Aircraft taxiing path optimization method containing multiple targets

Abstract

The invention discloses a multi-target aircraft taxiing path optimization method, which belongs to the technical field of aircraft path planning, and comprises the following steps: S1, abstracting the spatial layout of an airport into a network model diagram; s2, constructing a space-time state network of the taxiing path of the aircraft; s3, performing multi-objective optimization on the taxiing path of the aircraft by adopting a two-stage Gurobi solving method; s4, obtaining a group of Pareto solution sets through an NSGA-II algorithm; s5, analyzing the Pareto solution set, and balancing the balance among multiple targets; s6, comparing the solution time and the solution quality of the two-stage Gurobi solution method and the improved NSGA-II algorithm; and S7, evaluating the performance difference between the first-arrival first-service strategy and the approach priority strategy, and the method has the beneficial effects that the sliding path optimization model is constructed based on the improved NSGA-II algorithm, so that the overall operation efficiency of the airport is improved through path optimization, and meanwhile, the scene sliding safety is further enhanced on the basis of reducing the sliding time and carbon emission.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft path planning, and particularly to an aircraft taxiing path optimization method including multiple objectives. Background Art

[0002] Driven by both aviation technology and globalization, the civil aviation industry has become an important leading force in China's modernization process. With the advancement of the global decarbonization process and the policy orientation of "increasing flight density and facilitating travel", major airports not only need to cope with the challenges brought by the increasing flight density, but also need to promote the realization of low-carbon development goals while improving flight efficiency. In addition, with the increase in the number of flights, the workload of pilots has gradually increased, and the optimization of taxiing paths needs to take into account both reducing the workload of pilots and ensuring flight safety. At the same time, the selection of a reasonable avoidance strategy is crucial for improving airport operation efficiency. In this context, how to optimize the taxiing path of an aircraft driven by low-carbon goals has become the key to alleviating the bottleneck of airport ground traffic.

[0003] Currently, the commonly used aircraft taxiing path planning algorithms mainly include mixed integer programming, Dijkstra algorithm, genetic algorithm, and ant colony algorithm, etc. However, these algorithms have different limitations in practical applications. Although mixed integer programming can effectively solve complex NP-hard problems, its solution speed is slow and it is difficult to meet real-time requirements; although the Dijkstra algorithm is simple to calculate and has high efficiency, it performs poorly in dynamic scenarios and usually can only optimize a single objective; the genetic algorithm needs to simplify the multi-objective problem into a single-objective optimization, which may lead to insufficient diversity of the solution space; the ant colony algorithm is sensitive to parameter settings, is prone to falling into local optimal solutions, and has a slow convergence speed when dealing with large-scale problems. Traditional taxiing path optimization usually focuses on shortening the taxiing time, minimizing the taxiing distance, and reducing flight conflicts, but these goals often do not fully consider the needs of the green and low-carbon development of the aviation industry. In terms of avoiding taxiing path conflicts, existing methods do not consider dynamic priorities and are prone to causing unsafe events in high-density situations, reducing the safety of surface taxiing.

[0004] Numerous scholars at home and abroad have been working on solving the problem of aircraft taxiing path planning through various optimization methods. Pan Weijun et al. proposed a taxiing path optimization model based on conflict hotspots, aiming to optimize the taxiing path design by analyzing the conflict characteristics of hotspots in the airport; Jiang Yu et al. adopted a bilevel programming model to improve the taxiing scheduling efficiency and effectively reduce the operating cost; Zhang Zhaoning et al. constructed a dynamic taxiing path optimization model based on path detection methods and used the ant colony algorithm to improve the solution efficiency of the algorithm. EVERTSE et al. significantly reduced carbon emissions during the taxiing phase by optimizing the timed taxiing route; Sun Ruofei et al. combined the genetic algorithm and Yen algorithm to optimize the taxiing speed, thus effectively reducing exhaust emissions; CHEN et al. adopted a bilevel optimization model to both optimize the taxiing path and improve the time arrangement, achieving a dual optimization of fuel consumption and carbon emissions. SUN et al. proposed a joint optimization framework by combining NSGA-II and Dijkstra algorithms, which significantly improved the taxiing efficiency and effectively avoided path conflicts by simultaneously optimizing the taxiing time and gate matching; Wu Chuangyang et al. optimized the taxiing paths of inbound and outbound flights through a multi-objective ripple diffusion algorithm; Cheng Xiaokang et al. proposed a path optimization scheme aiming at minimizing cost and emissions based on an improved particle swarm algorithm.

[0005] The existing research provides valuable references for path optimization, but there are still some significant deficiencies. First, the optimization objectives of many studies mainly focus on reducing taxiing time, delays, and fuel consumption, etc., while relatively little attention is paid to carbon dioxide emissions during the aircraft taxiing process, and the impact of environmental factors is not fully considered. Second, most of the existing path optimization methods are based on static assumptions, ignoring the complexity of dynamic changes and being difficult to adapt to the dynamic fluctuations and uncertainties of the environment in actual operations. In the research on multi-objective optimization problems, many methods use the method of linear weighting to combine objectives. Although this method simplifies the solution of the problem, it ignores the complex interactions between different objectives and is difficult to fully reflect the requirements of multi-objective optimization. In addition, the research on pilot workload is still relatively scarce, and the existing optimization methods do not fully consider the workload of pilots in actual operations and its impact on decision-making. Finally, the research on the avoidance methods of dynamic priorities is relatively limited, and there is a lack of discussion on the specific roles and impacts of these avoidance strategies in path optimization. Therefore, the existing research still faces significant limitations and challenges in solving the path optimization problem in a high-density, multi-objective, and variable aviation environment. Summary of the Invention

[0006] To solve the above problems, the present invention provides a multi-objective aircraft taxiing path optimization method, which is implemented through the following technical solutions.

