A multi-objective apron allocation method based on a multi-strategy fast non-dominated sorting genetic algorithm

Abstract

The present invention discloses a multi-objective parking stand allocation method based on a multi-strategy fast non-dominated sorting genetic algorithm. Starting from airport operations and passenger satisfaction, the method selects the available time of the parking stand and the passenger walking distance as objectives to establish a multi-objective parking stand allocation model. An initialization method and a multi-crossing strategy are designed to improve the convergence of the method and search for better solutions. An external archive evolution mechanism is designed to improve the utilization rate of excellent individuals and generate better offspring individuals. Therefore, the method of the present invention can achieve effective allocation of parking stands. Compared with existing excellent multi-objective allocation methods, the method proposed by the present invention has improved diversity and convergence of the solution set in the multi-objective parking stand allocation problem and has obvious competitive advantages.

Description

Technical Field

[0001] The present invention relates to the technical field of apron position allocation, in particular to a multi-objective apron position allocation method based on a multi-strategy fast non-dominated sorting genetic algorithm. Background Art

[0002] Airport apron positions, as limited ground service resources, play a crucial role in the development of the civil aviation industry. Existing airport apron position allocation algorithms can be roughly divided into three types. One is the mathematical programming method, which establishes an abstract mathematical model for the actual airport apron position problem and uses mathematical theories such as integer programming, linear programming, branch and bound, etc., to accurately solve the problem. Another is the artificial intelligence method, mainly the construction of an expert system. There is also a simulation method, that is, modeling the real situation and using a computer to conduct simulation experiments to seek a better allocation plan. In recent years, airport apron position allocation algorithms based on heuristic evolutionary algorithms have also received more and more attention and research.

[0003] There are already many examples in the existing research results for solving the apron position allocation problem (GAP) by considering multiple aspects simultaneously. The satisfaction of passengers is still the focus of the current allocation. Most studies use the shortest passenger walking distance and parking time as the objective functions. When the focus is on airport operation efficiency, the focus of the objective function will be different. For example, objectives such as the maximum apron operation efficiency, the maximum matching degree between the aircraft and the apron position, and the maximum apron utilization rate. Due to different objective functions, there are various research results, and the solutions to the same problem will also be different.

[0004] In recent years, great progress has also been made in multi-objective solution methods. The NSGA-II method selected in the present invention is a multi-objective solution method with non-dominated sorting and layering. Many scholars have made many improvements and application results on the framework of the NSGA-II algorithm. Yeh used the K-means method to improve the NSGA-II algorithm and extended the search space to improve the search performance of the NSGA-II. Zhang et al. designed a sequential solution generation strategy to improve the NSGA-II algorithm and proved the advantages of this method in the example of epidemic detection resource allocation. Che et al. proposed the W-NSGA-II method in the tasks of optimal supplier portfolio and production resource allocation, and improved the search efficiency of the NSGA-II through an improved initialization strategy to achieve a reasonable allocation plan. Fernández et al. proposed the MPENSGA-II algorithm based on the memetic Pareto evolution framework, and it has a good performance in the allocation accuracy of artificial neural networks.

[0005] In recent years, airport gate assignment algorithms based on intelligent optimization and evolutionary algorithms have received increasing attention and research. Ding used the combination of simulated annealing and tabu search algorithms to solve the problem with the optimization goal of minimizing the number of unassigned flights, achieving good performance. Kim considered the passenger transit time and proposed using two metaheuristic algorithms to solve the problem. Zhang studied the effectiveness of several heuristic algorithms for solving the airport gate assignment problem. Lim combined the tabu search algorithm with the local search algorithm and solved the problem with the optimization goal of minimizing the number of conflicting gates, improving the robustness of the algorithm.

