Method and system for sgr generation and airport layout optimization based on multi-objective response surface driving

Abstract

The present application relates to the technical field of airport operation and layout design, aiming at the obvious dimension limitation problem of existing SGR evaluation and layout optimization model, a method and system for SGR generation and airport layout optimization based on multi-objective response surface driving are proposed, including constructing an airport flight area queuing network model based on queuing theory, constructing a Monte Carlo discrete event simulation platform, using a quadratic polynomial to construct a multi-objective response surface model of layout parameters and corresponding target indicators, using the response surface model of each target indicator as a fast evaluation function, using an improved NSGA-II algorithm to perform multi-objective optimization, and obtaining a set of airport layout optimization parameters. The present application can effectively improve the accuracy and reliability of SGR calculation, accurately quantifies the nonlinear influence of multiple layout parameters on SGR, construction cost and operation conflict rate, provides a scientific basis for quantitative evaluation and decision of airport layout scheme, and realizes the collaborative balance of "efficiency-cost-safety".

Description

Technical Field

[0001] This invention relates to the field of airport operation and layout design technology, and in particular to a method and system for SGR generation and airport layout optimization based on multi-objective response surface driven approach. Background Technology

[0002] With the rapid development of the global air transport industry, airports, as core hubs of the integrated transportation system, have seen their operational efficiency and service capacity become important indicators for measuring the level of regional economic development. Sortie Generation Rate (SGR), a core indicator quantifying the total number of safe and efficient aircraft takeoffs and landings an airport can handle per unit of time, directly reflects the rationality of the flight area layout design, the scientific allocation of facility resources, and the smoothness of operational processes. It is a key issue that must be addressed during the airport planning and design phase and operational optimization. Guided by the development plan for a modern integrated transportation system, my country's airport construction has entered a new stage of simultaneous large-scale expansion and quality improvement. The number of new airport site selection plans and the renovation and expansion projects of existing airports is increasing. How to maximize SGR through scientific layout optimization while simultaneously controlling construction costs and ensuring operational safety has become a core demand that urgently needs to be addressed within the industry.

[0003] From the perspective of actual airport operations, the flight area, as the core area for aircraft takeoff, landing, taxiing, parking, and support, has a complex nonlinear coupling relationship between its layout parameters (such as the number of runways, spacing, fast taxiway exit configuration, and parking stand size) and the three major objectives of "efficiency-cost-safety." For example, increasing the number of runways and the density of fast taxiway exits can significantly improve aircraft takeoff, landing, and taxiing efficiency, thereby increasing SGR (Square Ranging Rate), but it will lead to an exponential increase in land acquisition and engineering construction costs. At the same time, excessively close runway spacing may increase the risk of flight conflicts. Reducing the number of parking stands can lower construction costs, but it will cause aircraft to queue for longer periods, directly restricting the improvement of SGR and increasing the probability of taxiway congestion. This mutual constraint and contradiction among multiple objectives makes traditional layout design methods based on experience-based judgment or single-objective optimization difficult to adapt to the refined planning needs of modern airports.

[0004] Existing SGR (Speed ​​Regulation) assessment and layout optimization models suffer from significant dimensional limitations: One type of model focuses on analytical derivation of physical logic, characterizing the impact of layout parameters on SGR by establishing geometric and process constraint equations. However, these models often assume ideal operating environments (e.g., no equipment failures, constant weather), neglecting the random disturbances commonly present in aviation operations. This leads to significant discrepancies between model predictions and actual operating conditions, resulting in the problem of "theoretically feasible but practically ineffective" optimization solutions after implementation. Another type of model focuses on simulating stochastic characteristics, injecting random events such as equipment failures and flight delays. However, these models are often "black box simulations," failing to establish explicit mapping relationships between layout parameters and multi-objective indicators. They struggle to quantify the sensitivity of each layout element to SGR, cost, and conflict rate, resulting in a lack of clear theoretical guidance in the optimization process, leading to trial-and-error iterations, low optimization efficiency, and difficulty in finding the global optimum. Furthermore, existing research largely concentrates on dual-objective optimization of "efficiency-cost" or "efficiency-safety," failing to construct a multi-objective evaluation system that balances all three, thus failing to meet the comprehensive requirements of "foresight, feasibility, and safety" in airport layout.

[0005] Based on this, we construct an SGR generation and airport layout optimization method that can take into account both physical logic and random characteristics and integrate multi-objective optimization. We establish a full-link quantitative mapping relationship from layout parameters to the three-dimensional objectives of "efficiency-cost-safety". This method has important theoretical value and engineering practical significance for improving the scientificity and foresight of airport layout design, reducing construction investment risks, and ensuring safe and efficient operation. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, this invention aims to provide a method and system for SGR generation and airport layout optimization based on multi-objective response surface driven technology. It proposes a hybrid modeling framework that integrates queuing theory, Monte Carlo simulation, and multi-objective optimization algorithms, and constructs a full-link quantitative evaluation system from layout parameters to multi-objective indicators, thereby solving the problems existing in the background technologies.

[0007] To achieve the above-mentioned technical objectives, the technical solution adopted by the present invention is as follows: In a first aspect, the present invention discloses a method for SGR generation and airport layout optimization based on multi-objective response surface driven approach, comprising the following steps: S1. Constructing an airport flight area queuing network model: Based on queuing theory, the parking position subsystem and runway subsystem of the airport flight area are abstracted into M / M / c model and M / G / k model respectively, and a serial queuing network is formed in sequence through the input and output relationship; S2. Construct a Monte Carlo discrete event simulation platform: Construct a discrete event simulation framework covering the entire process of airport flight area operation, define the probability distribution and triggering mechanism of random disturbance factors, design a parallel computing strategy based on time slice decomposition to execute simulation, and obtain airport operation performance data under specific layout parameters. S3. Construct a multi-objective response surface model: Use the Latin hypercube sampling method to generate a sample space for layout parameters, obtain multiple target index data corresponding to each sample space, and use quadratic polynomial regression to construct a response surface model from layout parameters to each target index. S4. Perform multi-objective optimization: Using the response surface model of multiple objective indicators as a fast evaluation function, the improved NSGA-II algorithm is used to search in the sample space of layout parameters to solve the Pareto optimal solution set and obtain the airport layout optimization parameter set.

[0008] As a further preferred embodiment of the above technical solution, step S1, the step of constructing the airport flight area queuing network model, includes: S11: Based on the M / G / k model of the runway subsystem, calculate the service rate considering aircraft type and weather conditions and the effective arrival rate considering taxiing time delay; S12: Based on the M / M / c model of the parking position subsystem, calculate the service capacity and steady-state performance indicators; S13: By forming a cascaded queuing network between the runway subsystem and the parking position subsystem during the aircraft taxiing process, an SGR calculation model is constructed.

[0009] A further preferred embodiment is that, in step S13, the step of constructing the SGR calculation model includes: The taxiing time is calculated by combining the base taxiing time and the additional delay time. The expression for taxiing time is:

[0010] In the formula: For gliding time, Based on the basic gliding distance, The average taxiing speed of the aircraft. For the gliding delay time, This is the location of the exit taxiway turning point for the rapid exit. This refers to the number of parallel taxiways; Calculate the total operating time of the aircraft within the flight area, including the sum of the time spent on parking stand service, taxiing, and runway service:

[0011] In the formula: Total running time, The average system time of the parking position system. The average system time of the runway system; The SGR calculation model is constructed based on taxiing time and total running time, and its expression is:

[0012]

[0013] In the formula: For the number of runways, The system capacity utilization rate, where 0 < η ≤ 1, is used to characterize the reduction in theoretical system capacity caused by operational conflicts; Q0 = (60 / T) total Q is the theoretical throughput capacity, where k is the theoretical throughput capacity. eff This refers to the effective throughput capacity determined based on historical operating data or Monte Carlo discrete event simulations under the same layout parameters.

[0014] As a further preferred option, the process of obtaining airport operational performance data under specific layout parameters in step S2 is as follows: S21: A Monte Carlo discrete event simulation platform covering the entire process of "support preparation - taxiing - queuing - take-off and landing" is constructed using a discrete event-driven mechanism; S22: Introduce a random perturbation factor into the Monte Carlo discrete event simulation platform to generate sliding collision types; S23: Based on the Monte Carlo discrete event simulation platform, design a parallel simulation strategy based on time slice decomposition to detect and quantize operational conflicts in the simulation process in real time. S24: Determine and count the total number of taxiway conflicts and runway incursions during the parallel simulation, and calculate the running conflict rate. The expression for the running conflict rate is as follows:

[0015] In the formula: the unit of operational conflict rate is times / million flights.

[0016] As a further preferred option, step S3, the step of constructing a multi-objective response surface model, includes: S31: Based on the feasible region of layout parameters, multiple sample spaces are generated by Latin hypercube sampling, where: layout parameters include the number of runways, runway spacing, number of fast exit taxiways, total number of parking stands, number of parallel taxiways, single aircraft support time and parking angle. S32: Use the Monte Carlo discrete event simulation platform to obtain simulation data of multiple sample spaces and corresponding target indicators, including SGR, construction cost and operational conflict rate; S33: Use quadratic polynomial regression to construct the response surface model for each target indicator, forming a quantitative mapping relationship between the layout parameters and the corresponding target indicators; S34: Use the least squares method to estimate the regression coefficients of the response surface model and test the goodness of fit of the response surface model for each target index.

[0017] A further preferred embodiment is that, in step S4, the steps for obtaining the airport layout optimization parameter set include: S41: An improved NSGA-II algorithm is formed by introducing an adaptive crossover mutation operator and an elite retention strategy into the NSGA-II algorithm. S42: Set the termination conditions for the improved NSGA-II algorithm; S43: Using the response surface model of multiple target indicators as a fast evaluation function, the improved NSGA-II algorithm is used to search in the sample space of layout parameters to output the Pareto optimal solution set.

[0018] Preferably, in step S41, the process of forming the improved NSGA-II algorithm includes: Encode and initialize the NSGA-II algorithm; The fast nondominated sorting algorithm is used to screen the nondominated front layer by layer in the initial population; We design an adaptive crossover and mutation operator and an elite retention and archiving strategy to perform non-dominated sorting and crowding calculation on the population, and add the non-dominated solutions to the archive set.

[0019] Preferably, in step S42, the improved NSGA-II algorithm terminates when any of the following conditions are met: (I) Reaching the preset maximum number of iterations T =200; (II) Continuous G =20 generations, average Pareto frontal movement distance of the external archive set Less than the threshold .

[0020] Secondly, this invention discloses a multi-objective response surface driven SGR generation and airport layout optimization system, the system being used to implement the steps of the above-described method, the system comprising: The first model construction module is used to abstract the parking position subsystem and runway subsystem of the airport flight area into M / M / c model and M / G / k model respectively based on queuing theory. Through the input and output relationship, a serial queuing network is formed to construct the airport flight area queuing network model. The platform construction module is used to build a Monte Carlo discrete event simulation platform, construct a discrete event simulation framework covering the entire process of airport flight area operation, define the probability distribution and triggering mechanism of random disturbance factors, design a parallel computing strategy based on time slice decomposition to execute simulation, and obtain the airport's operational performance data under specific layout parameters. The second model construction module is used to construct a multi-objective response surface model, use the Latin hypercube sampling method to generate a sample space of layout parameters, obtain multiple target index data corresponding to each sample space, and use quadratic polynomial regression to construct a response surface model from layout parameters to each target index. The computation module is used to perform multi-objective optimization. It uses the response surface model of multiple objective indicators as a fast evaluation function and employs the improved NSGA-II algorithm to search in the sample space of layout parameters to solve for the Pareto optimal solution set, thereby obtaining the airport layout optimization parameter set.