[0007] A multi-objective aircraft taxiing path optimization method includes the following steps:

[0008] S1. Taking a busy airport as the background, abstract the spatial layout of the airport into a network model diagram;

[0009] S2. Integrate the three basic elements of the spatial position, time information, and status information of the aircraft, and construct a spatio-temporal state network for the taxiing path of the aircraft;

[0010] S3. Establish a mixed-integer programming model, adopt a two-stage Gurobi solution method, perform multi-objective optimization on the taxiing path of the aircraft, and output a reliable lower bound;

[0011] S4. Design an improved NSGA-II algorithm, and obtain a set of Pareto solution sets by introducing an adaptive parameter adjustment mechanism based on flight density changes and a path selection optimization strategy based on random factors;

[0012] S5. Analyze different Pareto solution sets and weigh the balance between multiple objectives;

[0013] S6. Compare the solution time and solution quality of the two-stage Gurobi solution method and the improved NSGA-II algorithm, combine the lower bound obtained by Gurobi, analyze the "gap" value between the solution of the NSGA-II algorithm and the lower bound, and determine the performance differences between the two-stage Gurobi solution method and the improved NSGA-II algorithm;

[0014] S7. Evaluate the performance differences of different strategies in terms of taxiing efficiency and safety by comparing the first-come-first-served strategy and the approach priority strategy.

[0015] Further, in the step S2, the spatial position is the key nodes and parking positions of the aircraft; the time information is the time when the aircraft arrives at each node and the waiting time; the status information is the status change during the taxiing process of the aircraft.

[0016] Further, in the step S3, when using the two-stage Gurobi solution, in the first stage, the objective function is to minimize the total path cost of the aircraft, and in the second stage, the objective functions are the load-weighted shortest total taxiing time and the load-weighted least carbon dioxide emissions of the aircraft.

[0017] Further, the objective function for minimizing the total path cost of the aircraft is:

[0018]

[0019] where k is the aircraft number; K is the set of aircraft; E is the set of edges; z (i,j) is the total of the time and carbon dioxide emissions required for the aircraft to travel from i to j; x k (i,j)It is 1 if aircraft k taxis from node i to node j, and 0 otherwise.

[0020] Furthermore, Equation (1) satisfies the following constraint conditions:

[0021] Conservation of flow at intermediate nodes:

[0022]

[0023] where s k is the starting point of aircraft k; e k is the ending point of aircraft k;

[0024] Flow constraint at the starting point:

[0025]

[0026] Flow constraint at the ending point:

[0027]

[0028] Path uniqueness constraint:

[0029]

[0030] where pre_path is the generated path, used to exclude duplicate paths;

[0031] Path quantity constraint:

[0032]

[0033] where is the set of the first s shortest paths of the generated aircraft k; is for aircraft k to select path ω in the path set;

[0034] Path storage constraint:

[0035]

[0036] Furthermore, in the second stage, optimization is performed based on the paths generated in the first stage. The objective function of the weighted shortest total taxiing time of the aircraft is:

[0037]

[0038] where is the sum of the times required for the path passed by aircraft k; is the sum of the waiting times of aircraft k on the path; is the sum of the push-out waiting times of aircraft k at the starting point; is the sum of the load values of aircraft k; V is the set of vertices; t (i,j) is the time required for aircraft to travel from i to j; is the waiting time of aircraft k at point j; K D is the set of departing aircraft; is the push - waiting time of departing aircraft k at the starting point; w_load is the weight of aircraft load; load k is the cumulative service load of aircraft k during taxiing, used to track the service status of the aircraft; f is the increment coefficient;

[0039] The objective function of minimizing the carbon dioxide emissions with weighted aircraft loads is:

[0040]

[0041] Among them, is the sum of the carbon dioxide produced by the path traveled by aircraft k; c (i,j) is the carbon dioxide emission of aircraft from i to j; c j is the sum of the carbon dioxide produced by the waiting time of aircraft k on the path;

[0042]

[0043] Among them, n k is the number of engines of aircraft k; F k is the fuel flow of each engine of aircraft k at different taxiing stages; EI is the published emission index of aircraft exhaust gas; m is the total number of aircraft.

[0044] Furthermore, equations (8) and (9) satisfy the following constraints:

[0045] Departure time constraint:

[0046] For arriving aircraft k:

[0047]

[0048] t ok is the starting taxiing moment of aircraft k; ETOP k is the estimated arrival and departure time of aircraft k; K A is the set of arriving aircraft;

[0049] For departing aircraft k:

[0050]

[0051] Among them, t_w is the time range within which the departing aircraft is allowed to be pushed after the estimated departure time;

[0052]

[0053] Time continuity constraint to ensure the continuity of path arrival time:

[0054]

[0055] where t jk is the time when aircraft k arrives at node j; t ik is the time when aircraft k arrives at node i; M is a preset sufficiently large positive integer;

[0056] Path selection constraint. For each aircraft k, a path must be selected from the candidate paths for taxiing:

[0057]

[0058] Path selection and association constraint. If aircraft k selects the i-th path, then all the edges (i, j) involved in the path must be selected:

[0059]

[0060] where if path ω involves edge (i, j), then otherwise it is 0;

[0061] Delay and waiting flag constraint. For each aircraft k, the delay flag and waiting flag variables are used to represent the waiting time and delay status of the aircraft at the node:

[0062]

[0063] where indicates whether aircraft k is waiting at node j. If so, it is 1, otherwise it is 0; ε is a preset very small positive number;

[0064]

[0065] where delay_f k indicates whether aircraft k is delayed. If so, it is 1, otherwise it is 0;

[0066] Load constraint. For each aircraft k, the load constraint is used to comprehensively measure the service load of the pilot, including path switching, waiting, and delay status:

[0067]