[0006] The multi-objective gate assignment problem is a combinatorial optimization problem, and the objectives are generally multiple conflicting objective functions. Dell'Orco M et al. used the improved bee colony algorithm to effectively solve the multi-objective gate assignment problem with the optimization goals of minimizing the number of remote gate assignments and the shortest passenger walking distance. Dorndorf et al. selected six objectives such as maximizing gate assignment, minimizing the number of towing vehicles, and minimizing the expected number of violations of two time limits, and used the improved jet chain algorithm to solve the problem and achieve gate assignment. Deng et al. aimed to minimize the passenger walking distance and the number of apron flights. Then, an improved ant colony optimization (ICQACO) algorithm based on the ant colony cooperation strategy and pheromone update strategy was designed to solve the established model to quickly achieve gate assignment and obtain reasonable and effective gate assignment results for all flights at different times. Kim considered the passenger transit time and proposed using two metaheuristic algorithms to solve the problem. Liang et al. introduced the elite strategy and parallel design concept into the genetic algorithm, enabling the algorithm to adaptively adjust the crossover probability and effectively solve large-scale gate assignment data. Seyedmirsajad et al. proposed a gate assignment model with the main optimization criteria of passenger walking distance and traditional cost, and verified that the proposed solution has great advantages through the NSGA-II algorithm. Deng Wu et al. established a multi-objective airport gate assignment model with the optimization goals of the shortest passenger walking distance, the minimum gate idle time, the fewest flights parked at remote gates, and the most reasonable utilization of large gates through the research on the airport gate assignment problem, and designed an improved particle swarm algorithm to solve the model.

[0007] In summary, there have been many various research results on the gate assignment problem. The common method is to perform linear optimization by establishing a multi-objective model, but there are also limitations. Focusing on one aspect will ignore other aspect objective functions and cannot fully meet the needs of modern airport operations. Summary of the Invention

[0008] The object of the present invention is to solve the deficiencies existing in the prior art and provide a multi-objective apron allocation method based on a multi-strategy fast non-dominated sorting genetic algorithm.

[0009] To achieve the above object, the present invention is implemented according to the following technical solutions:

[0010] A multi-objective apron allocation method based on a multi-strategy fast non-dominated sorting genetic algorithm, comprising the following steps:

[0011] S1. Establish a multi-objective airport apron allocation optimization model with the minimum apron free time and the shortest passenger walking distance;

[0012] S2. On the basis of the NSGA-II algorithm, design the EPINSGA-II algorithm to solve the multi-objective apron allocation model to obtain an apron allocation scheme:

[0013] S21. Design an initialization strategy with a real number coding method to improve the feasibility of the initial solution of the multi-objective airport apron allocation optimization model and the algorithm efficiency;

[0014] S22. Design a multi-crossing strategy to improve the convergence of the solution set;

[0015] S23. Design an external archive evolution strategy to increase the diversity of algorithm solutions;

[0016] S24. Design a multi-objective apron allocation based on a multi-strategy fast non-dominated sorting genetic algorithm to achieve effective apron allocation.

[0017] Specifically, the step S1 specifically includes:

[0018] Describe the multi-objective optimization problem, which is defined as follows:

[0019]

[0020] Among them, Ω is the decision variable space, represents the n-dimensional decision variable, f n (x) represents the nth sub-function, m is the total number of optimization objectives; g(x) represents d inequality constraint conditions; h(x) represents k equality constraint conditions; the constraint conditions constitute the feasible region;

[0021] Determine the optimization objectives:

[0022] (1) Take the total passenger walking distance as the optimization objective:

[0023]

[0024] (2) The total idle time of the apron

[0025] The idle time of the j-th aircraft position consists of three parts, namely the start idle time, the end idle time, and the flight idle time. The start idle time refers to the time between the opening time of the airport and the arrival time of the first flight at this aircraft position. The end idle time refers to the time between the closing time of the airport and the departure time of the last flight at this aircraft position. The flight idle time refers to the time between the arrival time of the latter flight and the departure time of the former flight among two adjacent flights at this aircraft position:

[0026]

[0027] Among them The constraint conditions are:

[0028] (1) Flight uniqueness

[0029] The same flight can only dock at one near aircraft position or far aircraft position, that is, it satisfies:

[0030]

[0031] (2) Aircraft position uniqueness

[0032] At most one flight is allowed to dock at one aircraft position at the same time, that is, it satisfies:

[0033] NI j,t ≤1;

[0034] (3) Aircraft type matching

[0035] The type of the aircraft position should match the type of the flight. That is, small aircraft are allowed to dock at small aircraft positions, medium aircraft positions, and large aircraft positions. Medium aircraft are allowed to dock at medium aircraft positions and large aircraft positions. Large aircraft are only allowed to dock at large aircraft positions, that is, it satisfies:

[0036] GT j ∈AT i ,if s i,j =1;

[0037] (4) Time interval between adjacent flights at the same aircraft position

[0038] For safety considerations, it is required that the push-out time of the previous flight and the push-in time of the next flight at the same aircraft position are greater than a certain time interval, that is, it satisfies:

[0039] LE p -AR q ≥T cur ;

[0040] p,q∈A i , the p-th flight is the next flight of the q-th flight;

[0041] (5) Push-in and push-out interval time between adjacent aircraft positions

[0042] For adjacent aircraft positions, for safety considerations, it is generally required that flights are not pushed in and out simultaneously at adjacent aircraft positions, that is, the push-in and push-out times of flights at adjacent aircraft positions are greater than a certain time interval, that is, it satisfies:

[0043]

[0044] (6) Special flights must satisfy

[0045] For flights in some special situations, such as VIP flights, etc., it is required that they must be assigned to near aircraft positions, that is, it satisfies:

[0046]

[0047] Specifically, the step S21 specifically includes:

[0048] Assuming there are three types of aircraft positions and flights, namely S, M, and L, the following real number initialization method is proposed:

[0049] 1(S) 2(L) 3(M) ...... 249(L) 250(S)

[0050] First, process flights with L-type attributes, store their L-type aircraft position numbers among 30 aircraft positions in the list_L string, and encode them with rand(list_L). Secondly, process M-type flights, store the L-type and M-type aircraft position numbers in list_M, and encode them with rand(list_M). Finally, process S-type flights, which can be parked at any of the 30 aircraft positions, and random encoding can be used.

[0051] Specifically, the multi-cross strategy in the step S22 is a multi-strategy cross method that combines the SBX cross strategy with good diversity distribution ability and the BLX-α strategy with Pareto solution set ability. Its algorithm pseudocode:

[0052]

[0053] Specifically, the external archive evolution strategy in the step S23 specifically includes:

[0054] S231. External archive update strategy

[0055] By setting an external archive to save all non-dominated solutions searched during the evolution process, store the optimal individual in each generation in the external archive matrix. When the scale is greater than the set scale, update according to the following table mechanism and eliminate relatively poor individuals;

[0056]

[0057]

[0058] S232. Using the excellent individuals searched by the algorithm stored in the external archive, in order to make full use of the excellent genetic characteristics of the non-dominated solutions in the external archive, by selecting several non-dominated solutions among them and making them participate in the crossover and mutation of the next generation to generate excellent offspring individuals, the purpose of accelerating the convergence of the algorithm is achieved.

[0059] Compared with the prior art, the multi-objective parking bay allocation method based on the multi-strategy fast non-dominated sorting genetic algorithm of the present invention starts from airport operation and passenger satisfaction, selects the free time of the parking bay and the walking distance of the passenger as the objectives to establish a multi-objective parking bay allocation model, designs an initialization method and a multi-crossover strategy to improve the convergence of the method and search for better solutions; designs an external archive evolution mechanism to improve the utilization rate of excellent individuals and generate better offspring individuals; therefore, the method of the present invention can realize the effective allocation of parking bays; compared with the existing excellent multi-group multi-objective allocation methods, the method proposed by the present invention has improved the diversity and convergence of the solution set in the multi-objective parking bay allocation problem and has obvious competitive advantages. Brief Description of the Drawings

[0060] Figure 1 It is a flowchart of the existing NSGA-II method.

[0061] Figure 2 It is an external archive solution evolution strategy.

[0062] Figure 3 It is a flowchart of the EPINSGA-II method of the present invention.