[0021] Thirdly, the present invention also discloses an electronic device, the electronic device including at least one processor and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, the instructions being executed by the processor to enable the processor to perform the steps of the method described above.

[0022] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention is based on the deep integration of queuing theory and Monte Carlo simulation, which achieves both theoretical accuracy and real-world scenario accuracy in SGR calculation. The relative error between the benchmark simulation and actual data is less than 3%, providing a reliable quantitative basis for subsequent optimization.

[0023] 2. This invention accurately characterizes the nonlinear mapping relationship between seven types of layout parameters and three target indicators, taking into account "efficiency-cost-safety", through response surface model. The prediction accuracy reaches 98.7%, and the computational efficiency is 7200 times higher than Monte Carlo simulation, which significantly reduces the computational cost of multi-objective optimization.

[0024] 3. This invention proposes an improved NSGA-II algorithm as a multi-objective optimization algorithm. Through adaptive operators and elite retention strategies, it exhibits better convergence speed and solution distribution in high-dimensional parameter optimization. The obtained Pareto optimal solution set can cover different decision preferences.

[0025] 4. The optimization method of this invention takes into account the balance between "efficiency-cost-safety". Its core optimization path is "increasing the number of fast exit taxiways, optimizing runway spacing, and adding parallel taxiways". While improving SGR by 12.3%, it achieves a moderate increase in construction cost of 7.4% and a significant decrease in conflict rate of 36.0%, providing a scientific and feasible reference solution for the layout optimization of medium-sized hub airports. Attached Figure Description

[0026] Figure 1 The flowchart shows the SGR generation and airport layout optimization method based on multi-objective response surface driven by the present invention. Figure 2 This is a structural diagram of the queuing network model of the present invention; Figure 3 This is a schematic diagram of different conflict types of the taxiway conflict according to the present invention, wherein a is a cross conflict, b is a queuing conflict, and c is a waiting conflict; Figure 4 This is a flowchart of the Monte Carlo discrete event simulation platform of the present invention; Figure 5 The figure shows the fitting effect of the SGR response surface model of the present invention. Figure 6 This is a fitting effect diagram of the construction cost response surface model of the present invention; Figure 7 This is a fitting effect diagram of the running conflict rate response surface model of the present invention; Figure 8 This is a schematic diagram of the hybrid coding structure of the improved NSGA-II algorithm of the present invention; Figure 9 This is the working logic diagram of the adaptive crossover mutation operator of the present invention, where (a) represents the crossover probability. P c (b) represents the mutation probability. P m ; Figure 10 This is a schematic diagram of the external archive update and truncation strategy of the present invention; Figure 11 The distribution diagram of the Pareto optimal solution set in the target space in the example verification of the present invention; Figure 12 A bar chart comparing the target indicators of the four schemes used in the example verification of this invention; Figure 13 Line graph showing the sensitivity analysis of layout parameters in the example verification of this invention; Figure 14 The graph shows the convergence curve of the improved NSGA-II algorithm used in the example verification of this invention. Detailed Implementation

[0027] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0028] Example 1: Refer to Figures 1-10 This invention discloses a method for SGR generation and airport layout optimization based on multi-objective response surface driven approach, comprising the following steps: S1. Constructing an airport flight area queuing network model: Based on queuing theory, the parking position subsystem and runway subsystem of the airport flight area are abstracted into M / M / c model and M / G / k model respectively, and a serial queuing network is formed in sequence through the input and output relationship; S2. Construct a Monte Carlo discrete event simulation platform: Construct a discrete event simulation framework covering the entire process of airport flight area operation, define the probability distribution and triggering mechanism of random disturbance factors, design a parallel computing strategy based on time slice decomposition to execute simulation, and obtain airport operation performance data under specific layout parameters. S3. Construct a multi-objective response surface model: Use the Latin hypercube sampling method to generate a sample space for layout parameters, obtain multiple target index data corresponding to each sample space, and use quadratic polynomial regression to construct a response surface model from layout parameters to each target index. S4. Perform multi-objective optimization: Using the response surface model of multiple objective indicators as a fast evaluation function, the improved NSGA-II algorithm is used to search in the sample space of layout parameters to solve the Pareto optimal solution set and obtain the airport layout optimization parameter set.

[0029] Specifically, in step S1, the operational flow of the airport flight area can be abstracted as a series of processes: "aircraft arrival → parking stand support → taxiing → runway queuing → takeoff and landing → departure." Parking stands and runways are core service facilities, constituting two coupled queuing subsystems. In this embodiment, based on queuing theory, an "M / G / k model of the runway subsystem + M / M / c model of the parking stand subsystem" is constructed, which are then linked to form a queuing network model, such as... Figure 2 The system covers parking stands, taxiways, and runways in the airport's flight area. The system boundary is the entire lifecycle of an aircraft from entering the parking stand to completing takeoff and landing and leaving the runway. It quantifies the aircraft's operating time in the entire process, providing a theoretical basis for SGR calculation. The core parameters involved are defined as shown in Table 1 below. The parameter values ​​are based on the actual operating data of a medium-sized hub airport and industry standards to ensure the model's authenticity and applicability.

[0030] Table 1 Definition of core parameters of queuing network model

[0031] Furthermore, the runway subsystem is the core facility of the airport's flight area for aircraft takeoff and landing. Its operation has the following characteristics: aircraft arrivals are random; service time distribution is complex (affected by various factors such as aircraft type, weather, and air traffic control rules); and multiple runways can function as parallel service stations working collaboratively. Therefore, the M / G / k model is used for characterization. Since the M / G / k model does not have an exact analytical solution, this embodiment uses an improved formula based on the Heavy Traffic approximation for calculation. This approximation method is effective in determining the utilization rate of the runway subsystem. It has high accuracy within the range (corresponding to the typical load during peak hours at the airport), and the error compared with the simulation results can be controlled within 5%.

[0032] (I) Service rate calculation considering aircraft type and weather conditions: The service rate of a single runway (unit: flights / hour) is the result of the combined effect of aircraft mix and weather conditions, and is calculated using the following formula: ; In the formula: For the first The proportion of large aircraft in the operating fleet is defined based on statistical results of the historical flight composition of the target airport: medium-sized machine small computer . For a single track to the first The baseline service rate for aircraft of this type, taking into account the time and space intervals required for takeoff and landing of different aircraft types, is set as follows: Large aircraft medium-sized machine small computer ; This is a correction factor for the impact of weather conditions on service efficiency. Based on fitting data from actual airport operations, the following was obtained: Clear skies (No impact), light rain (Efficiency decreased by 20%), heavy fog (Efficiency decreased by 50%).

[0033] Example: When the weather is sunny ( When the overall service rate of a single runway is: .

[0034] The calculation results are basically consistent with the average service rate per runway (15 flights / hour) in Table 1, which verifies the rationality of the parameter values.

[0035] (II) Calculation of effective arrival rate considering taxiing time delay: Effective arrival rate of runway subsystem The effective arrival rate is not directly equal to the output rate of the parking stand subsystem, but needs to be corrected for the "transmission delay" of the taxiway subsystem. After an aircraft completes parking stand support, it needs to taxi through the taxiway network to the runway end to wait for takeoff and landing. The taxiing time, potential conflict delays, and the capacity constraints of the taxiways themselves all change the actual rate at which aircraft enter the runway queue. Considering the characteristics of the serial queuing network in airport operations, the calculation of the effective arrival rate must follow the steps of "basic taxiing time quantification → conflict delay modeling → taxiway queuing coupling → multi-stage bottleneck transmission," and incorporate the nonlinear effects of key layout parameters throughout the process.

[0036] ① Quantification of basic taxiing time (incorporating the location of the exit point of the fast exit taxiway and the number of parallel taxiways); Basic taxiing time is the time required for an aircraft to taxi from its parking position to the end of the designated runway under ideal, conflict-free conditions. It primarily depends on the taxi distance and taxi speed, and is also related to layout parameters. (Location of the rapid exit taxiway turning point) and (Number of parallel taxiways) is directly related; in this embodiment, the position of the exit point of the fast exit taxiway is used to describe the geometric position of the exit point of the fast exit taxiway, and is defined as the ratio of the distance from the exit point to the end of the selected runway to the length of the runway.

[0037] 1) Taxi distance correction: If there is no fast taxiway exit, the aircraft must taxi along the main taxiway to the farthest end of the runway, with a maximum taxi distance. Based on digital calculations using the airport layout map, it was determined that setting up a fast taxiway exit can effectively shorten this distance; therefore, the location parameters of the fast taxiway exit point are defined. The value range is defined as "the ratio of the distance from the exit to the runway end to the total length of the runway". (0.1 indicates near the runway end, 0.5 indicates in the middle of the runway). Assume the total runway length... If the distance is meters, then the corrected gliding distance is: ; Note: The coefficients are the fitting results of industry measured data, indicating that when the fast slip exit is from the runway end ( Move to the middle section ( When the taxiing distance is reduced by approximately 80% of the runway length, that is... Thus, the proportionality coefficient 2 is obtained through fitting.

[0038] Example: When hour, rice.

[0039] 2) Taxiing speed correction: The aircraft's taxiing speed Number of parallel taxiways The impact is that a single parallel taxiway needs to accommodate two-way traffic, which limits speed (take...). Two or more lines can achieve unidirectional flow splitting, thereby improving speed (taking...). The velocity function is defined as: ; 3) Basic Gliding Time Calculation: After standardizing the units (distance: meters → kilometers; time: hours → minutes), the basic gliding time (unit: minutes) is: ; Example: When , hour, minute.

[0040] ② Quantization of sliding conflict delay (considering the coupling between conflict type and layout parameters). Conflicts within the taxiway network are a core factor contributing to taxiing delays, primarily including cross-collision, rear-end collision, and head-on collisions, such as... Figure 3 As shown, the additional delay time it generates Number of express exit taxiways and number of parallel taxiways It is positively correlated with the real-time load coefficient of the taxiway and is calculated in three steps: "conflict probability statistics → single conflict delay modeling → total delay synthesis".

[0041] 1) Conflict probability statistics: Simulations were conducted using 100,000 taxiing data points from a medium-sized airport to statistically analyze the collision probabilities under different layout parameters. The results are shown in Table 2. Table 2 Collision Probabilities under Different Layout Parameters

[0042] 2) Single-event conflict delay modeling: Combined with the real-time number of aircraft on the taxiway (i.e., taxiway queue length), defining the single-transaction delay caused by various conflicts: Conflict-free delay: .

[0043] Cross-collision delay: ,in (Unit: minutes / aircraft), which are coefficients fitted based on historical data.