[0068] where judges whether aircraft k switches from path p to path q. If so, it is 1, otherwise it is 0;

[0069] Cross - conflict and rear - end conflict avoidance constraints. To prevent cross - conflicts and rear - end conflicts between aircraft, corresponding constraints need to be imposed on each node i and each pair of aircraft k1, k2 (k1 ≠ k2):

[0070]

[0071] where t s is the safety time interval between aircraft; is the order decision variable of aircraft k1, k2 at point i. If k1 arrives at point i before k2, it is 1, otherwise it is 0;

[0072] Head - on conflict avoidance constraints. To prevent head - on conflicts between aircraft, corresponding constraints need to be imposed on each edge (i, j) and each pair of aircraft k1, k2 (k1 ≠ k2):

[0073]

[0074] where is the order decision variable of aircraft k1, k2 on edge (i, j). If k1 arrives at edge (i, j) before k2, it is 1, otherwise it is 0.

[0075] Furthermore, in step S4, the optimization steps of the improved NSGA - II algorithm are as follows:

[0076] S41, Chromosome encoding: Adopt a hybrid encoding method. Each chromosome represents a feasible taxiing path plan. Each chromosome consists of three parts: the path of the aircraft from the starting point to the ending point, the estimated arrival time at each node on the path, and the cumulative load status of the aircraft when arriving at each node;

[0077] S42, Initialize the population and parameters: Set an appropriate population size, use the backtracking algorithm to randomly generate the initial taxiing path, and assign an initial departure time to each path to construct the initial individuals in the population. Subsequently, introduce an adaptive parameter adjustment mechanism based on the change of flight density to adapt to the changes in the number of different aircraft and the number of iterations. By simulating different aircraft scenarios and dynamically adjusting the population and parameters according to the iteration process, ensure that the algorithm converges to the optimal solution within a reasonable iteration range and improve the global search ability;

[0078] S43, Fitness evaluation: In the NSGA - II algorithm, the individual fitness is jointly determined by its non - dominated level and crowding degree. First, stratify the population through fast non - dominated sorting, assign individuals to different non - dominated levels, and make high - quality individuals close to the Pareto front; the crowding degree is measured based on the local distance between two adjacent points in the objective space to maintain the diversity of the population;

[0079] S44, Selection: Adopt the elite selection strategy, preferentially select individuals with a lower non-dominated level in the population, and preferentially select individuals with a lower crowding degree in the same level, so as to ensure that the selected individuals have better potential;

[0080] S45, Crossover: Use the multi-point crossover strategy, randomly select two crossover points and exchange their gene segments, thereby generating two new offspring individuals. The crossover part is the path part;

[0081] S46, Mutation: Perform mutation judgment on each chromosome. If mutated, each gene of the chromosome randomly selects a point to generate a mutated path to the end point. In order to enhance the diversity of solutions and avoid local optima, a mutation strategy based on a random factor is adopted. The mutation process is implemented through an improved Dijkstra algorithm. The introduced random factor combines the product of the path weight and a random number to determine the intensity of mutation;

[0082] S47, Optimize the departure time: Further optimize the path planning by adjusting the departure time of the aircraft, avoid the algorithm falling into a local optimal solution prematurely, and increase the diversity of the solution space;

[0083] S48, Select the next generation population: Combine the new population obtained after the crossover and mutation operations with the previous generation population, and generate the next generation population through the selection operation;

[0084] S49, Repeat iteration: Continuously repeat steps S44 to S48 until the termination condition is met;

[0085] S410, Algorithm end: When the termination condition is met, the algorithm stops running and outputs the final Pareto solution set.

[0086] The beneficial effect of the present invention is that this application constructs a taxiing path optimization model based on the improved NSGA-II algorithm, aiming to improve the overall operation efficiency of the airport through path optimization, and further strengthen the surface taxiing safety on the basis of reducing taxiing time and carbon emissions.

[0087] Compared with traditional methods, the model proposed in this application shows significant advantages in the dual-objective optimization of weighted taxiing time and weighted carbon emissions. At the same time, by introducing a load-based avoidance strategy, the operation safety is significantly improved. Compared with traditional static path planning methods, the application of the dynamic optimization strategy not only significantly improves the airport resource utilization rate and flight punctuality rate, but also effectively reduces the conflict probability between aircraft, showing strong applicability and superiority in comprehensively improving the operation efficiency of the aircraft taxiing stage. Brief Description of the Drawings

[0088] To more clearly illustrate the technical solution of the present invention, the following will briefly introduce the drawings required for use in the description of the specific embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0089] Figure 1 : Network model diagram of Guiyang Longdongbao Airport;

[0090] Figure 2 : Two-dimensional plane network schematic diagram of a taxiing area;

[0091] Figure 3 : Three-dimensional expanded schematic diagram of the spatio-temporal state network;

[0092] Figure 4 : Encoding rule for aircraft taxiing path;

[0093] Figure 5 : Relationship diagram between the number of aircraft and the number of iterations;

[0094] Figure 6 : Schematic diagram of the multi-point crossover strategy;

[0095] Figure 7 : Flowchart of the NSGA-II algorithm;

[0096] Figure 8 : Schematic diagram of the Pareto front;

[0097] Figure 9 : Schematic diagram of Pareto solution information;

[0098] Figure 10 : Total taxiing time iteration process;

[0099] Figure 11 : Carbon emission iteration process;

[0100] Figure 12 : Comparison of the solution times of the NSGA-II and Gurobi algorithms under different numbers of aircraft. Specific embodiments

[0101] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0102] As Figures 1-12As shown in the figure, an aircraft taxiing path optimization method including multiple objectives is characterized by the following steps:

[0103] S1. Taking a busy airport as the background, abstract the spatial layout of the airport into a network model diagram;

[0104] This application takes Guiyang Longdongbao Airport, a 4E-class civil international airport and an important aviation hub in Southwest China, as the research background, and draws the network model of Longdongbao Airport according to the released airport map as Figure 1 shown.