[0063] Figure 4 It is a comparison chart of the Hv index for different population sizes.

[0064] Figure 5 It is a comparison chart of the Hv index of the self-algorithm.

[0065] Figure 6 It is a comparison chart of the Hv index of six excellent algorithms.

[0066] Figure 7 It is a parking bay allocation plan chart.

[0067] Figure 8 It is a chart of the number of flights designated at the boarding gate. Detailed Embodiments

[0068] In order to make the purpose, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with embodiments. The specific embodiments described here are only used to explain the present invention and are not used to limit the invention.

[0069] Multi-objective Problem Description Based on the Prior Art

[0070] In practical engineering applications, there are many multi-objective optimization applications. There are conflicts among multiple objectives, and it is impossible to satisfy all objectives reaching the minimum simultaneously. When optimizing one objective, the other objective functions will inevitably deteriorate. This type of problem with two or more objectives is called a multi-objective optimization problem (Mops), which is defined as follows:

[0071]

[0072] Among them, Ω is the decision variable space, represents the n-dimensional decision variable, and f n (x) represents the nth sub-function, and m is the total number of optimization objectives. g(x) represents d inequality constraint conditions; h(x) represents k equality constraint conditions; the constraint conditions constitute the feasible region.

[0073] Parameter Introduction

[0074] Assume that the number of flights is m and the number of parking positions is n. The meanings of the symbols used in this paper are summarized as follows

[0075]

[0076] P i : The number of passengers on flight i

[0077] D j : The distance between parking position j and the exit

[0078] E j : The idle time of parking position j

[0079] NI j,t : The number of flights parked at parking position j at time t

[0080]

[0081] GT j : The type of parking position j

[0082] AT: The type of flight i

[0083] A i : The set of flights parked at parking position i

[0084] AR p : The push-in time of flight p

[0085] LE p : The push-out time of flight p

[0086] AN i : The set of flights parked at the adjacent parking positions of parking position i

[0087] F VIP : VIP flight set

[0088] Airport parking positions, as essential ground service resources, play a crucial role in the development of the civil aviation industry. A reasonable airport parking position allocation algorithm can greatly improve the efficiency of airport operations, reduce airport operating costs, and enhance the comfort of passengers' travel. Existing airport parking position allocation models often take the shortest passenger walking distance as the optimization goal. However, as the airport situation becomes increasingly complex, it is not very reasonable to only take the shortest passenger walking distance as the optimization goal. Therefore, this invention starts from the perspectives of passengers and the airport, considers the flights arriving on the same day, and establishes a multi-objective airport parking position allocation optimization model.

[0089] The optimization goals of this invention are as follows:

[0090] (1) The shortest total walking distance of passengers

[0091] The walking distance of passengers can largely determine the satisfaction of passengers' travel. Therefore, this invention takes the total walking distance of passengers as the optimization goal.

[0092]

[0093] Among them

[0094] (2) Total idle time of parking positions

[0095] The idle time of the j-th parking position consists of three parts, namely the start idle time, the end idle time, and the flight idle time. The start idle time refers to the time between the opening time of the airport and the arrival time of the first flight at this parking position; the end idle time refers to the time between the closing time of the airport and the departure time of the last flight at this parking position; the flight idle time refers to the time between the arrival time of the latter flight and the departure time of the former flight among two adjacent flights at this parking position.

[0096]

[0097] Among them

[0098] Constraints

[0099] (7) Flight uniqueness

[0100] The same flight can only be parked at one near parking position or one far parking position.

[0101]

[0102] (8) Parking position uniqueness

[0103] At most one flight is allowed to dock at a single position at the same time

[0104] NI j,t ≤1 (5)

[0105] (9) Aircraft type matching

[0106] The type of the position should match the type of the flight. That is, small aircraft are allowed to dock at small, medium, and large positions; medium aircraft are allowed to dock at medium and large positions; and large aircraft are only allowed to dock at large positions.

[0107] GT j ∈AT i ,if s i,j =1 (6)

[0108] (10) Interval time between adjacent flights at the same position

[0109] For safety reasons, it is required that the push-out time of the previous flight and the push-in time of the next flight at the same position be greater than a certain time interval.