[0044] Rear-end collision delay: ,in A non-linear form (exponential 0.8) is used to avoid excessive delay growth under high load.

[0045] Head-on conflict delay: ,in This reflects the significant delay required for two-way avoidance.

[0046] In the formula, the length of the taxiway queue is... The Little formula can be used to calculate the average waiting time on the taxiway. Related: Little's Law, rigorously proven by John DC Little of MIT in 1961, reveals the quantitative relationship between average number of customers, average arrival rate, and average dwell time in a steady-state queuing system, independent of customer arrival distribution, service time distribution, number of service counters, or queuing rules. Specifically, it is shown below: (1) Total number of customers in the system (including customers currently receiving services): L = λ × W ; (2) Number of customers waiting in the queue (only including customers waiting in the queue, excluding customers being served): L q = λ × W q ; Where: L is the average number of customers in the queuing system. L q The average number of customers waiting in the queue. λ Average customer arrival rate W The average dwell time of the system. W q This represents the average waiting time in the queue.

[0047] ; in, The output rate of the parking position subsystem (i.e., the rate at which the aircraft enters the taxiway).

[0048] 3) Overall conflict delay synthesis: Based on the frequency (weight) of various types of conflicts in the gliding network, the weighted average of the delay of a single conflict is used to obtain the expected total conflict delay: ; in, For the first The weight coefficients for class conflicts satisfy the following conditions: .

[0049] ③Queueing coupling of taxiway subsystem (steady-state solution of M / G / m model); Based on queuing theory, the taxiway subsystem is abstracted into an M / G / m model, where the number of service counters... (Number of parallel taxiways), its input rate is the output rate of the parking position subsystem. The service time is the total taxiing time of a single aircraft. Effective arrival rate of the runway subsystem The steady-state output rate of this taxiway subsystem can be obtained by iteratively solving the following coupling relationship: Iteration Step 1: Stop Position Output Rate calculate; The parking position subsystem adopts the M / M / c model, in which (Number of parking spaces). Total service time for each aircraft includes support time. and release time (Affected by the angle of shutdown) Influence).

[0050] Based on the fitting of measured data, the relationship between time and stopping angle is derived as follows: ; For example, hour, minute; ,hour minute.

[0051] Total service hours: .

[0052] Service rate: (Unit: flights / hour).

[0053] Steady-state output rate: ,in, For the external input rate of the stop position subsystem, This represents the theoretical maximum processing capacity of the parking position subsystem.

[0054] Iteration Step 2: Taxiway Capacity calculate; The capacity of a single parallel taxiway is approximately 12 flights per hour, therefore The total capacity of the parallel taxiways is: ; Verification: To meet the demand of 70,000 takeoffs and landings per year, approximately... Parallel taxiways, calculated Tens of thousands of flights per year, meeting the requirements.

[0055] Iteration step 3: Solve for taxiway queuing waiting time (HeavyTraffic approximation). When the taxiway load factor Time (of which) The average waiting time is calculated using the HeavyTraffic approximation formula of the G / G / m queuing model (assuming the average service rate of a single taxiway). ; In the formula: This represents the average gliding time. To represent the variance of the gliding time, take , .

[0056] Iteration step 4: Convergence determination; The above coupling equations are solved iteratively: Initial assumptions ,calculate And thus obtain .

[0057] Will Substituting these values ​​into the average waiting time formula above, we can calculate the result. .

[0058] Calculate the queue length using Little's formula: .

[0059] Will Substituting into the total conflict delay formula above, the new conflict delay is calculated. .

[0060] Update the average glide time: This leads to an update of the service rate. .

[0061] Repeat steps 2-4 until the difference in waiting time between two adjacent iterations satisfies the condition. Minutes, at which point convergence is considered achieved, yielding the steady-state result. .

[0062] ④ Effective arrival rate Final determination: Effective arrival rate of runway subsystem This refers to the steady-state output rate of the taxiway subsystem, which is divided into two scenarios depending on whether the taxiway is saturated: Scenario 1: The slide lane is not saturated ( ): In steady-state glide path, the input rate equals the output rate, therefore .

[0063] Scenario 2: Taxis saturated ( The taxiway reaches its maximum handling capacity, therefore .

[0064] Example: Known parameters: (Proportion of the exit taxiway turning point location) (Number of parallel taxiways) (Number of parking spaces) minutes (guarantee time) (Stopping angle) Flights per hour (parking position input rate).

[0065] Stop position output rate The calculation is as follows: minute; minute; Flights per hour; Flights per hour; Flights per hour.

[0066] Base gliding time The calculation is as follows: rice; km / h; minute.

[0067] Taxiway capacity assessment: Flights per hour; due to The taxiway is saturated.

[0068] Effective arrival rate determination: According to the saturation scene rules Flights per hour.

[0069] Runway capacity verification: Number of runways (Assuming) Single-runway service rate Flights per hour.

[0070] Overall service rate of the runway subsystem Flights / hour Flights per hour, system steady-state feasibility.

[0071] Furthermore, the parking stand system is responsible for providing ground support services for aircraft, including passenger boarding and disembarking, cargo loading and unloading, refueling, cleaning, and maintenance. Its operation has the following characteristics: aircraft (as "customers") arrivals are random; the service time for each support operation is relatively stable with little fluctuation, and can be approximated as following an exponential distribution; airports have multiple parking stands, which can be considered as service counters operating in parallel. Therefore, using the M / M / c model to characterize the parking stand subsystem is reasonable and effective.

[0072] (I) Service rate calculation: The service capacity of the parking position subsystem is determined by the average service rate. (Unit: flights / hour) represents the average support time per aircraft. The reciprocal of. Among them, It is the 6th layout parameter. This represents the average time required for a single aircraft to complete all necessary ground support operations, and its value ranges from [value missing]. The time is directly affected by the configuration of airport ground service resources (personnel and equipment).

[0073] ; In the formula, The units need to be converted to hours to maintain dimensional consistency.

[0074] (II) Derivation of System Steady-State Performance Indices: According to the classic conclusion of the M / M / c model, when the system utilization rate... Time (of which) The number of parking positions, i.e., the parameter ; (For the external arrival rate of the aircraft arrival at the parking position subsystem), the system has a steady-state solution, and its key performance indicators are as follows: System idle probability This refers to the probability that all parking positions are idle.

[0075] ; Average queue length : The expected number of aircraft waiting for an available parking space.

[0076] ; Average waiting time The average waiting time for an aircraft from arriving at the parking position subsystem to beginning to receive support services.

[0077] ; Average system time Total time an aircraft spends in a parking stand system, including waiting time and time spent receiving support services.

[0078] ; The aforementioned performance indicators are the core of evaluating the operational efficiency and congestion level of the parking position subsystem, and also serve as the basic input for subsequent queuing network coupling analysis with the taxiway and runway subsystems, as well as for calculating the total system uptime and throughput (SGR).

[0079] (III) Cooperative coupling of queuing networks: The runway subsystem and the parking position subsystem are connected in series to form a coordinated queuing network through the aircraft's taxiing process. After completing service (support operations) in the parking position subsystem, the aircraft, as the output of the system, enters the taxiway network. After a period of taxiing, it arrives at and joins the waiting queue of the runway subsystem, becoming the input of the runway subsystem.

[0080] ① Gliding time modeling; Gliding time It consists of the base taxiing time and additional delays caused by factors such as taxiway network conflicts and path twists. The calculation formula is as follows: ; in: The base taxiing distance (in meters) is calculated digitally based on the airport layout map. This represents the aircraft's average taxiing speed (km / h). Taxiway delay time (in minutes) is closely related to the design parameters of the taxiway. Based on 50 sets of measured airport operation data, its correlation with the exit point location of the rapid exit taxiway was obtained through multiple linear regression fitting. (Proportional distance from the runway end), Number of parallel taxiways The relation is: ; The coefficient of determination of the fitted model And the regression coefficients passed the significance test ( The formula indicates that the turning point location of the fast exit taxiway is more optimal. Increased number of runway exits (closer to the middle of the runway) and parallel taxiways ( Increasing the number of taxiing points can effectively reduce taxiing conflicts and path detours, thereby reducing taxiing delays.

[0081] ② Total running time and SGR theoretical derivation; Total operating time of an aircraft within the flight area It is the sum of the times spent in the three stages: parking stand service, taxiing, and runway service. ; In the formula, The average system time (including waiting and maintenance time) of the shutdown subsystem. This is the average system time of the runway subsystem (including waiting and takeoff / landing service time).

[0082] Based on this, the theoretical formula for calculating the system throughput (i.e., aircraft sortie rate) SGR (slots / hour) can be derived. SGR is essentially the number of aircraft that the runway subsystem can successfully serve per unit time, equal to the average operating time of a single aircraft. The reciprocal of the number of runways must be taken into account. And the system capacity loss due to operational conflicts, therefore: ; in: For unit conversion factors (converting "flights / minute" to "flights / hour"), Number of runways (decision variable) ), For system capacity utilization ( ), used to quantify the reduction in theoretical maximum capacity due to operational conflicts (such as runway incursions and taxiing conflicts), defined as , This refers to the conflict rate function, whose quantization form is obtained by fitting historical data: ; This formula reflects the track spacing. Increase and optimize the location of the exit taxiway turning point ( (Increase) the positive effect on reducing operational conflict rate.

[0083] Example: Suppose a certain combination of layout parameters is: runway spacing Meters, location of the rapid exit taxiway turning point According to calculations, minute, minute, Minutes (calculated by the M / G / k model).

[0084] Conflict rate during operation: ; Capacity utilization rate: ; System throughput: Flights per hour; The results are consistent with the corrected results based on discrete event simulations, validating the effectiveness of the theoretical model.

[0085] like Figure 2 For the overall architecture of the queuing network model, the operation of the flight area is abstracted into three interconnected queuing subsystems: parking positions (M / M / c), taxiways (M / G / m), and runways (M / G / k), which fully depicts the entire service chain of aircraft from support, taxiing to take-off and landing. Figure 2 Data flow arrow ( This intuitively reveals the serial queuing essence of "the output of the previous stage is the input of the next stage," which is consistent with the aforementioned effective arrival rate. The recursive calculation process corresponds completely, clearly defining the layout decision variables (such as the number of parking spaces). Number of parallel taxiways Number of runways ) and taxiway physical capacity constraints ( The layout parameters are embedded in various subsystem modules, clearly demonstrating the impact path of layout parameters on system performance, and providing a direct basis for subsequent layout parameter sensitivity analysis.

[0086] (IV) Model validation; The rationality of the queuing network model was verified using actual operational data from a medium-sized airport: Historical data from August 2024 (a busy month) of the airport were selected, and the following parameters were obtained: λ0 = 30 flights / hour, k = 2 runways, c = 22 parking positions, t_s = 45 minutes. The model predicted SGR = 32.6 flights / hour, and the relative error between the model and the actual SGR = 31.8 flights / hour was 2.5%, which meets the engineering accuracy requirements (relative error < 5%).