[0105] S2. Integrate the basic elements of the three dimensions of the aircraft's spatial position, time information, and state information to construct a spatio-temporal state network of the aircraft taxiing path;

[0106] The spatial position is the key nodes and parking positions of the aircraft; the time information is the time when the aircraft arrives at each node and the waiting time; the state information is the state change during the aircraft taxiing process.

[0107] In the aircraft taxiing path planning, the construction of the spatio-temporal state network (TSSN) is a key step. Compared with the traditional two-dimensional plane network, the spatio-temporal state network can more comprehensively describe the aircraft taxiing path by integrating the three dimensions of time, space, and state. The traditional static path planning method mainly focuses on spatial nodes and taxiing costs, ignoring the time progress and state changes, which may lead to redundant calculations and low efficiency. The spatio-temporal state network effectively reduces redundancy by comprehensively considering time and state information, thus improving the efficiency of path optimization.

[0108] The basic elements for constructing the spatio-temporal state network include: 1) Spatial position, that is, key nodes and parking positions; 2) Time information, that is, the time when the aircraft arrives at each node and the possible waiting time; 3) State information, including state changes during taxiing, such as waiting, delay, or path adjustment, etc. These information provide the necessary basis for the spatio-temporal state network and can dynamically describe the aircraft taxiing process at different times and states.

[0109] Figure 2 Figure shows a two-dimensional plane network of a taxiing area, where the nodes (such as N1 to N7) represent the key positions in the taxiway, the edges represent the connectivity between the nodes, and their weights reflect the taxiing costs of the aircraft (such as time, carbon emissions, or distance, etc.). Although the two-dimensional network can effectively represent the static topological structure, it cannot consider the time progress and state changes, so it needs to be further extended to a spatio-temporal state network.

[0110] Figure 3Shows the three-dimensional expansion of the spatio-temporal state network, which comprehensively reflects the dynamic characteristics of the taxiing path through three dimensions: time, space, and state. In this network, the space axis represents each node in the taxiing area (such as N1 to N7); the time axis shows the time process of the aircraft at each node; the state axis reflects the possible state changes during taxiing, such as detouring or waiting. Nodes not only represent spatial positions but also incorporate time and state information. For example, the position of node N2 on the time axis represents different time points when the aircraft arrives at N2, and the state axis shows the state changes caused by reasons such as waiting or rerouting. Paths and state changes are identified by colors and line types: the green path indicates that the aircraft actually taxis along the original route without being affected by path adjustments; the black dashed line represents the original path that is not actually taxied due to path adjustments; the blue arrow indicates the path re-planned due to conflicts; the red dashed line represents possible state changes that affect taxiing time or path selection. State changes usually occur at specific nodes. For example, at node N2, waiting due to conflicts increases the load; at node N3, detouring due to path adjustments increases the load. The gray dashed line represents the waiting time, and the green dot represents the conflict point.

[0111] By constructing the spatio-temporal state network, various dynamic changes during the aircraft taxiing process can be more accurately simulated, providing a more comprehensive solution for optimizing the taxiing path.

[0112] S3. Establish a mixed-integer programming model and adopt a two-stage Gurobi solution method to perform multi-objective optimization on the aircraft taxiing path and output a reliable lower bound.

[0113] When using the two-stage Gurobi solution, in the first stage, the objective function is to minimize the total path cost of the aircraft, and in the second stage, the objective functions are the load-weighted shortest total taxiing time and the load-weighted least carbon dioxide emissions of the aircraft.

[0114] The objective function for minimizing the total path cost of the aircraft is:

[0115]

[0116] where k is the aircraft number; K is the set of aircraft; E is the set of edges; z (i,j) is the total time and carbon dioxide emissions required for the aircraft to travel from i to j; x k (i,j) is whether aircraft k taxis from node i to node j. If so, it is 1; otherwise, it is 0.

[0117] Equation (1) satisfies the following constraints:

[0118] Flow conservation at intermediate nodes:

[0119]

[0120] Among them, s k is the starting point of aircraft k; e k is the end point of aircraft k;

[0121] Starting point flow constraint:

[0122]

[0123] End point flow constraint:

[0124]

[0125] Path uniqueness constraint:

[0126]

[0127] Among them, pre_path is the generated path, which is used to exclude duplicate paths;

[0128] Path quantity constraint:

[0129]

[0130] Among them, is the set of the first s shortest paths of the generated aircraft k; is for aircraft k to select the path ω in the path set;

[0131] Path storage constraint:

[0132]

[0133] In the second stage, optimization is carried out based on the paths generated in the first stage. The objective function of the weighted shortest total taxiing time of the aircraft load is:

[0134]

[0135] Among them, is the sum of the times required for the path passed by aircraft k; is the sum of the waiting times of aircraft k on the path; is the sum of the push-out waiting times of aircraft k at the starting point; is the sum of the load values of aircraft k; V is the set of vertices; t (i,j) is the time required for the aircraft to reach j from i; is the waiting time of aircraft k at point j; K D is the set of departing aircraft; is the push-out waiting time of departing aircraft k at the starting point; w_load is the weight of the aircraft load; load kis the cumulative service load of aircraft k during taxiing, used to track the service status of the aircraft; f is the increment coefficient;

[0136] The objective function of the least carbon dioxide emissions weighted by the load of the aircraft is:

[0137]

[0138] Among them, is the sum of carbon dioxide generated by the path passed by aircraft k; c (i,j) is the carbon dioxide emission of the aircraft from i to j; c j is the sum of carbon dioxide generated by the waiting time of aircraft k on the path;

[0139]

[0140] Among them, n k is the number of engines of aircraft k; F k is the fuel flow rate of each engine of aircraft k at different taxiing stages; EI is the published emission index of the exhaust gas of the aircraft; m is the total number of aircraft.