[0110] LE p -AR q ≥T cur (7)

[0111] p,q∈A i , Flight p is the next flight of flight q

[0112] (11) Interval time between push-in and push-out of adjacent positions

[0113] For adjacent positions, for safety reasons, it is generally required that flights are not pushed in and out at adjacent positions simultaneously, that is, the push-in and push-out times of flights at adjacent positions are greater than a certain time interval

[0114]

[0115] (12) Special flights must meet

[0116] For some special flights, such as VIP flights, etc., it is required that they must be assigned to nearby positions.

[0117]

[0118] The NSGA-II algorithm mainly adopts fast non-dominated sorting and crowding distance. Compared with the NSGA algorithm, it greatly reduces the time complexity and improves the accuracy of the algorithm. In solving multi-objective algorithms, the NSGA-II algorithm has great advantages. The main steps of the algorithm are as followsFigure 1 as shown

[0119] Based on the existing NSGA-II algorithm, aiming at the problems of poor diversity and convergence of the solution set in the solution of the multi-objective apron allocation model by the NSGA-II algorithm. In the present invention, in order to reduce the waste of computing resources, a coding method for multi-objective apron allocation is designed to improve the feasibility of the initial solution and the algorithm efficiency. In terms of the diversity of the solution set, the present invention fully combines the SBX crossover strategy with good diversity distribution ability in the decision space and the BLX-α strategy with Pareto solution set ability, and designs a multi-strategy crossover method to improve the convergence of the algorithm. The present invention proposes a new evolutionary strategy for the external archive, and uses the excellent solutions in the external archive to participate in the generation of offspring solutions to improve the diversity of the algorithm. The algorithm flow chart of the present invention is as Figure 3 shown, and the specific improvements are as follows:

[0120] (1) Initialization strategy

[0121] For such problems, the apron positions have different attributes, including three models of S, M, and L. The flights also have these three attributes. The ultimate goal of our solution is to place the flights that meet the attributes on the appropriate positions. In order to reduce the number of initialized conflicting flights, we propose the following real number initialization method:

[0122]

[0123] First, process the flights with L-type attributes, store the L-type apron position numbers among 30 apron positions in the list_L string, and encode them with rand(list_L). Secondly, process the M-type flights, store the L-type and M-type apron position numbers in list_M, and encode them with rand(list_M). Finally, process the S-type flights, which can be parked in all 30 apron positions, and random encoding can be used.

[0124]

[0125] (2) Multi-crossover strategy

[0126] In the NSGA-II algorithm, the SBX

[31] crossover strategy has better advantages in terms of the diversity of the PF when solving multi-objective problems, but has poor effects in terms of convergence. The BLX-α crossover strategy has better advantages in terms of convergence when solving low-dimensional multi-objective problems, but has poor effects in terms of diversity. For this problem, in the present invention, the SBX crossover strategy with good diversity distribution ability and the BLX-α strategy with Pareto solution set ability are fully combined to design a multi-strategy crossover method to ensure the balanced convergence and diversity of the algorithm. The algorithm pseudocode is shown in Algorithm2:

[0127]

[0128]

[0129] (3) External Archive Update Strategy

[0130] In the random mating of the algorithm, under certain uncertain factors, it may cause the loss of excellent individuals. Therefore, in the present invention, an external archive is set up to save all non-dominated solutions searched during the evolutionary process, so as to prevent the loss of high-quality solutions caused by random factors. In the present invention, the optimal individual in each generation is stored in the external archive matrix. When the scale is larger than the set scale, we will update according to a certain mechanism and eliminate relatively poor individuals.

[0131]

[0132] (4) External Archive Population Evolution Strategy

[0133] The present invention utilizes the excellent individuals searched by the storage algorithm in the external archive. In order to make full use of the excellent genetic characteristics of the non-dominated solutions in the external archive, by selecting several non-dominated solutions among them and making them participate in the crossover and mutation of the next generation to generate excellent offspring individuals, the purpose of accelerating the convergence of the algorithm is achieved. The principle of population participation in evolution is as Figure 2 shown.