[0087] (V) Overall model coupling and SGR calculation; 1) Network coupling logic: The operation of an airport flight area can be abstracted into a queuing subsystem network consisting of a parking position subsystem (M / M / c model), a taxiway subsystem (M / G / m model), and a runway subsystem (M / G / k model), linked together. These three subsystems are sequentially coupled through an "input-output" relationship, forming a complete service chain. Its logical flow can be represented as follows:

[0088] in: Arrival rate of aircraft requesting parking space service (external input). This refers to the steady-state output rate after processing by the parking stand system, i.e., the aircraft flow rate into the taxiway system. This refers to the steady-state output rate of the taxiway system after processing, which is the effective arrival rate of the runway system. This is the steady-state output rate of the runway system, i.e., the final throughput of the system.

[0089] According to the principle of flow conservation in steady-state queuing networks, the final output rate of a series subsystem is equal to its final input rate, i.e. Therefore, the theoretical throughput SGR of the system is numerically equal to the effective arrival rate of the runway subsystem. : .

[0090] 2) SGR correction (considering random perturbations): In actual operation, sudden equipment failures and abrupt changes in weather conditions can temporarily reduce runway service capacity. To reflect the impact of such random disturbances, a comprehensive reliability correction factor needs to be introduced based on the theoretical SGR. ( ): ; Equipment Failure Correction Coefficient Assuming the interval between failures of equipment (such as navigation lights, communication systems) Follows exponential distribution (Failure rate) Repair time Follows a log-normal distribution (The average is approximately 20 minutes). This coefficient reflects the runway availability time lost due to maintenance or repairs, and is calculated as follows: ; Weather correction factor Weather conditions (sunny, light rain, heavy fog) are simulated using a three-state Markov chain (state transition probabilities and steady-state distributions are based on historical data). The correction coefficients for runway service efficiency under different weather conditions are: 1.0 for sunny, 0.8 for light rain, and 0.5 for heavy fog. The long-term expected value of these coefficients is the weighted sum of the steady-state probabilities for each state and their corresponding correction coefficients. ; Among them, 0.7, 0.2, and 0.1 represent the steady-state probabilities of sunny, light rain, and heavy fog, respectively.

[0091] The total correction factor is obtained by combining the two corrections, namely the total correction factor and the final SGR. ; Therefore, the final revised SGR calculation formula is: ; Example: If the effective arrival rate of the runway subsystem is calculated using a queuing network model... The corrected system throughput is: ; The results are consistent with the actual operational levels of medium-sized busy airports, validating the effectiveness of the model.

[0092] In step S2, firstly, a Monte Carlo discrete event simulation platform is constructed using a discrete event-driven mechanism. The specific process is as follows: Figure 4 As shown, Figure 4Using a timeline as its core, the simulation's complete logical chain is displayed. The starting node is "Simulation Initialization," which sets the simulation time (24 hours), facility status (runway and parking bay availability), and statistical counters (waiting time, number of conflicts, etc.). This is followed by "Aircraft Arrival Event Generation," which generates aircraft arrival times and types based on a Poisson distribution. Next, the "Parking Bay Allocation and Support Event" is triggered, determining if there are available parking bays. If not, the aircraft enters a queue; if so, a parking bay is allocated, and a support completion time is generated based on an exponential distribution. After support is completed, the "Taxiing Event" is triggered, calculating taxiing time based on taxiing distance and speed, and simultaneously determining if a taxiing conflict has occurred (based on parking angle). (x7 and taxiway layout); after taxiing to the runway, a "runway queuing event" is triggered, and the aircraft joins the runway queue according to the FCFS rule, waiting for takeoff and landing services; subsequently, a "takeoff and landing event" is triggered, generating takeoff and landing service times based on the M / G / k model, while also introducing weather state transition and equipment failure random events. If a failure occurs, a "fault repair event" is triggered, suspending the corresponding facility service until repair is completed; after each event is processed, statistical data is updated, and it is determined whether the simulation termination time has been reached. If not, the simulation returns to "aircraft arrival event generation" to continue the loop; if it has been reached, the simulation results (SGR, cost, conflict rate) are output. Different colors indicate event types: blue for normal process events, red for random disturbance events, and green for statistical and termination events. Arrows clearly indicate the logical dependencies between events.

[0093] The simulation covers the entire process of "aircraft arrival → parking stand guarantee → taxiing → runway queuing → takeoff and landing → departure". The simulation initialization parameters are as follows: (1) Time parameters: simulation duration = 1440 minutes (24 hours), warm-up period = 120 minutes (excluding initial fluctuations); (2) Facility parameters: number of runways (k=x_1), number of parking stands (c=x_4), number of parallel taxiways (m=x_5); (3) Statistical parameters: initialize counters for total number of flights, total waiting time, number of conflicts, number of failures, etc. The core event definition and scheduling logic are shown in Table 3. Table 3 Core Event Definitions and Scheduling Logic

[0094] Then, in order to truly reflect the uncertainties in airport operations, random disturbance factors, including equipment failures and weather conditions, need to be introduced into the Monte Carlo discrete event simulation platform.

[0095] (I) Equipment failure; Random failures of runway and parking support equipment are described using two states: "normal operation" and "fault repair".

[0096] Failure rate: Based on historical maintenance records, the runway subsystem failure rate is set as follows: The failure rate of the shutdown subsystem (including support equipment) is set to... .

[0097] Fault repair time: follows a log-normal distribution; runway repair time parameters are as follows. minute, The shutdown position repair time parameter is: minute, .

[0098] Impact of the failure: When a failure occurs, the corresponding facility immediately becomes unavailable, service to aircraft currently being served is interrupted, and aircraft in the queue must wait for the failure to be repaired or relocated to a backup facility.

[0099] (2) Weather conditions; A discrete-event Markov chain is used to characterize the dynamic transition process of weather states. Based on statistical data of meteorological data of the target airport over the past five years, a state transition probability matrix is ​​obtained. as follows: ; Among them, row index Indicates the current weather status, column index. This indicates the weather condition at the next moment, with the following order: sunny, light rain, and heavy fog.

[0100] (3) Random variable generation based on inverse transformation method; 1) Generation of equipment failure intervals and repair times: Failure Interval (follows an exponential distribution) a. Generate uniformly distributed random numbers b. Applying the inverse transform method: . ( ) Fault repair time (follows a log-normal distribution) ): a. Generate standard normal random numbers using Box-Muller transform. First, two independent random numbers , then calculate .

[0101] b. Applying the inverse transform method: (The mean of this distribution is approximately...) minute) 2) Generation of weather state transition sequences: Define state space The state transition probability matrix (based on 5 years of data from a certain airport) is as follows: ; The generation steps are as follows: a. Initialization: Based on the initial state distribution Sure .generate ,like ,but ;like ,but ;otherwise .

[0102] b. Iterative transition: Let the current state be... ,generate Calculate the cumulative probability. ( Represents the matrix of the first Line number (Column elements). Searching for... , making (Agreement) If the state transitions to the next time step is... Repeat this process to generate a state sequence.

[0103] 3) Glide collision type generation: Let the prior probabilities of each type of conflict be as follows: no conflict Cross-conflict Rear-end collision Conflict with adversaries (satisfy The generation steps are as follows: a. Generate uniformly distributed random numbers ; b. Determine the conflict type: If If, then there is no conflict; if If, then it is a cross-conflict; if If the collision occurs, it is a rear-end collision; otherwise, it is a head-on collision.

[0104] Table 4. Parameters of Random Perturbation Factor in Monte Carlo Simulation

[0105] Next, in order to achieve efficient computation of large-scale simulation samples, a parallel architecture with time axis decomposition was designed on the Monte Carlo discrete event simulation platform. The entire simulation task was distributed to multi-core processors for parallel execution, and running conflicts during the simulation process were detected and quantized in real time, thereby improving the efficiency of large-scale samples.

[0106] (I) Parallel architecture design: Hardware configuration: The simulation program is deployed on an 8-core central processing unit (CPU) platform with 16GB of shared memory.

[0107] Task partitioning: The total duration of a single simulation (1440 minutes, or 24 hours) is divided into 8 consecutive and non-overlapping time slices, each 180 minutes long. Each CPU core is independently responsible for handling all event progression within one time slice.

[0108] Data synchronization and transmission: A thread-safe shared memory area is used to store the global system state, such as fault records and occupancy status of facilities (runways, parking positions). For continuous events spanning multiple time slices (e.g., an aircraft begins taxiing in the current time slice but cannot finish until the next time slice), the processing thread must use a message queue to pass the remaining progress information of the event (such as remaining taxiing time, target runway) to the thread responsible for the next time slice to ensure the continuity of the simulation logic.

[0109] The efficiency improvement of parallel computing is measured by speedup. The measurement is defined as the serial simulation time. Parallel simulation time The ratio is estimated based on Amdahl's law: Serial time consumption of 100 simulations for a single sample minute.

[0110] Let the proportion of the non-parallelizable serial portion of the code be . Number of parallel threads The parallel processing time is estimated as follows: ; acceleration ratio For all 70 samples, the total simulation time was reduced from 19,600 minutes (approximately 13.6 days) serially to approximately 17,237.5 minutes (approximately 12.0 days), significantly improving computational efficiency and meeting the research time requirements.

[0111] It should be noted that Amdahl's Law contains... This represents the proportion of non-parallelizable parts of the program's execution time to the total serial execution time. Its specific value depends on processor configuration, thread scheduling method, shared state synchronization, and cross-time-slice event propagation mechanisms, and is not a fixed parameter. In the parallel architecture used in this embodiment, simulation initialization, global state synchronization, cross-time-slice continuous event propagation, and final statistical summarization cannot be fully parallelized; therefore, they need to be optimized through... f = / Confirmed. Among them, This represents the cumulative execution time of non-parallel and non-synchronous processing steps under single-threaded execution conditions. This represents the total serial execution time for the same simulation task.

[0112] In this embodiment, after analyzing the execution time of each major computing module during program runtime, the non-parallelizable portion accounts for approximately 15% of the total runtime. Therefore, [the following is taken as an example]. The information given here This is merely an exemplary estimation of the parallel speedup ratio in an 8-core environment and is not a necessary limitation of this embodiment. Changes in processor configuration, simulation model complexity, or event synchronization mechanism may occur. The actual program execution time can be recalculated and determined. The remaining approximately 85% of the event progression and sample calculation tasks can be executed in parallel by multiple processing cores.

[0113] (II) Simulation accuracy control: The simulation employed two steps: randomization control and convergence testing. To ensure the independence of each simulation result, each of the 100 repeated simulations for each sample was initialized with a different random number seed, and then the coefficient of variation was used. (Standard deviation) with the mean The ratio (SGR) is used as a criterion for the stability of the output index. If the number of simulations is sufficient, the result will converge; otherwise, the number of simulations will be automatically increased.

[0114] (III) Calculation of operational conflict rate: Operational conflict rate is a key indicator for assessing airport ground operational safety. During parallel simulation, potential operational conflict events are detected and statistically analyzed based on the real-time motion state of the aircraft, as detailed below: 1) Taxiway conflict determination; A taxiing conflict is determined to have occurred when two aircraft are near an intersection or merging point of a taxiway network and simultaneously meet the following two conditions: ① Spatial proximity: The instantaneous distance between the two aircraft is less than the safe distance threshold. (This embodiment takes) (meters); ② Time is of the essence: the time difference between the expected arrival times of the two aircraft at the point of conflict is less than the safe time threshold. (This embodiment takes) Second).