[0141] Equations (8) and (9) satisfy the following constraints:

[0142] Departure time constraint:

[0143] For arriving aircraft k:

[0144]

[0145] t ok is the start taxiing moment of aircraft k; ETOP k is the estimated arrival and departure time of aircraft k; K A is the set of arriving aircraft;

[0146] For departing aircraft k:

[0147]

[0148] Among them, t_w is the time range within which the departing aircraft is allowed to be pushed back after the estimated departure time;

[0149]

[0150] Time continuity constraint, ensuring the continuity of the path arrival time:

[0151]

[0152] Among them, t jk is the moment when aircraft k arrives at node j; tik is the arrival time of aircraft k at node i; M is a preset sufficiently large positive integer;

[0153] Path selection constraint: For each aircraft k, a path must be selected from the candidate paths for taxiing:

[0154]

[0155] Path selection and association constraint: If aircraft k selects the i-th path, then all edges (i, j) involved in the path must be selected:

[0156]

[0157] where if path ω involves edge (i, j), then otherwise it is 0;

[0158] Delay and waiting flag constraint: For each aircraft k, the waiting time and delay status of the aircraft at the node are represented by delay flags and waiting flag variables:

[0159]

[0160] where indicates whether aircraft k is waiting at node j, if so it is 1, otherwise it is 0; ε is a preset very small positive number;

[0161]

[0162] where delay_f k indicates whether aircraft k is delayed, if so it is 1, otherwise it is 0;

[0163] Load constraint: For each aircraft k, the load constraint is used to comprehensively measure the service load of the pilot, including path switching, waiting, and delay status:

[0164]

[0165] where judges whether aircraft k switches from path p to path q, if so it is 1, otherwise it is 0;

[0166] Cross-collision and tailgating collision avoidance constraint: To prevent cross-collisions and tailgating collisions between aircraft, corresponding constraints need to be imposed on each node i and each pair of aircraft k1, k2 (k1 ≠ k2):

[0167]

[0168] where ts is the safety time interval between aircraft; is the sequential decision variable of aircraft k1 and k2 at point i. If k1 arrives at point i before k2, it is 1; otherwise, it is 0.

[0169] For head-on conflict avoidance constraints, to prevent head-on conflicts between aircraft, corresponding constraints need to be imposed on each edge (i, j) and each pair of aircraft k1 and k2 (k1 ≠ k2):

[0170]

[0171] where is the sequential decision variable of aircraft k1 and k2 on edge (i, j). If k1 arrives at edge (i, j) before k2, it is 1; otherwise, it is 0.

[0172] S4. Design an improved NSGA-II algorithm. By introducing an adaptive parameter adjustment mechanism based on flight density changes and an optimization strategy for path selection based on random factors, a set of Pareto optimal solutions is obtained.

[0173] The optimization steps of the improved NSGA-II algorithm are as follows:

[0174] S41. Chromosome encoding: Adopt a hybrid encoding method. Each chromosome represents a feasible taxiing path plan. Each chromosome consists of three parts: the path of the aircraft from the starting point to the ending point, the estimated arrival time at each node on the path, and the cumulative load status of the aircraft when arriving at each node.

[0175] As Figure 4 shown, this application constructs an encoding method based on a space-time-state model. Chromosome genes can comprehensively consider the spatial position, time progress, and load status of aircraft, providing a more comprehensive path description.

[0176] S42. Initialize the population and parameters: Set an appropriate population size, use the backtracking algorithm to randomly generate an initial taxiing path, and assign an initial departure time to each path, thereby constructing the initial individuals in the population. Subsequently, introduce an adaptive parameter adjustment mechanism based on flight density changes to adapt to changes in the number of different aircraft and the number of iterations. By simulating different aircraft scenarios and dynamically adjusting the population and parameters according to the iteration process, ensure that the algorithm converges to the optimal solution within a reasonable iteration range and improve the global search ability. The specific results of this process are as Figure 5 shown.

[0177] S43, Fitness Evaluation: In the NSGA-II algorithm, the individual fitness is jointly determined by its non-dominated rank and crowding distance. First, the population is stratified through fast non-dominated sorting, and individuals are assigned to different non-dominated levels, bringing high-quality individuals closer to the Pareto front. The crowding distance is measured based on the local distance between adjacent points in the objective space to maintain the diversity of the population.

[0178] S44, Selection: The elitist selection strategy is adopted. Individuals with a lower non-dominated rank are preferentially selected in the population, and among those at the same level, individuals with a lower crowding distance are preferentially selected, thus ensuring that the selected individuals have better potential.

[0179] S45, Crossover: The multi-point crossover strategy is used. Two crossover points are randomly selected and their gene segments are exchanged to generate two new offspring individuals. The crossover part is the path part.

[0180] Specifically as Figure 6 shown.

[0181] S46, Mutation: A mutation judgment is made for each chromosome. If a mutation occurs, each gene of the chromosome randomly selects a point to generate a mutated path to the end point. To enhance the diversity of solutions and avoid local optima, a mutation strategy based on a random factor is adopted. The mutation process is implemented through an improved Dijkstra algorithm. The introduced random factor combines the product of the path weight and a random number to determine the intensity of the mutation;

[0182] By gradually adjusting the path and approaching the optimal solution, the flexibility of the search and the diversity of solutions are improved.

[0183] S47, Optimize Departure Time: The path planning is further optimized by adjusting the departure time of the aircraft, avoiding the algorithm falling into a local optimal solution prematurely, and increasing the diversity of the solution space.

[0184] S48, Select the Next Generation Population: The new population obtained after the crossover and mutation operations is merged with the previous generation population, and the next generation population is generated through the selection operation.