[0134] Application Example

[0135] To verify the effectiveness of the proposed algorithm, the algorithm performance is tested using the flight data of a day at Guangzhou Baiyun International Airport in China. The stand information and partial flight information are listed in Table 1 and Table 2 respectively. The data contains 250 flights and 30 stands. The stands include three types: large, medium and small, which are represented by L, M, and S respectively. The corresponding flights also have three types, which are also represented by L, M, and S. The safety interval time is set to 8 minutes. When the flight is pushed in and out, flights at adjacent stands are not allowed to move within 5 minutes.

[0136] Table 1

[0137]

[0138] Table 2

[0139]

[0140] To measure the performance of multi - objective optimization methods, we need to use performance metrics to measure the solutions found by the algorithms and display the algorithm performance through the metric data. For multi - objective algorithms, convergence and diversity are important criteria for retaining solutions. We hope that the solution set obtained can better approach the Pareto front and be more evenly distributed across the entire Pareto front. Therefore, we select the hypervolume metric and the set - coverage metric.

[0141] (1) Set - coverage metric (Set coverage, c - metric): Suppose A and B are two approximate solution sets obtained by a multi - objective optimization method. C(A,B) is defined as the percentage of the number of solutions in set B that can be dominated by at least one solution in set A among all the solutions in set B. The formula is as follows:

[0142]

[0143] Similarly, C(B,A) is defined as the percentage of the number of solutions in set A that can be dominated by at least one solution in set B among all the solutions in set A. C(A,B) and 1 - C(A,B) are not necessarily equal. When C(A,B)=1, it indicates that all solutions in B can find a solution in A to dominate them. When C(A,B)=0, it indicates that no solution in B is dominated by a solution in A. Through this metric, we can compare the convergence between two solution sets.

[0144] (2) Hypervolume metric (Hypervolume, Hv). Give a reference point in the objective - space domain This reference point is dominated by all Pareto - optimal objective vectors. Suppose P is the approximate solution set obtained by the multi - objective method. When calculating the Hv value of P, we select Z * as the boundary, and calculate the hypervolume of the region dominated by the solutions in P. The formula is as follows:

[0145]

[0146] m is the number of solutions in the solution set. It can be seen from the formula that the larger the Hv value, the better the performance and diversity of the algorithm.

[0147] Experimental parameter settings and operating environment

[0148] When verifying the effectiveness of its own algorithm in the present invention, the experimental parameters are unified and are the same data. The parameters of the BLX crossover strategy are consistent with those set in the paper.

[0149]

[0150]

[0151] The EPINSGA-II and the comparative algorithms were run and tested on an Intel(R) Core(TM) i7-10700 CPU @ 2.90 GHz in a Windows 10 environment and PyCharm Community Edition 2020.3 x64 with Python 3.8. All experiments were independently run 20 times.

[0152] In the optimization method, each parameter has a certain influence on the result. The population size has a very important influence on the experimental result. In this section, the algorithm of the present invention was run 10 times under different population sizes, and the mean and variance of Hv were calculated. By studying the Hv indexes of different population sizes, the pop-size to be selected in the comparative experiment of the present invention was determined. The evaluation times of each method were set to 10,000 times, and the evaluation times were the same when the population sizes were different. The experimental results are shown in Table 3.

[0153] Table 3 Hv index data of the algorithm of the present invention under different population sizes

[0154]

[0155] From Table 3, Figure 4 it can be concluded from the data that when the population sizes are different, the Hv indexes also fluctuate. From the Hv indexes of the four sizes, it can be seen that when the size is 150, the mean value of Hv is the largest, and the best value obtained at this time is better than the other three sizes, and the worst value is also better than the other three sizes. From the perspective of stability, the size of 100 is the most stable, but 150 ranks second, and the stability is slightly worse. Considering stability and the optimal value comprehensively, it is more appropriate to set the population size of the comparative algorithm of the present invention to 150 for the comparative experiment.