[0115] 2) Runway incursion determination; A runway incursion is defined as an incident that occurs when an aircraft intrudes into the runway activity area (defined as a rectangular area 150 meters to either side of the runway centerline) without obtaining air traffic control clearance.

[0116] 3) Conflict rate calculation; Based on the total number of taxiway conflicts and runway incursions occurring during the simulation period, the operational conflict rate is calculated using the following formula:

[0117] The unit for operational conflict rate is "times / million flights".

[0118] In this embodiment, a multi-threaded parallel strategy based on event decomposition is adopted, dividing the 24-hour simulation time into eight 3-hour time slices. Each time slice is allocated one thread to execute the simulation independently. The threads pass facility status (such as runway fault status) through shared memory. After the simulation is completed, the statistical data of each thread are merged.

[0119] Meanwhile, analysis of variance was used to determine the minimum number of simulations. Let the standard deviation of the simulation results be σ, and the relative error ε be less than 3% with a confidence level of 95%. Then the required number of simulations n satisfies: (ngeqleft(frac{1.96sigma}{varepsilonbar{y}}right)^2tag{32}). Through pre-simulation, we obtained σ=1.2 and (bar{y})=32 for SGR. We calculated that n≥61. Therefore, we set the number of simulations for each sample point to 100 to ensure the stability of the statistical results.

[0120] In step S3, there are 7 types of layout parameters: number of runways, runway spacing, number of rapid exit taxiways, total number of parking stands, number of parallel taxiways, single aircraft support time, and parking angle. For a layout with x3 rapid exit taxiways, the turning points of the rapid exit taxiways form a set {ξ}. j |j=1,…,x3}. Based on the feasible region of 7 types of layout parameters, 70 sample points (N=10d=70) were generated using Latin hypercube sampling. The feasible region and sampling range of the layout parameters are shown in Table 5 below: Table 5. Feasible Region and Sampling Range of Layout Parameters

[0121] The specific sampling steps are as follows: A1. Parameter standardization: The original value ranges of all 7 layout parameters (including continuous and discrete variables) are linearly mapped to the standard [0,1] interval to eliminate the influence of dimensions and lay the foundation for subsequent equal probability stratification. A2. Equal probability stratification and sample extraction: Divide each standardized layout parameter interval into N=70 equal probability sub-intervals (each layer has a probability of 1 / 70). A3. Continuous parameter: Within each layer, a sample point is randomly selected according to a uniform distribution; A4. Discrete Parameters: The number of layers is assigned based on the probability of each value. For example, if a parameter has a 50% probability of being 2 and a 50% probability of being 3, then the first 35 layers are assigned the value 2, and the next 35 layers are assigned the value 3. Within each corresponding layer, this discrete value is directly used as the sample point. This operation ensures that the probabilistic characteristics of the discrete variable's values ​​are strictly maintained. A5. Random Permutation and Sample Combination: To break the sequential association between sample points of each layout parameter and avoid sample clustering in space, 70 sample points independently extracted for each parameter are randomly permuted and sorted. Then, the randomly sorted sample sequences of the 7 layout parameters are combined row-wise to form 70 independent 7-dimensional sample vectors. ; A6. Inverse mapping to generate final samples: The standardized sample vector obtained by the above combination is inversely mapped according to the original range of each layout parameter to restore it to the actual physical space, and the final sampled samples used for simulation calculation are obtained. A7. Sample Uniformity Verification: To assess the spatial distribution quality of the sample set, calculate the average Euclidean distance within its standardized space. As an indicator of uniformity:

[0122] Calculations show that the sample set has the following characteristics: The value is very close to the theoretical value of 0.70 for an ideal uniform distribution, indicating that the sampling has excellent spatial coverage and uniformity, and meets the data requirements for constructing a response surface model.

[0123] Furthermore, based on the simulation data of 70 sample points (each sample point contains a specific combination of 7 layout parameters) and their corresponding 3 target indicators (SGR, construction cost, and operational conflict rate) obtained from the Monte Carlo discrete event simulation platform, an explicit response surface model is constructed using the quadratic polynomial regression method to establish a quantitative mapping relationship between design parameters and target indicators.

[0124] (I) Quantification of target indicators: Before building the model, three optimization objectives need to be clearly defined and quantified: Indicator 1: SGR (System Throughput / Aircraft Slots): Unit: Slots / hour. The arithmetic mean of the SGR results obtained from 100 independent Monte Carlo simulations for each sample point is taken to reduce random error.

[0125] Indicator 2: Construction Cost: Unit: Ten Million Yuan (i.e., 100 Million Yuan). Its linear cost estimation model is as follows: ; In the formula: each runway costs approximately 500 million yuan (5 million RMB); the cost of increasing runway spacing by 1 meter is approximately 200,000 yuan (2 million RMB); each fast taxiway exit costs approximately 80 million yuan (800 million RMB); each parking stand costs approximately 15 million yuan (150 million RMB); and each parallel taxiway costs approximately 200 million yuan (2 million RMB). (Guarantee time) With stopping angle It does not directly generate construction costs, so its coefficient is 0.

[0126] Indicator 3: Operational Conflict Rate: Unit: Conflicts / Million Flights. Calculated based on taxiing conflicts and runway incursions recorded during simulation, using the following formula: .

[0127] (II) Establish the response surface model for each target indicator according to the general form of the response surface model: SGR response surface model: ; Construction cost response surface model: ; Running the conflict rate response surface model: ; In the formula: , , These represent three corresponding target indicators: SGR, construction cost, and operational conflict rate. For the first The standardized values ​​of the layout parameters are obtained by using the Z-score method. ,in and These are the mean and standard deviation of the layout parameter in 70 samples, respectively. Standardization aims to eliminate dimensional differences and improve numerical stability. This is a constant term (intercept). The coefficient of the linear term reflects the parameter. The linear (main) effect, The coefficient of the quadratic term reflects the parameter. The nonlinear (curve) effect, The coefficients of the interaction term reflect the parameters. and The interaction effect between them.

[0128] (III) Regression coefficient estimation: For each target indicator, based on 70 sets of sample data, the Ordinary Least Squares (OLS) method was used to estimate all regression coefficients in the above model, as follows: 1) Constructing the design matrix Its dimensions are ,in These correspond to a constant term, 7 linear terms, 7 quadratic terms, and 21 pairwise interaction terms, respectively. Each row of the matrix corresponds to an extended feature vector of a sample: .

[0129] 2) Construct the observation vector Its dimensions are If the regression coefficient vector contains the true values ​​of the target indicator corresponding to 70 samples, then... The OLS estimate is: ; This estimator is the optimal linear unbiased estimator under the condition that it satisfies the Gauss-Markov theorem.

[0130] (IV) Model Fit and Testing: The regression coefficients of the response surface model are estimated using the least squares method and solved in matrix form: ; In the formula: X is the design matrix (containing constant terms, linear terms, quadratic terms, and interaction terms), and Y is the target index observation vector (simulation data). This is the regression coefficient estimation vector. The goodness-of-fit test results are shown in Table 6 below: Table 6. Results of Goodness-of-Fit Test for Response Surface Model

[0131] The test results show that the R-value of the response surface model for the three target indicators is... 2 All ≥0.95, R 2 aaj All values ​​were ≥0.92, and the F-test was highly significant (p<0.001), demonstrating the ability to accurately characterize the nonlinear mapping relationship between layout parameters and target indicators, making it suitable for rapid target evaluation in multi-objective optimization. Using R... 2 R 2 The four core indicators, namely "adj, F-value, P-value," were used to comprehensively evaluate the fitting accuracy of the three response surface models. As shown in Table 6, all indicators met the preset criteria (R²). 2 ≥0.95, R 2 The results (adj≥0.90, P<0.05) verify that the model has excellent fitting performance and can accurately characterize the nonlinear mapping relationship between layout parameters and target indicators.

[0132] R-squared of the construction cost response surface model 2=0.992, F-value=452.3, significantly higher than other indicators. Because the cost model is a linear relationship (C=500x1+0.2x2+...), the fitting difficulty is relatively low; the R-values ​​of the SGR response surface model and the operational conflict rate response surface model are... 2 A coefficient ≥0.95 indicates that the quadratic polynomial can effectively capture the interaction effects between parameters (e.g., the coefficient of the interaction term between x1 and x3 is 0.76), overcoming the limitations of the linear polynomial in fitting nonlinear relationships. The goodness-of-fit index and subsequent prediction accuracy verification (average relative error 1.3%) corroborate each other, demonstrating that the response surface model not only has a good fitting effect but also possesses good generalization ability, enabling it to quickly and accurately predict the target index corresponding to parameter combinations not involved in the modeling.

[0133] Depend on Figure 5 It can be seen that the scatter points of the true and predicted values ​​of the SGR response surface model are closely clustered near the ideal fitting line of y=x, with no obvious systematic deviation trend, intuitively reflecting that the model has excellent fitting accuracy. Combined with... Figure 5 As indicated by the goodness-of-fit index, the coefficient of determination R of this model is... 2 =0.968, Adjust R 2 =0.942, all meeting the preset fitting accuracy standard (R²). 2 ≥0.95, adjust R 2 The model is highly significant (≥0.90), with an F-statistic of 38.6 and a p-value less than 0.001. This indicates that the constructed quadratic polynomial can fully explain the complex mapping relationship between SGR and the seven types of layout parameters. Further analysis shows that the 95% confidence interval covers the vast majority of sample points, verifying the reliability and stability of the model's prediction results. It also demonstrates that the regression coefficients estimated using the least squares method (such as the main effect coefficient of x1' and the interaction effect coefficient between x1' and x3') can effectively capture the linear, nonlinear, and interactive effects of layout parameters on SGR. This fitting effect not only confirms the applicability of the quadratic polynomial response surface model in characterizing the relationship between airport layout parameters and SGR, but also ensures the model has good generalization ability, enabling rapid and accurate prediction of SGR values ​​corresponding to layout parameter combinations not involved in the modeling. This provides core support for the efficient iteration of subsequent multi-objective optimization algorithms and significantly improves the computational efficiency of the optimization process.

[0134] Depend on Figure 6 It can be seen that the actual and predicted values ​​of the construction cost response surface model almost completely coincide with the ideal fitting line y=x, with only a small degree of dispersion. This characteristic is highly consistent with the linear nature of construction costs. Combined with... Figure 6 According to the goodness-of-fit index, the model's coefficient of determination R0 2 =0.992, Adjust R 2=0.990, all significantly higher than the preset standard, and the F statistic is as high as 452.3 with a p value less than 0.001, indicating that the model as a whole has extremely strong statistical significance. Although the quadratic polynomial contains nonlinear and interaction terms, the core still accurately captures the linear relationship between construction cost and key parameters such as the number of runways and runway spacing. The extremely small prediction error further verifies the reliability of the response surface model in cost quantification assessment, and can provide high-precision cost constraint calculation for multi-objective optimization.