[0185] S49, Repeat Iteration: Continuously repeat steps S44 to S48 until the termination condition is met;

[0186] The termination condition is reaching the maximum number of iterations, Figure 7 where g is the current iteration number and gmax is the maximum number of iterations.

[0187] S410, Algorithm End: When the termination condition is met, the algorithm stops running and outputs the final Pareto solution set.

[0188] S5, Analyze different Pareto solution sets and balance among multiple objectives;

[0189] In this application, the real flight data of Longdongbao Airport on a certain day in October 2024 was selected for simulation experiments. In actual operation, due to the control of air traffic controllers over the parking positions and push-back times, conflicts usually do not occur between flights. Therefore, in the experiment, the original flight plan (with an interval of about 30 minutes) was reasonably adjusted to simulate the high-density operation of the airport. To ensure safety, it is assumed that the aircraft taxis at a constant speed during the taxiing process. At the same time, since the maximum straight taxiing speed of the aircraft is 50 km / h and the maximum turning speed is 15 km / h, considering the safety limitations of actual flight operations, the straight taxiing speed and the turning taxiing speed are set to 40 km / h and 10 km / h respectively. The flight information is shown in Table 1. All cases were solved on a personal laptop configured with Windows10-64bits, an Intel Core i9-13900HX 4.70GHz CPU, and 16GB of RAM.

[0190] Table 1 Flight Information

[0191]

[0192] The flights numbered 1 to 12 were simulated and optimized, and the obtained Pareto front is as Figure 8 shown. The Pareto front is the set of solutions in a multi-objective optimization problem that represents the solutions where one objective cannot be further improved without sacrificing other objectives.

[0193] Figure 8 It shows the optimization results between different objectives and reflects the solution set in the multi-objective optimization process. Table 2 lists the detailed information of three typical non-dominated solutions, including the taxiing time of the aircraft, carbon dioxide emissions, straight and curved taxiing times, waiting and delay times, and service load.

[0194] Table 2 Detailed Information of Pareto Solutions

[0195]

[0196] Figure 9 It shows the Pareto solution information. By analyzing Table 2 and Figure 9 it can be seen that the Pareto solutions with lower carbon emissions usually perform better in terms of curved taxiing time and waiting time, while the solutions that reduce taxiing time are usually accompanied by lower delay times.

[0197] If the controller gives priority to reducing taxiing time and shortening delays, Pareto solution 1 would be a better choice, saving 18.1 s compared to Pareto solution 3; if the focus is on reducing carbon emissions and waiting time, Pareto solution 3 is more suitable, reducing 14.03 kg of carbon dioxide emissions compared to solution 1 and having a lower service load of only 2 times. If a balance needs to be found between the two, Pareto solution 2 can be a reasonable choice.

[0198] As Figure 10 shown, after optimization, the total taxiing time of the aircraft decreased from 4027.7 s to 3577.7 s, a reduction of 11.18%; Figure 11 shows that the carbon dioxide emissions decreased from 2737.1 kg to 2361.8 kg, a reduction of 13.71%. These results verify the effectiveness of the NSGA-II algorithm in multi-objective optimization. Figure 12 shows the taxiing paths of a certain aircraft among different Pareto solutions.

[0199] S6. By comparing the solution times and solution qualities of the two-stage Gurobi solution method and the improved NSGA-II algorithm, and combining with the lower bound obtained by Gurobi, analyze the "gap" value between the solution of the NSGA-II algorithm and the lower bound to determine the performance differences between the two-stage Gurobi solution method and the improved NSGA-II algorithm;

[0200] To evaluate the performance of different algorithms, this paper conducts a comparative analysis of the computational time and solution quality of the Gurobi solution method and the NSGA-II algorithm in the simulation. At the same time, use the two-stage Gurobi linear solution method to calculate the values of the two objectives respectively to obtain a reliable lower bound, and calculate the "gap" value between the heuristic solution of the NSGA-II algorithm and the lower bound based on this lower bound.

[0201] To compare the performance of different algorithms, this application conducts simulation experiments on 2 to 20 aircraft respectively, analyzes the differences in solution time and solution quality between the improved NSGA-II algorithm and the two-stage Gurobi linear solution method. Table 3 shows the average values of 10 simulation results, showing the performance changes of the two algorithms when the number of aircraft increases.

[0202] Table 3 Simulation time of aircraft with different numbers of flights

[0203]

[0204] The data in Table 3 show that when the number of aircraft is small, the difference in the solution times between NSGA-II and the Gurobi algorithm is small. For example, when there are 2 aircraft, the solution time of NSGA-II is 1.4 s and that of Gurobi is 4.9 s, with a difference of only 3.5 s. However, as the number of aircraft increases, the solution time of NSGA-II increases relatively smoothly, while the solution time of Gurobi increases exponentially. Specifically, when the number of aircraft is 10, the solution time of NSGA-II is 79.5 s, while the solution time of Gurobi is 2998.4 s, with a difference of 2918.9 s. Further, when the number of aircraft is 12, the solution time of NSGA-II is 143.1 s, and the solution time of Gurobi has increased to 10956.9 s, with a difference of 10813.8 s. In addition, there is a 1% gap between the quality of the solution obtained by Gurobi at this time and the lower bound.

[0205] In addition, as the problem scale increases, due to memory limitations, Gurobi cannot continue to handle more than 12 aircraft. Therefore, it is necessary to obtain the initial lower bound by solving the relaxed problem. When the number of aircraft reaches 20, NSGA-II can still successfully complete the solution, and by comparing with the Gurobi relaxed solution, the gap between the solution and the lower bound is obtained as 4.22%. Figure 12 It shows the changing trends of the solution times of NSGA-II and Gurobi as the number of aircraft increases, highlighting the advantages of NSGA-II in large-scale problems.

