and the taxiing time of departing aircraft CSN6310 is 276 s. Therefore, the aircraft CES5348 has the longest taxiing time, so the aircraft is given the priority to pass the hotspot area; the inbound aircraft CES2558 occupies the hotspot area first, and the cost of its deceleration and waiting strategy is much larger than that of the alternative path, so the aircraft CES2558 needs to choose the suboptimal alternative path to avoid the hotspot area HS64.

(2) Aircraft CES5348 and aircraft CSN6310 will occupy the critical conflict hotspot area HS64 one after another, since both aircraft are departing aircraft and will occupy the same sequence of same-direction path nodes in the future; therefore, the time cost of selecting the suboptimal alternative path will be much larger than the deceleration waiting time, so aircraft CSN6310 chooses the conflict resolution strategy of deceleration waiting, with a waiting time of 13 s. The waiting time is 13.

(3) Aircraft CSN3210 and aircraft CCA4314 are both inbound aircraft with taxi times of 179 s and 204 s, respectively, so aircraft CCA4314 is prioritized to pass through hotspot area HS23. Since aircraft CSN3210 occupies the hotspot area first, its deceleration waiting time cost is the 60 s, and the time cost of rerouting the second-best alternative path is 43 s; therefore, the solution strategy of rerouting the suboptimal alternative path is chosen to ensure that all conflicts are avoided with the shortest possible total taxiing time of the aircraft.

The taxiing time of each aircraft before and after the optimization of the field hotspot area is shown in Figure 9. After optimization, the taxiing time of aircrafts YZR7537, CES2558, and CSZ9806 is reduced, and the taxiing time of aircrafts CSN6310 and CSN3210 is increased because of avoiding the conflict hotspot area; secondly, the number of aircraft passing through the key conflict hotspot area is reduced, which prevents the occurrence of taxiing conflicts and reduces the risk level of the key hotspot area effectively, and the total aircraft taxiing time is reduced by 53 s after optimization, which improves the airport field operation efficiency to a certain extent. After the optimization, the total taxiing time of aircraft is reduced by 53 s, which improves the airport field operation efficiency to a certain extent. Although the absolute savings of 53 s may seem limited, it is worth pointing out that this experimental window only covers 29 trips and 60 min of peak hours, and the baseline scenario has already been pre-optimized once by the first-come-first-served rule. On this basis, 53 s can still be squeezed out, which translates to an average of 1.8 s for a single sortie, equivalent to a 0.8% compression on the average taxiing time of 225 s. In the case of a high-density operation at 10 million airports, the average taxiing time can be reduced by 0.8%. Under the high-density operation conditions of 10 million airports, even if a single airplane saves only 1–2 s, it is still enough to advance the tail flights in the taxi sequence to the previous control instruction, thus reducing the number of “stop-and-go” times and energy-intensive acceleration segments. In addition, the simulation records show that the savings are mainly concentrated in the three hotspot segments of HS23, HS62, and HS64, which are also the most frequent conflict alarms in the history of operation, indicating that the optimization is not averaged out, but accurately cuts down the waiting time of the high-risk nodes, which has obvious safety spillover benefits.

5. Conclusions

(1) Based on the identified key conflict hotspot areas, this chapter establishes a field hotspot area path optimization model for aircraft that may be in conflict to reduce the likelihood of conflict in the hotspot area. Based on the considerations of aircraft taxi path feasibility constraints and continuity constraints, and safety interval constraints, as well as head-to-head constraints and overrun constraints to prevent conflicts from occurring, the field taxi path optimization model is established to minimize the total taxiing time. Establish the glide path optimization algorithm integrating the hotspot area avoidance mechanism to realize the dynamic adjustment of the glide path, reduce the number of aircraft passing through the hotspot area in the corresponding period, use the taxiway in a more dispersed way, reduce the operation risk of the key hotspot area, reduce the glide time of aircraft, and improve the operation efficiency of the airport.

(2) Subsequent research can consider collecting more extensive data related to human–aircraft–vehicle operations on airport surfaces to further improve the identification method of potential conflict hotspots and the path optimization model. It can further focus on the temporal and spatial evolution of key conflict hotspots on surfaces, as well as the evolution of conflict risk on the effectiveness of surface operation and management, etc., to further optimize the model and the method.

Author Contributions

Conceptualization, W.T. and M.Y.; methodology W.T. and M.Y.; software, W.T. and M.Y.; validation, W.T., M.Y., and X.Z.; formal analysis, W.T.; investigation, J.Y.; resources, W.T. and J.Y.; data curation, M.Y.; writing—original draft preparation, M.Y.; writing—review and editing, M.Y. and X.S.; visualization, M.Y.; supervision, J.Y.; project administration, J.Y.; funding acquisition, W.T. and J.Y. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

Our data comes from third parties and cannot be shared.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1 Aircraft prioritization schematic.

Figure 2 Conflict resolution process.

Figure 3 Example of a chromosome coding path sequence.

Figure 4 Initial feasible solution generation algorithm flow.

Figure 5 Algorithm flow for path optimization in hotspot areas of the field.

Figure 6 Shenzhen Bao’an International Airport field topography structure plan.

Figure 7 Predicted results of the risk index for each hotspot region.

Figure 8 Plot of change in fitness value during algorithm evolution.