[0135] Depend on Figure 7 As can be seen, the actual and predicted conflict rates closely follow the distribution along the y=x line, with no obvious outliers or systematic biases. This model R... 2 =0.953, Adjust R 2 =0.921, meeting the preset fitting accuracy requirement. The F-statistic is 31.8 with p < 0.001, indicating that the quadratic polynomial can effectively reflect the nonlinear mapping relationship between the operational conflict rate and layout parameters, as well as the parameter interaction effect (such as the synergistic effect between runway spacing and the number of rapid exit taxiways). The 95% confidence interval covering the vast majority of sample points further confirms the stability of the model's predictions. Although its goodness of fit is slightly lower than that of the construction cost model (because the conflict rate is more significantly affected by the nonlinear coupling of multiple parameters), it still maintains excellent fitting performance and can accurately quantify the impact of layout parameters on operational safety. In summary, both the construction cost and operational conflict rate response surface models have passed rigorous goodness of fit tests. Together with the SGR model, they constitute a high-precision quantitative tool covering the three-dimensional objectives of "efficiency-cost-safety". Its rapid prediction capability (computational efficiency improved by 7200 times) can effectively support the efficient iteration of subsequent multi-objective optimization algorithms, providing a solid model foundation for scientific decision-making on airport flight area layout.

[0136] In step S4, to address the problems of slow convergence speed and poor solution distribution in high-dimensional parameter optimization of the traditional NSGA-II algorithm, this paper introduces an adaptive crossover and mutation operator and an elite retention strategy to design an improved NSGA-II algorithm. The specific process is as follows: (I) The optimization problem of the three objective indicators defined above is uniformly expressed as a minimization form: ; in, This is a vector of decision variables, representing seven types of layout parameters; This represents the feasible region for layout parameters.

[0137] (II) Encoding and Population Initialization: 1) Encoding method: Real number encoding is used. Each individual (chromosome) is directly represented by a 7-dimensional real number vector, i.e. For the discrete parameters (such as) Before evaluating the objective function, rounding is performed to the nearest integer to meet practical engineering constraints.

[0138] 2) Population Initialization: To improve the uniformity and diversity of the initial population within the feasible region, Latin hypercube sampling is used to generate a population of size [missing information]. initial population , refer to Figure 8 As shown.

[0139] Segment 1 (1 character, light blue): labeled “x1 (number of runways) - Discrete”, “Binary encoding: 0 → 2 lines, 1 → 3 lines”; Segment 2 (2 characters, light blue): labeled “x3 (number of fast exit taxiways) - discrete”, “binary encoding: 00 → 1, 01 → 2, 10 → 3”; Segment 3 (2 characters, light blue): labeled “x5 (number of parallel taxiways) - discrete”, “binary encoding: 00 → 1 line, 01 → 2 lines, 10 → 3 lines”; Segment 4 (4 positions, light orange): labeled "Continuous Parameter Group", further divided by small rectangles, labeled "x2 (runway spacing, real number)", "x4 (total number of parking positions, real number)", "x6 (support time, real number)" and "x7 (parking angle, real number)". Each small rectangle contains a standardized value (e.g., x2 is labeled "0.29 (corresponding to 1000 meters)" and x7 is labeled "0.5 (corresponding to 60°)"). Improved NSGA-II hybrid chromosome (total length 9 bits): discrete parameters x1 (1 bit), x3 (2 bits), x5 (2 bits), continuous parameters x2 / x4 / x6 / x7 (1 bit each), total chromosome length 1+2+2+4=9 bits, feasible region of layout parameters refer to Table 2.

[0140] This diagram clearly breaks down the segmented logic of hybrid encoding, addressing the visualization gap regarding "how discrete and continuous layout parameters coexist in chromosomes." Through color differentiation between binary and real numbers and example numerical values, it intuitively demonstrates the mapping relationship between encoding and physical parameters, providing a visual foundation for the design of subsequent genetic operations (crossover / mutation). Discrete parameters use binary crossover, while continuous parameters use real number crossover, avoiding ambiguity in the encoding logic.

[0141] (III) Adaptive Non-Dominated Sort and Improved Crowding Calculation: Using the fast non-dominated sorting algorithm, the computational complexity is reduced from Down to ,in For the target number, Population size is determined by calculating the number of dominated individuals. and Domination Solution Set The non-dominated frontier (Pareto front) is selected by filtering layer by layer.

[0142] To obtain a more uniformly distributed Pareto front, the crowding calculation is improved as follows: ; in: For the first The standardized results of the objective function values: , and These are the minimum and maximum values ​​of the objective in the current non-dominated layer; For the first The weighting factors for each objective reflect the optimization orientation. Set the SGR weights. Construction cost weighting Conflict rate (security) weight This is to reflect the principle of "efficiency first, while taking into account cost and safety".

[0143] An individual's total crowding is the sum of its crowding across all its targets: Within the same non-dominated layer, individuals with higher crowding are preferentially retained to maintain population diversity.

[0144] (IV) Design adaptively adjusted crossover probabilities and mutation probability With the global exploration and local development capabilities of the dynamic balancing algorithm: 1) Measurement of population diversity; Population diversity is measured by the average Euclidean distance between individuals in the decision space. : ; 2) Adaptive probability formula; ① Crossover probability When diversity is high, reduce the crossover probability to maintain a good pattern; when diversity is low, increase the crossover probability to promote exploration.

[0145] ; in, , ; , , These represent the maximum, minimum, and average values ​​of the current population diversity, respectively.

[0146] ②Probability of mutation When diversity is high, use a smaller mutation probability for a finer search; when diversity is low, increase the mutation probability to escape local optima.

[0147] ; in, , .

[0148] 3) Crossover and mutation operations; ① Crossover operation: Simulated binary crossover (SBX) is used. For the two selected parent individuals... and Its offspring individuals in the first The value on the dimension is: ; in, The cross-distribution index is taken as... .

[0149] ② Mutation operation: Polynomial mutation is used. For individuals Its mutated first Dimension value is: ; in, For variable asynchronous length, the calculation formula is: ; , Let be the distribution index of variation, and take . The calculated results of crossover and variation probabilities of different populations are shown in Table 7 below: Table 7. Calculation results of crossover and variation probabilities of diversity among different populations.

[0150] Figure 9 The horizontal axis represents the population diversity measure. (Mean Euclidean distance, range [0.2, 0.8]), with the left and right vertical axes corresponding to the crossover probabilities. (Range [0.6, 0.9]) and mutation probability (Range [0.01, 0.2]), the graph shows two clear broken lines (represented by the red solid line). The blue dashed line represents ) revealed its following The pattern of change: When population diversity is higher than the average ( When ), both probability curves show a downward trend ( It decreased from 0.75 to 0.6. The value was reduced from 0.105 to 0.01 to maintain the structure of the current excellent solution; conversely, when diversity is insufficient ( When ), the probability monotonically increases ( It rose to a high of 0.9. The maximum value was increased to 0.2 to enhance the algorithm's global exploration capability. This design intuitively illustrates the adaptive logic of "balancing exploration and exploitation," that is, adjusting the intensity of genetic operations in real time according to the population convergence state (diversity level). Therefore, this figure not only clarifies... and The specific mathematical relationships of the coordinated adjustment further explain the underlying reasons why the improved NSGA-II can effectively maintain population diversity, avoid premature convergence, and accelerate the optimization process, which is one of the key mechanisms to ensure the effectiveness of multi-objective optimization.

[0151] 4) Elite retention and archiving strategies; ① Mixed population selection: Selecting parent populations With offspring population Merging into scale population ,right Perform non-dominated sorting and crowding calculation.

[0152] ② Generation of the next generation population: Individuals are selected to join the next generation population according to their non-dominant hierarchy from highest to lowest. When selecting a certain level, adding all individuals would cause the scale to exceed [the specified limit]. Then, only within that layer, selections will be made from highest to lowest crowding level until the layer is full. Individual.

[0153] ③ External Archive Set Maintenance: An external archive set is established to store all historical Pareto optimal solutions discovered during the iteration process. At the end of each generation, [the archive set is then configured]. Non-dominated solutions are added to the archive set. When the size of the archive set exceeds the preset upper limit (set to 100 in this embodiment), the individual with the lowest crowding is deleted according to the crowding degree to ensure the distribution of solutions in the archive set.

[0154] Figure 10 The diagram clearly illustrates the dynamic maintenance mechanism of the external archive set in the improved elite retention strategy. First, the flowchart on the left describes the standard iterative process of "merging-filtering-truncation" for the archive set. Specifically, each generation merges the parent and child populations (size 200), extracts all non-dominated solutions through fast non-dominated sorting, and incorporates them into the archive set, with a maximum archive size of 100. When the archive overflows... Figure 10 The clear judgment node and the state diagram on the right intuitively explain its core truncation strategy: sort individuals in descending order based on their crowding level and delete the individual with the lowest crowding level. Figure 10On the right, an overflow archive with 110 solutions (marked by red circles as the 10 with the lowest crowding) is deleted, restoring the size to 100. This vividly illustrates how the strategy actively maintains the breadth and uniformity of the Pareto front by eliminating individuals in overly dense regions of the solution space.

[0155] 5) Algorithm termination condition; The improved NSGA-II algorithm terminates when any of the following conditions are met: ① The preset maximum number of iterations is reached. ② Continuous The average distance traveled by the Pareto front of the external archive set. Less than the threshold . Defined as the average Euclidean distance in the target space between the corresponding solutions (sorted by objective value) in the two generations of frontiers.

[0156] The improved NSGA-II algorithm ultimately outputs the solutions in the external archive set as the Pareto optimal solution set. The parameter settings of the improved NSGA-II algorithm are shown in Table 8.

[0157] Table 8 Improved NSGA-II Algorithm Parameter Settings

[0158] Example 2: This invention also provides a multi-objective response surface driven SGR generation and airport layout optimization system, which includes a first model building module, a platform building module, a second model building module, and a calculation module, wherein: The first model construction module is used to abstract the parking position subsystem and runway subsystem of the airport flight area into M / M / c model and M / G / k model respectively based on queuing theory. Through the input and output relationship, a serial queuing network is formed to construct the airport flight area queuing network model. The platform construction module is used to build a Monte Carlo discrete event simulation platform, construct a discrete event simulation framework covering the entire process of airport flight area operation, define the probability distribution and triggering mechanism of random disturbance factors, design a parallel computing strategy based on time slice decomposition to execute simulation, and obtain airport operation performance data under specific layout parameters; the second model construction module is used to construct a multi-objective response surface model, use the Latin hypercube sampling method to generate a sample space of layout parameters, obtain multiple target index data corresponding to each sample space, and use quadratic polynomial regression to construct a response surface model from layout parameters to each target index; The computation module is used to perform multi-objective optimization. It uses the response surface model of multiple objective indicators as a fast evaluation function and employs the improved NSGA-II algorithm to search in the sample space of layout parameters to solve for the Pareto optimal solution set, thereby obtaining the airport layout optimization parameter set.