[0206] These results indicate that the NSGA-II algorithm has strong scalability and stability in dealing with large-scale aircraft routing optimization problems, can provide a relatively good solution in a short time, while for Gurobi, when the scale is large, the solution time and the demand for computing resources increase significantly, resulting in the inability to handle larger-scale problems.

[0207] S7, by comparing the first-come-first-served strategy and the approach-first strategy, evaluates the performance differences of different strategies in terms of taxiing efficiency and safety.

[0208] To explore the advantages and disadvantages of different avoidance strategies, the load-based first-come-first-served (FCFS) and the load-based approach-first strategy are analyzed. The first-come-first-served strategy aims at optimizing the overall operation efficiency, while the approach-first strategy takes into account the specific needs of approaching aircraft. By comparing the two strategies, it aims to evaluate their applicability and the impact on taxiing efficiency.

[0209] In order to evaluate the advantages and disadvantages of different avoidance strategies, this section conducts a comparative analysis of the load-based first-come-first-served strategy and the load-based approach priority avoidance strategy. The experiment selected aircraft numbered 1 to 12, simulated the taxiing paths under the two strategies, and recorded the total taxiing time, carbon emissions, and service load.

[0210] Table 4 Aircraft parameters under the first-come-first-served strategy based on load priority

[0211]

[0212]

[0213] Table 5 Aircraft parameters under the approach priority strategy based on load priority

[0214]

[0215] Table 6 Comparison of aircraft parameters under different strategies

[0216]

[0217] As shown in Tables 4 and 5, the aircraft taxiing paths and related data under the load-based FCFS strategy and the load-based approach priority avoidance strategy are different. For example, the taxiing path of aircraft 5 has changed, and the cumulative amount of the service load of the aircraft under different strategies is different. According to the data in Table 6, the total amount of the load-based FCFS strategy is 5911.73, while the total amount of the load-based approach priority avoidance strategy is 5938.33. Overall, the approach priority avoidance strategy has increased by 26.6 units compared with the FCFS strategy. This shows that the approach priority avoidance strategy is slightly higher than the FCFS strategy in resource consumption. Although the difference between the two is not large, the load-based FCFS strategy has more advantages in overall resource utilization efficiency.

[0218] In addition, the load-based approach priority avoidance strategy shows obvious advantages in optimizing incoming aircraft. Compared with the load-based FCFS strategy, the approach priority avoidance strategy reduces the taxiing time of incoming aircraft by 29.06s and reduces carbon emissions by 7.97kg. In addition, the service load of the incoming aircraft is 0, which means that the incoming flight does not need to wait or perform additional avoidance operations during taxiing and can directly execute its scheduled taxiing path. For aircraft that have just experienced a long period of air flight, this strategy not only improves efficiency, but also effectively reduces safety risks during taxiing.

[0219] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific embodiments only. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can well understand and utilize the present invention. The present invention is only limited by the claims and their full scope and equivalents.

Claims

1. A multi-objective aircraft taxi path optimization method, characterized in that: The following steps are involved: S1, taking a busy airport as the background, abstracts the spatial layout of the airport into a network model diagram; S2, integrates the basic elements of the three dimensions of aircraft spatial position, time information and status information to construct the spatiotemporal state network of the aircraft taxi path; S3, establish a mixed integer programming model, use a two-stage Gurobi solution method to perform multi-objective optimization on the aircraft taxi path, and output a reliable lower bound; S4, designed an improved NSGA-II algorithm, and obtained a set of Pareto solutions by introducing an adaptive parameter adjustment mechanism based on flight density changes and a path selection optimization strategy based on random factors; S5, analyze different Pareto solution sets and weigh the balance between multiple objectives; S6, compare the solution time and solution quality of the two-stage Gurobi solution method and the improved NSGA-II algorithm, analyze the "gap" value between the NSGA-II algorithm solution and the lower bound obtained by Gurobi, and determine the performance difference between the two-stage Gurobi solution method and the improved NSGA-II algorithm; S7, by comparing the first-come-first-served strategy and the approach priority strategy, the performance differences of different strategies in taxiing efficiency and safety are evaluated.

2. The multi-objective aircraft taxi path optimization method according to claim 1, characterized in that: In step S2, the spatial position is the key nodes and parking positions of the aircraft; the time information is the time when the aircraft arrives at each node and the waiting time; and the state information is the state change of the aircraft during taxiing.

3. The multi-objective aircraft taxi path optimization method according to claim 1, characterized in that: In step S3, during the two-stage Gurobi solution, the first stage takes minimizing the total path cost of the aircraft as the objective function, and the second stage takes the load-weighted shortest total taxiing time of the aircraft and the load-weighted minimum carbon dioxide emissions as the objective functions.

4. The multi-objective aircraft taxi path optimization method according to claim 3, characterized in that: The objective function to minimize the total cost of the aircraft path is: Where k is the aircraft number; K is the aircraft set; E is the edge set; z (i,j) x is the time and total carbon dioxide emissions required for an aircraft to reach j from i; k (i,j) Whether aircraft k taxis from node i to node j, if yes, it is 1, otherwise it is 0.