Figure 9 Comparison of glide time before and after optimization.

Table 1

Shenzhen Airport flight data.

Serial Number	Flight Number	Aircraft Type	Inbound/Outbound	Runway/Node Number	Parking Spot/Node Number	Start of Taxiing Time
1	CES5758	B738	D	33/10	354/170	17:00:58
2	EPA6282	B738	A	34/96	336/164	17:02:46
3	SNG4345	A320	A	33/10	503/155	17:05:57
4	CQH8882	A320	D	33/10	318/173	17:05:57
5	CXA8317	B738	A	33/10	566/156	17:09:02
6	CSN3744	A320	D	33/10	330/164	17:09:02
7	CSN6610	A321	D	33/10	316/172	17:10:18
8	CSN5540	B737	A	34/96	320/172	17:13:44
9	CES5343	A359	D	33/10	564/156	17:17:01
10	CSZ9409	A320	D	33/10	372/169	17:20:36
11	CSN8717	A320	D	33/10	541/159	17:22:29
12	CHH7724	B738	D	33/10	373/166	17:27:03
13	YZR7537	B738	A	33/10	527/161	17:27:04
14	CES6371	A320	D	34/96	332/164	17:29:20
15	CSZ8269	B738	D	33/10	525/161	17:30:12
16	CSN3369	A321	D	33/10	337/174	17:32:06
17	CSZ9236	A319	D	34/96	508/160	17:37:39
18	CES2558	B738	A	33/10	348/169	17:41:14
19	CSZ9806	B738	A	33/10	510/160	17:44:57
20	CES5348	A359	D	33/10	324/171	17:44:58
21	CSN6310	A320	D	33/10	340/167	17:46:05
22	CHH7759	B738	D	33/10	347/165	17:49:19
23	CJX6655	B738	A	33/10	328/164	17:51:06
24	CXA8068	B738	A	33/10	333/174	17:54:15
25	CES2888	A20N	D	33/10	358/170	17:54:16
26	CDG1188	B738	D	33/10	319/173	17:55:28
27	CSS7350	B752	A	34/96	386/178	17:56:38
28	CSN3210	A321	A	33/10	544/158	17:58:36
29	CCA4314	A332	A	33/10	567/157	17:58:56

Table 2

Partial aircraft taxi paths and crossing moments.

Flight Number	Taxiing Path	Moment of Aircraft Crossing Point
CES2558	[10, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 40, 107, 106, 61, 76, 75, 74, 73, 72, 64, 135, 118, 136, 169]	[2474-2483-2497-2513-2527-2543-2553-2563-2577-2602-2609-2616-2623-2648-2671-2696-2703-2710-2717-2731-2739-2749-2753-2758-2763-2767]
CES5348	[171, 133, 120, 130, 66, 65, 64, 63, 62, 109, 108, 41, 42, 43, 44, 45, 46, 47, 48, 49, 11, 10]	[2698-2703-2711-2721-2726-2737-2764-2788-2795-2820-2843-2868-2875-2900-2927-2937-2953-2967-2983-2991-2998-3013]
CSN6310	[167, 137, 117, 118, 135, 64, 63, 62, 109, 108, 41, 42, 43, 44, 45, 46, 47, 48, 49, 11, 10]	[2765-2768-2771-2780-2777-2791-2816-2823-2848-2871-2896-2903-2928-2955-2965-2981-2995-3011-3019-3026-3041]
CSN3210	[10, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 38, 150, 158]	[3516-3525-3539-3555-3569-3585-3595-3605-3619-3644-3651-3658-3666-3676-3683-3691-3695]
CCA4314	[10, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 37, 151, 157]	[3516-3545-3559-3575-3589-3605-3615-3625-3639-3664-3671-3678-3686-3696-3709-3721-3728-3736-3740]

Table 3

Optimized routes and crossing times for selected aircraft.

Flight Number	Taxiing Path	Moment of Aircraft Crossing Point
CES2558	[10, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 40, 107, 106, 109, 111, 140, 138, 117, 118, 136, 169]	[2474-2483-2497-2513-2527-2543-2553-2563-2577-2602-2609-2616-2623-2648-2671-2679-2686-2690-2694-2708-2716-2722-2726]
CES5348	[171, 133, 120, 130, 66, 65, 64, 63, 62, 109, 108, 41, 42, 43, 44, 45, 46, 47, 48, 49, 11, 10]	[2698-2703-2711-2721-2726-2737-2764-2788-2795-2820-2843-2868-2875-2900-2927-2937-2953-2967-2983-2991-2998-3013]
CSN6310	[167, 137, 117, 118, 135, 64, 63, 62, 109, 108, 41, 42, 43, 44, 45, 46, 47, 48, 49, 11, 10]	[2765-2768-2771-2780-2777-2804-2829-2836-2861-2884-2909-2916-2941-2968-2978-2994-3008-3024-3032-3039-3054]
CSN3210	[10, 9, 8, 7, 6, 5, 4, 24, 25, 37, 38, 150, 158]	[3516-3525-3554-3581-3606-3635-3660-3685-3696-3703-3726-3734-3738]
CCA4314	[10, 9, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 37, 151, 157]	[3516-3545-3559-3575-3589-3605-3615-3625-3639-3664-3671-3678-3686-3696-3709-3721-3728-3736-3740]

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