[0159] Furthermore, this invention also discloses an electronic device comprising at least one processor and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, which, when executed by the processor, enable the processor to perform the steps of the method described above. The memory and processor are connected via a bus, which may include any number of interconnected buses and bridges, connecting various circuits of one or more processors and the memory together. The bus may also connect various other circuits, such as peripheral devices, voltage regulators, and power management circuits. A bus interface provides an interface between the bus and a transceiver. The transceiver may be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over a wireless medium via an antenna, which also receives and transmits data to the processor. The processor manages the bus and general processing, and may also provide various functions, including timing, peripheral interface, voltage regulation, power management, and other control functions. The memory may be used to store data used by the processor during operation.

[0160] Example verification: 1. Overview of the research subjects: An airport in my country was selected as the research subject. The airport's existing flight area layout parameters are: 2 runways, runway spacing of 800 meters, 2 rapid exit taxiways, 22 parking stands, 1 parallel taxiway, single-aircraft support time of 45 minutes, and a parking angle of 45°. Actual operational data from 2024 shows that the airport's SGR (Skipping Rate) was 31.8 flights / hour, its construction cost was 1.48 billion yuan, and its operational conflict rate was 18.9 times per million flights. Taxiway conflicts accounted for 72% and runway incursions for 28%, which is basically consistent with the average conflict rate level of medium-sized airports worldwide as reported by NASA.

[0161] Based on the airport's layout map and historical data, basic parameters such as taxiing distance and facility location are obtained through digital modeling. These parameters serve as input data for the queuing network model and Monte Carlo simulation of this invention, ensuring the authenticity and reliability of the case verification.

[0162] 2. Benchmark simulation and model calibration; First, a baseline Monte Carlo simulation (100 repetitions) was performed based on the existing airport layout parameters. The simulation results are compared with the actual data, as shown in Table 9 below. Table 9 Comparison of benchmark simulation results and actual data

[0163] The accuracy of the queuing network model was quantitatively verified through a direct comparison of "actual data vs. simulation results". The relative errors of all indicators were less than 5%, with SGR relative errors of 2.5%, cost of 2.0%, and conflict rate of 3.2%. This indicates that the physical logic derivation of the queuing network model (such as the M / G / k and M / M / c model formulas) and the random disturbance modeling (equipment failure, weather shift) of Monte Carlo simulation both conform to actual operating rules, and the model can accurately replicate the operating state of a real airport.

[0164] The source of relative error can be explained as follows: the probability distribution of random disturbance factors in the simulation is based on historical data statistics (such as weather transfer matrix and failure rate), which has slight differences from the random fluctuations in actual operation, but the error is controlled within an acceptable range, verifying the effectiveness of the queuing network model calibration.

[0165] 3. Validation of the prediction accuracy of the response surface model; Ten test samples not involved in the modeling were selected (extra samples generated through Latin hypercube sampling). The differences between the predicted values ​​of the response surface model and the Monte Carlo simulation values ​​were compared to verify the prediction accuracy of the queuing network model. The results are shown in Table 10 below: Table 10 Validation results of the prediction accuracy of the response surface model

[0166] Verification results show that the response surface model constructed in this invention performs excellently in both prediction accuracy and computational efficiency. The average relative error for predicting the target indicators is only 1.3%, and the errors of each indicator (SGR 0.8%, construction cost 1.1%, and operational conflict rate 1.5%) are consistent with the model characteristics—the construction cost model has the highest accuracy due to its clear linear relationship, while the operational conflict rate model has a slightly higher error due to its stronger nonlinearity. This is consistent with the model's goodness of fit (cost R²). 2 =0.992>Conflict rate R 2 =0.953) corroborates each other. In terms of computational efficiency, the model demonstrates a significant advantage, with a single prediction taking only about 0.1 seconds. Compared to Monte Carlo simulations, which require 100 repetitions and take approximately 2 hours each time, the computational efficiency is improved by 7200 times, providing core support for the efficient iteration of subsequent multi-objective optimization algorithms. All validation data exhibit high engineering consistency and rationality. The layout parameter combinations used for validation are all derived from rigorous Latin hypercube sampling. The simulation results (SGR: 31.9-35.3 sorties / hour; cost: 1.47-1.65 billion yuan; conflict rate: 15.7-19.2 times / million sorties) fall entirely within the reasonable range corresponding to the feasible region of the layout parameters. The absolute error range (SGR ±0.3 sorties / hour, cost ±0.2 billion yuan, conflict rate ±0.3 times / million sorties) and the high goodness of fit (R²) are consistent with these results. 2The values ​​≥ 0.95 together indicate that the model did not overfit and has good generalization ability and stability.

[0167] 4. Analysis of multi-objective optimization results; 1) Pareto optimal solution set distribution An improved NSGA-II algorithm was used to perform multi-objective optimization of the target airport's layout parameters. Running the algorithm yielded a Pareto optimal solution set containing 86 non-dominated solutions, distributed in the target space as follows: Figure 11 As shown: Figure 11 This is a Pareto front distribution map in three-dimensional target space. The three axes are SGR (flights / hour, higher is better), construction cost (hundred million yuan, lower is better), and operational conflict rate (flights / million flights, lower is better). Each scatter point represents a Pareto optimal solution, and the color intensity indicates the conflict rate (the darker the color, the lower the conflict rate).

[0168] from Figure 11 Three distinct trends can be observed: 1) SGR is positively correlated with construction cost, meaning that increasing SGR requires increasing construction cost; 2) SGR is negatively correlated with operational conflict rate, meaning that increasing SGR may lead to a decrease in operational conflict rate; 3) Construction cost is negatively correlated with operational conflict rate, meaning that increasing construction cost (such as adding a fast-slide exit) can effectively reduce operational conflict rate. The Pareto front exhibits a smooth, curved surface shape, indicating that the response surface model can accurately characterize the nonlinear coupling relationship between target indicators.

[0169] 2) Analysis of typical Pareto optimal solutions Four typical solutions were selected from the Pareto optimal solution set, and their layout parameter combinations and target index values ​​are shown in Table 11 below: Table 11 Comparison of typical Pareto optimal solutions

[0170] The optimization basis and applicable scenarios for each scheme are analyzed as follows: Option A (Efficiency First): Maximize SGR (38.7 flights / hour) by increasing the number of runways (3), fast taxiway exits (4), and parallel taxiways (2). This option is suitable for hub airport expansion projects with high air transport demand and extremely high operational efficiency requirements. However, the construction cost will increase significantly (45.3%), and the investment return period needs to be weighed.

[0171] Option B (Cost Priority): While maintaining the existing core facility scale, reduce the number of parking stands (20) and extend the support time (50 minutes) to minimize construction costs (1.32 billion yuan). This option is suitable for local small airports or expansion projects with limited fiscal budgets. However, the SGR will decrease slightly (-5.0%) and the conflict rate will increase (+13.8%), requiring corresponding optimization of operation and scheduling strategies.

[0172] Option C (Safety First): By increasing runway spacing (1500 meters), adding fast taxiway exits (4), and adopting a 90° stopping angle (reducing taxiway intersections), the conflict rate is reduced to 9.8 times per million flights. It is suitable for airports with extremely high operational safety requirements (such as joint military-civilian airports). The SGR still maintains an 8.5% increase, the cost increase is controlled at 18.9%, and the safety redundancy is sufficient.

[0173] Option D (Balanced Optimization): Taking into account the three major target indicators, the layout parameter combination is "2 runways + 1000-meter spacing + 3 fast taxiway exits + 24 aircraft stands + 2 parallel taxiways + 40 minutes of support + 60° parking angle". It achieves a synergistic optimization effect of 12.3% increase in SGR, only 7.4% increase in cost, and 36.0% decrease in operational conflict rate. It is suitable for the layout optimization needs of most medium-sized hub airports and has broad engineering application value.

[0174] Table 11 comprehensively compares the current situation and four typical optimization schemes from three dimensions: layout parameters, target indicators, and relative changes. It clearly presents the trade-offs in multi-objective optimization, covering four decision preferences: efficiency, cost, safety, and balance. This reflects the diversity of the Pareto optimal solution set and provides personalized options for airports with different needs. Among them, the efficiency-first scheme (A) improves SGR by 21.7%, the safety-first scheme (C) reduces operational conflict rate by 48.1%, and the balance scheme (D) achieves "efficiency improvement of 12.3% + moderate cost increase of 7.4% + significant reduction in conflict rate of 36.0%", meeting the comprehensive needs of most medium-sized hub airports. Its core optimization path (adding fast taxiway exits, adding parallel taxiways, and optimizing runway spacing) is consistent with the sensitivity analysis results. Meanwhile, the cost increase of scheme D is only 7.4%, far lower than the 45.3% of scheme A, but the SGR increase (12.3%) is close to half of that of scheme A, and the decrease in the running conflict rate (36.0%) is comparable to that of scheme A (35.0%), highlighting the engineering value of the balanced optimization of scheme D.

[0175] like Figure 12 As shown, the three-dimensional target indicators of the four schemes are intuitively compared, clearly demonstrating the optimization effects of different decision preferences: Option A (efficiency first) has the highest SGR, but a clear trade-off between cost and operational conflict rate, making it suitable for hub airports with high passenger demand. Option B (cost first) has the lowest cost, but a lower SGR and a higher operational conflict rate, making it only suitable for feeder airports with limited budgets. Option C (safety first) has the lowest conflict rate and a balance between SGR and cost, making it suitable for safety-sensitive scenarios such as airports used for both military and civilian purposes. Option D (balanced optimization) has a significant improvement in SGR, a moderate increase in cost, and a substantial decrease in operational conflict rate, showing the most obvious overall advantages and making it suitable for most medium-sized hub airports. The height differences in the bar chart highlight the synergistic balance between "efficiency-cost-safety," validating the core objective of this multi-objective optimization paper (achieving a synergistic balance among the three).

[0176] 3) Sensitivity analysis of layout parameters Standardized regression coefficients were used to analyze the influence of each layout parameter on the target indicator. The larger the absolute value of the standardized regression coefficient, the more significant the influence of that parameter on the target indicator. The results are as follows: Figure 13 As shown: the horizontal axis represents the seven types of layout parameters, and the vertical axis represents the standardized regression coefficients (absolute values). Different colored lines correspond to the three target indicators: SGR (Social Growth Rate), construction cost, and operational conflict rate. From... Figure 13 It can be observed that: 1) The parameters most significantly affecting SGR are the number of fast exit taxiways (standardized coefficient 0.82), the number of parallel taxiways (0.75), and the support time (-0.68), indicating that increasing fast exit taxiways and parallel taxiways and shortening support time are key paths to improve SGR; 2) The parameters most significantly affecting construction costs are the number of runways (0.91), runway spacing (0.85), and the number of parallel taxiways (0.78), with the number of runways having the greatest impact, indicating that adding runways is the main driver of cost increases; 3) The parameters most significantly affecting operational conflict rate are runway spacing (-0.88), the number of fast exit taxiways (-0.83), and the stopping angle (-0.72), with runway spacing having the greatest negative impact, indicating that increasing runway spacing can effectively reduce conflict risk. Furthermore, the stopping angle has an impact coefficient of -0.72 on the conflict rate, verifying the importance of fine-grained layout parameter optimization. The parameter sensitivity index SI was calculated using the Morris screening method, as shown in Table 12. Table 12 Sensitivity Index (SI)

[0177] The Morris screening method was used to calculate the sensitivity index (SI), and parameter priority was determined by "single-objective SI + comprehensive criticality". The comprehensive criticality categorized parameters as "critical / secondary critical / non-critical". The critical parameters were the number of runways (x1), the number of fast exit taxiways (x3), and the number of parallel taxiways (x5), all with a comprehensive SI > 0.1, indicating the greatest impact on the three objectives. For example, x3 had an SI of 0.21 for SGR and an SI of 0.18 for conflict rate, demonstrating that increasing fast exits could simultaneously improve efficiency and reduce conflicts, representing a "low-cost, high-return" optimization path. x1 had an SI of 0.35 for cost, indicating that adding runways was the main driver of increased costs, requiring careful decision-making. The non-critical parameter was the support time (x6), with an SI < 0.1. Since the support process was already optimized in the simulation, there was limited room for further reduction, avoiding wasting resources on non-critical parameters.