5. The multi-objective aircraft taxi path optimization method according to claim 4, characterized in that: Formula (1) satisfies the following constraints: Traffic conservation at intermediate nodes: Among them, s k is the starting point of aircraft k; e k is the destination of aircraft k; Starting point flow constraints: End point flow constraints: Path uniqueness constraint: Among them, pre_path is the generated path, which is used to exclude duplicate paths; Path number constraints: in, is the set of the first s shortest paths generated for aircraft k; For aircraft k, select path ω in the path set; Path storage constraints:

6. The multi-objective aircraft taxi path optimization method according to claim 5, characterized in that: The second stage is optimized based on the path generated in the first stage. The objective function of the aircraft's load-weighted shortest total taxiing time is: in, is the sum of the time required for the path traversed by aircraft k; is the sum of the waiting time of aircraft k on the path; is the sum of the waiting time of aircraft k at the starting point; is the sum of the load values ​​of aircraft k; V is the vertex set; t (i,j) is the time required for an aircraft to reach j from i; K is the waiting time of aircraft k at point j; D Mustering for departing aircraft; is the pushback waiting time of departing aircraft k at the starting point; w_load is the weight of the aircraft load; load k is the accumulated service load of aircraft k during taxiing, used to track the service status of the aircraft; f is the incremental coefficient; The objective function for aircraft load-weighted minimum carbon dioxide emissions is: in, is the sum of carbon dioxide produced by the path of aircraft k; c (i,j) is the carbon dioxide emissions of aircraft from i to j; c j is the sum of the carbon dioxide generated by the waiting time of aircraft k on the path; Among them, n k is the number of engines of aircraft k; F k is the fuel flow of each engine of aircraft k at different taxiing stages; EI is the published emission index of aircraft exhaust gas; m is the total number of aircraft.

7. The multi-objective aircraft taxi path optimization method according to claim 6, characterized in that: Formula (8) and Formula (9) satisfy the following constraints: Departure time constraints: For approaching aircraft k: t ok is the taxi start time of aircraft k; ETOP k is the expected arrival and departure time of aircraft k; K A Mustering for incoming aircraft; For departing aircraft k: Where t_w is the time range within which the departing aircraft is allowed to push back after the estimated departure time; Time continuity constraints ensure the continuity of path arrival time: Among them, t jk is the time when aircraft k arrives at node j; t ik is the time when aircraft k arrives at node i; M is a preset sufficiently large positive integer; Path selection constraints: For each aircraft k, it must choose a candidate path Choose a path to glide on: Path selection and association constraints: if aircraft k selects the i-th path, then all edges (i, j) involved in the path must be selected: in, If a path ω involves an edge (i,j), then Otherwise, 0; Delay and waiting flag constraints, for each aircraft k, the delay flag and waiting flag variables are used to represent the waiting time and delay status of the aircraft at the node: in, is whether aircraft k is waiting at node j, if yes, it is 1, otherwise it is 0; ε is a preset very small positive number; Among them, delay_f k Is aircraft k delayed, if yes, it is 1, otherwise it is 0; Load constraint,For each aircraft k, the load constraint is used to comprehensively measure the pilot's service load, including path switching, waiting and delay states: in, Determine whether aircraft k switches from path p to path q, if yes, then it is 1, otherwise it is 0; Cross-collision and rear-end collision avoidance constraints. To prevent cross-collision and rear-end collision between aircraft, it is necessary to impose corresponding constraints on each node i and each pair of aircraft k1, k2 (k1≠k2): Among them, t s The safe time interval between aircraft; is the order decision variable of aircraft k1 and k2 at point i. If k1 arrives at point i before k2, it is 1, otherwise it is 0; Head-on collision avoidance constraints. To prevent head-on collisions between aircraft, it is necessary to impose corresponding constraints on each edge (i, j) and each pair of aircraft k1, k2 (k1≠k2): in, is the order decision variable of aircraft k1 and k2 on the (i, j) edge. If k1 arrives at the (i, j) edge before k2, it is 1, otherwise it is 0.

8. The multi-objective aircraft taxi path optimization method according to claim 7, characterized in that: In step S4, the optimization steps of the improved NSGA-II algorithm are as follows: S41, chromosome coding: adopts a hybrid coding method, each chromosome represents a feasible taxiing path plan, and each chromosome consists of three parts: the path of the aircraft from the starting point to the end point, the estimated arrival time of each node on the path, and the cumulative load status of the aircraft when it arrives at each node; S42, Initialize population and parameters: Set an appropriate population size, use the backtracking algorithm to randomly generate the initial taxi path, and assign an initial departure time to each path, so as to construct the initial individuals in the population. Then, introduce an adaptive parameter adjustment mechanism based on the change of flight density to adapt to the changes in the number of different aircraft and the number of iterations. By simulating different aircraft scenarios and dynamically adjusting the population and parameters according to the iteration process, ensure that the algorithm converges to the optimal solution within a reasonable iteration range and improve the global search capability. S43, fitness evaluation: In the NSGA-II algorithm, the fitness of an individual is determined by its non-dominated layer and crowding degree. First, the population is stratified by fast non-dominated sorting, individuals are assigned to different non-dominated layers, and high-quality individuals are brought close to the Pareto frontier; the crowding degree is measured based on the local distance between two adjacent points in the target space, so as to maintain the diversity of the population; S44, selection: adopting an elite selection strategy, giving priority to individuals with lower non-dominated layers in the population, and giving priority to individuals with lower crowding in the same layer, thus ensuring that the selected individuals have better potential; S45, crossover: using a multi-point crossover strategy, randomly select two crossover points and exchange their gene fragments to generate two new offspring individuals, with the crossover part being the path part; S46, mutation: mutation judgment is performed on each chromosome. If mutation occurs, each gene of the chromosome randomly selects a point to generate a mutation path to the end point. In order to enhance the diversity of solutions and avoid local optimality, a mutation strategy based on random factors is adopted. The mutation process is implemented through the improved Dijkstra algorithm. The introduced random factor combines the product of the path weight and the random number to determine the intensity of the mutation. S47, Optimize departure time: Further optimize path planning by adjusting the departure time of aircraft to avoid the algorithm falling into the local optimal solution too early and increase the diversity of the solution space; S48, select the next generation population: merge the new population obtained after the crossover and mutation operations with the previous generation population, and generate the next generation population through selection operations; S49, repeat iteration: continuously repeat steps S44 to S48S until a termination condition is met; S410, end of algorithm: When the termination condition is met, the algorithm stops running and outputs the final Pareto solution set.

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