[0156] Effectiveness of its own method

[0157] NSGA-II and NSGA-II (BLX) represent the algorithms that only use the BLX crossover for NSGA-II. INSGA-II represents the NSGA-II algorithm that only uses the multi-crossover strategy. The method that only uses the external archive evolution mechanism is EP-NSGA-II. EP-INSGA-II represents the algorithm that combines the external archive evolution mechanism, the multi-crossover strategy and the improved initialization, which is the algorithm proposed by the present invention. The sub-population size is 150, and the maximum evaluation times are set to 20,000 times. The algorithms are independently run 20 times. The following shows the Hv and C-metric (%) index values obtained by running the 5 algorithms 20 times respectively. Table 4 shows the Hv index results obtained by running NSGA-II, NSGA-II (BLX), INSGA-II, EP-NSGA-II and EP-INSGA-II 20 times in the apron allocation problem.

[0158] Table 4

[0159]

[0160] Table 4, Figure 5 shows the Hv metrics of 5 algorithms running 20 times each on the multi-objective apron allocation problem. Analyzing the results of the NSGA-II algorithm and the NSGA-II(BLX) algorithm, it can be seen that the BLX strategy can effectively improve the convergence of the algorithm. Comparing the results of INSGA-II with NSGA-II and NSGA-II(BLX) algorithms shows that the multi-crossover strategy can effectively improve the convergence and diversity of the algorithm, with better results than using only the BLX strategy alone. By comparing the EPNSGA-II algorithm and the NSGA-II algorithm, it can be concluded that the external archive mechanism can effectively improve the diversity of the algorithm, but the convergence is poor; comparing the results obtained by EP-INSGA-II with the other 4 algorithms, it can be seen that the method proposed in the present invention has great advantages in terms of diversity and convergence, obtaining the optimal Hv metric, and the stability is also better than the other four methods, proving that the EPINSGA-II algorithm proposed in the present invention has great advantages in the multi-objective apron allocation problem. Table 5 shows the C-metric(%) metrics obtained by running the NSGA-II, NSGA-II(BLX), INSGA-II, and EPNSGA-II algorithms 20 times each on the apron allocation problem.

[0161] Table 5

[0162]

[0163] Where A represents the EP-INSGA-II algorithm and B represents the comparison algorithm.

[0164] The table shows the comparison results of the C-metric of all algorithms running 20 times on the multi-objective apron allocation problem. By comparing the metric results of the NSGA-II algorithm and the results of the NSGA-II (BLX) algorithm, it can be seen that the EPINSGA-II algorithm proposed in the present invention has better convergence in 18 runs, and the average value is much higher than that of the NSGA-II algorithm; analyzing the comparison results of the NSGA-II (BLX) algorithm shows that the EPINSGA-II algorithm proposed in the present invention is superior to it in 19 runs, and the average value of 85.1335 is much greater than 3.725; INSGA-II using only the multi-crossover strategy is superior to the EPINSGA-II algorithm in 9 results, and the average value of the metric obtained by the EPINSGA-II algorithm, 36.45, is superior to 32.0335, indicating that the multi-crossover strategy can effectively improve the convergence of the algorithm, but is only second to the EPINSGA-II algorithm; comparing with the EP-NSGA-II algorithm, it can be seen that the EPINSGA-II algorithm proposed in the present invention is superior to EPNSGA-II in all 20 runs, indicating that the external archive evolution mechanism has a small improvement in terms of convergence. Comprehensive analysis of the experimental data shows that the EPINSGA-II algorithm proposed in the present invention has great advantages in terms of convergence.

[0165] Comparison with other algorithms

[0166] In this embodiment, the classical decomposition-based multi-objective optimization method MOEA / D

[33] (PBI, WS, TCH), the multi-objective optimization algorithm NSGA-II based on the Pareto solution set dominance relationship, and the multi-objective particle swarm (MOPSO) method are selected for comparative experiments to verify the effectiveness of the method in solving the multi-objective apron allocation. Table 6 shows the Hv metrics obtained by running NSGA-II, MOPSO, MOEA / D (PBI), MOEA / D (WS), MOEA / D (Tch) and the EPINSGA-II algorithm 20 times respectively.