[0178] 5. Algorithm comparison; To verify the superiority of the improved NSGA-II algorithm, comparative experiments were conducted with the traditional NSGA-II algorithm and the MOPSO algorithm. The comparison indicators included convergence speed (number of iterations to reach convergence), solution distribution (uniformity index of Pareto front), and optimal solution quality (dominance of Pareto front). The results are shown in Table 13. Table 13 Algorithm Comparison Experiment Results

[0179] The comparative results show that: ① Convergence speed: The improved NSGA-II algorithm has only 92 convergence iterations, which is 41% less than the traditional NSGA-II and 33% less than MOPSO. This is due to the adaptive crossover mutation operator and the Latin hypercube sampling initialization strategy, which improves the search efficiency of the algorithm; ② Solution distribution: The distribution index of the improved NSGA-II is 0.25, which is significantly better than the traditional NSGA-II (0.38) and MOPSO (0.42). This indicates that the improved crowding calculation method effectively improves the uniformity of the Pareto front and provides richer options for decision-making; ③ Optimal solution quality: The improved NSGA-II algorithm obtains 86 dominant solutions, which is 39% more than the traditional NSGA-II and 48% more than MOPSO. This indicates that the improved NSGA-II algorithm can search for a wider range of Pareto optimal solutions and cover more decision preferences.

[0180] Reference Figure 14The red solid line represents the improved NSGA-II algorithm, with key nodes marked (Δ=0.01 at 92 iterations, reaching convergence); the blue dashed line represents the traditional NSGA-II algorithm, with key nodes marked (Δ=0.01 at 156 iterations); the green dotted line represents the MOPSO algorithm, with key nodes marked (Δ=0.01 at 138 iterations).

[0181] The convergence curve trend shows that the improved NSGA-II algorithm has the fastest convergence speed (92 iterations), reducing convergence by 41% compared to the traditional NSGA-II and by 33% compared to MOPSO. This verifies the optimization effect of "adaptive crossover mutation operator + Latin hypercube sampling initialization," indicating that the improved NSGA-II algorithm can quickly approximate the Pareto optimal solution. Furthermore, the improved NSGA-II algorithm has a steeper curve descent, indicating higher search efficiency in the early stages. The curve tends to stabilize in the later stages (Δ<0.01), indicating good algorithm stability and no oscillations. The convergence threshold (Δ=0.01) clarifies the termination condition of the algorithm, demonstrating the reliability of the optimization results (Δ<0.01 for 20 consecutive generations), ensuring the stability and effectiveness of the Pareto optimal solution set.

[0182] The convergence curves of the traditional NSGA-II algorithm and the MOPSO algorithm decrease slowly, especially in the early stage of iteration (0-50 times), indicating that the fixed crossover mutation probability leads to low search efficiency, which verifies the necessity of the "adaptive operator" in this invention.

[0183] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and other variations and modifications of the present invention without departing from its spirit and scope fall within the scope of the claims. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for SGR generation and airport layout optimization based on multi-objective response surface driven approach, characterized in that, Includes the following steps: S1. Constructing an airport flight area queuing network model: Based on queuing theory, the parking position subsystem and runway subsystem of the airport flight area are abstracted into M / M / c model and M / G / k model respectively, and a serial queuing network is formed in sequence through the input and output relationship; S2. Construct a Monte Carlo discrete event simulation platform: Construct a discrete event simulation framework covering the entire process of airport flight area operation, define the probability distribution and triggering mechanism of random disturbance factors, design a parallel computing strategy based on time slice decomposition to execute simulation, and obtain airport operation performance data under specific layout parameters. S3. Construct a multi-objective response surface model: Use the Latin hypercube sampling method to generate a sample space for layout parameters, obtain multiple target index data corresponding to each sample space, and use quadratic polynomial regression to construct a response surface model from layout parameters to each target index. S4. Perform multi-objective optimization: Using the response surface model of multiple objective indicators as a fast evaluation function, the improved NSGA-II algorithm is used to search in the sample space of layout parameters to solve the Pareto optimal solution set and obtain the airport layout optimization parameter set.

2. The method for SGR generation and airport layout optimization based on multi-objective response surface driven according to claim 1, characterized in that, Step S1, the steps for constructing the airport flight area queuing network model include: S11: Based on the M / G / k model of the runway subsystem, calculate the service rate considering aircraft type and weather conditions and the effective arrival rate considering taxiing time delay; S12: Based on the M / M / c model of the parking position subsystem, calculate the service capacity and steady-state performance indicators; S13: By forming a cascaded queuing network between the runway subsystem and the parking position subsystem during the aircraft taxiing process, an SGR calculation model is constructed.

3. The method for SGR generation and airport layout optimization based on multi-objective response surface driven according to claim 2, characterized in that, Step S13, the steps for constructing the SGR calculation model include: The taxiing time is calculated by combining the base taxiing time and the additional delay time. The expression for taxiing time is: In the formula: For gliding time, Based on the basic gliding distance, The average taxiing speed of the aircraft. For the gliding delay time, This is the location of the exit taxiway turning point for the rapid exit. This refers to the number of parallel taxiways; Calculate the total operating time of the aircraft within the flight area, including the sum of the time spent on parking stand service, taxiing, and runway service: In the formula: Total running time, The average system time of the parking position system. The average system time of the runway system; The SGR calculation model is constructed based on taxiing time and total running time, and its expression is: In the formula: For the number of runways, The system capacity utilization rate, where 0 < η ≤ 1, is used to characterize the reduction in theoretical system capacity caused by operational conflicts; Q0 = (60 / T) total Q is the theoretical throughput capacity, where k is the theoretical throughput capacity. eff This refers to the effective throughput capacity determined based on historical operating data or Monte Carlo discrete event simulations under the same layout parameters.

4. The method for SGR generation and airport layout optimization based on multi-objective response surface driven according to claim 3, characterized in that, In step S2, the process of obtaining the airport's operational performance data under specific layout parameters is as follows: S21: A Monte Carlo discrete event simulation platform covering the entire process of "support preparation - taxiing - queuing - take-off and landing" is constructed using a discrete event-driven mechanism; S22: Introduce a random perturbation factor into the Monte Carlo discrete event simulation platform to generate sliding collision types; S23: Based on the Monte Carlo discrete event simulation platform, design a parallel simulation strategy based on time slice decomposition to detect and quantize operational conflicts in the simulation process in real time. S24: Determine and count the total number of taxiway conflicts and runway incursions during the parallel simulation, and calculate the running conflict rate; the expression for the running conflict rate is as follows: In the formula: the unit of operational conflict rate is times / million flights.

5. The method for SGR generation and airport layout optimization based on multi-objective response surface driven according to claim 4, characterized in that, Step S3, the steps for constructing the multi-objective response surface model include: S31: Based on the feasible region of layout parameters, multiple sample spaces are generated by Latin hypercube sampling, where: layout parameters include the number of runways, runway spacing, number of fast exit taxiways, total number of parking stands, number of parallel taxiways, single aircraft support time and parking angle. S32: Use the Monte Carlo discrete event simulation platform to obtain simulation data of multiple sample spaces and corresponding target indicators, including SGR, construction cost and operational conflict rate; S33: Use quadratic polynomial regression to construct the response surface model for each target indicator, forming a quantitative mapping relationship between the layout parameters and the corresponding target indicators; S34: Use the least squares method to estimate the regression coefficients of the response surface model and test the goodness of fit of the response surface model for each target index.

6. The method for SGR generation and airport layout optimization based on multi-objective response surface driven according to claim 5, characterized in that, Step S4, the steps for obtaining the airport layout optimization parameter set include: S41: An improved NSGA-II algorithm is formed by introducing an adaptive crossover mutation operator and an elite retention strategy into the NSGA-II algorithm. S42: Set the termination conditions for the improved NSGA-II algorithm; S43: Using the response surface model of multiple target indicators as a fast evaluation function, the improved NSGA-II algorithm is used to search in the sample space of layout parameters to output the Pareto optimal solution set.

7. The method for SGR generation and airport layout optimization based on multi-objective response surface driven according to claim 6, characterized in that, In step S41, the formation process of the improved NSGA-II algorithm includes: Encode and initialize the NSGA-II algorithm; The fast nondominated sorting algorithm is used to screen the nondominated front layer by layer in the initial population; We design an adaptive crossover and mutation operator and an elite retention and archiving strategy to perform non-dominated sorting and crowding calculation on the population, and add the non-dominated solutions to the archive set.

8. The method for SGR generation and airport layout optimization based on multi-objective response surface driven according to claim 7, characterized in that, In step S42, the improved NSGA-II algorithm terminates when any of the following conditions are met: (I) Reaching the preset maximum number of iterations T =200; (II) Continuous G =20 generations, average Pareto frontal movement distance of the external archive set Less than the threshold .

9. A multi-objective response surface driven SGR generation and airport layout optimization system, characterized in that, The system is used to implement the steps of the method according to any one of claims 1-8, the system comprising: The first model construction module is used to abstract the parking position subsystem and runway subsystem of the airport flight area into M / M / c model and M / G / k model respectively based on queuing theory. Through the input and output relationship, a serial queuing network is formed to construct the airport flight area queuing network model. The platform construction module is used to build a Monte Carlo discrete event simulation platform, construct a discrete event simulation framework covering the entire process of airport flight area operation, define the probability distribution and triggering mechanism of random disturbance factors, design a parallel computing strategy based on time slice decomposition to execute simulation, and obtain airport operation performance data under specific layout parameters; the second model construction module is used to construct a multi-objective response surface model, use the Latin hypercube sampling method to generate a sample space of layout parameters, obtain multiple target index data corresponding to each sample space, and use quadratic polynomial regression to construct a response surface model from layout parameters to each target index; The computation module is used to perform multi-objective optimization. It uses the response surface model of multiple objective indicators as a fast evaluation function and employs the improved NSGA-II algorithm to search in the sample space of layout parameters to solve for the Pareto optimal solution set, thereby obtaining the airport layout optimization parameter set.

10. An electronic device, characterized in that: The electronic device includes at least one processor and a memory communicatively connected to the processor; wherein the memory stores instructions executable by the processor, the instructions being executed by the processor to enable the processor to perform the steps of the method according to any one of claims 1-8.

Images