[0167] Table 6

[0168]

[0169]

[0170] Table 6, Figure 6The Hv index data shows that in the results of 20 independent runs, the obtained results of MOEA / D(Tch), MOEA / D(PBI), and MOEA / D(WS) indicate that MOEA / D(ws) achieved the optimal average value. MOEA / D(PBI) has a significant advantage over the other two algorithms in terms of algorithm stability. The results comparison between the MOPSO algorithm and MOEA / D(Tch), MOEA / D(PBI), MOEA / D(WS), and NSGA-II algorithms proves its advantage in the multi-objective apron allocation problem, with a better average value index and the best best index among the 20 runs. The proposed EPINSGA-II algorithm in the present invention is compared with several other excellent multi-objective algorithms, obtaining the best HV index data among the 20 runs, and the worst index is also better than others, achieving the best average value data of the HV index. In terms of stability, MOEA / D(PBI) performs the best. Table 7 shows the C-metric(%) indices obtained by running the NSGA-II, MOPSO, MOEA / D(Tch), MOEA / D(WS), and MOEA / D(PBI) algorithms 20 times respectively in the apron allocation problem.

[0171] Table 7

[0172]

[0173] Table 7 shows the comparison results of the c-metric indices obtained by running all the comparison algorithms 20 times. In terms of the convergence of the proposed EPINSGA-II in the present invention, compared with the results of NSGA-II, MOPSO, and MOEA / D(Tch), it is superior to the comparison algorithms 19 times, 19 times, and 18 times respectively. And the proposed EPINSGA-II method in the present invention is entirely superior to the two methods of MOEA / D(WS) and MOEA / D(PBI) in terms of convergence.

[0174] Diagram of allocation results

[0175] Select an excellent allocation scheme in the final solution obtained by the EPINSGA-II algorithm for drawing as Figure 7 shown, and analyze the advantages and some deficiencies of the method proposed in the present invention.

[0176] Analysis Figure 8 From the diagram of the number of flights allocated to boarding gates, it can be seen that the number of flights allocated to each apron is relatively average, and there is no extreme phenomenon of a large number of flights allocated to individual aprons. The number of flights allocated to boarding gates 26, 27, and 30 is relatively small. Figure 7 From the allocation scheme in the present invention, it can be seen that flight 135 at position 27 occupies the apron for a long time and conflicts with other flights. Therefore, no other flights are arranged, so the number of allocated flights is small.

[0177] In summary, compared with excellent multi-objective algorithms, the EPINSGA-II algorithm proposed in the present invention has greatly improved convergence and diversity. Since the apron gate allocation is a complex combinatorial optimization problem, the present invention utilizes the SBX crossover strategy with good diversity in the decision space and the BLX-α crossover strategy with the ability to obtain Pareto solution sets to improve the convergence performance of the NSGA-II method in the gate allocation problem, and fully utilizes the advantages of the process solutions to design an external archive evolution strategy to improve the diversity performance of the NSGA-II method by enhancing the search ability of the algorithm.

[0178] The present invention studies a multi-objective gate allocation method. Starting from airport operations and passenger satisfaction, we select the apron free time and passenger walking distance as objectives to establish a multi-objective apron allocation model. To effectively solve the multi-objective apron allocation problem, we design an initialization method and multiple crossover strategies to improve the convergence of the method and search for better solutions. To increase the diversity of the solution set, we design an external archive evolution mechanism to improve the utilization rate of excellent individuals and generate better offspring individuals. We also use the example data of Guangzhou Baiyun Airport to verify the performance of the method. In the allocation task of 250 flights, the allocation rate of EPINSGA-II can reach 97.6%, and the average assignment rate reaches  97.16%. By comparing with excellent multi-objective methods such as NSGA-II, MOEA / D(PBI), MOEA / D(WS), MOEA / D(TCH), and MOPSO, we select C-metric and H v as performance indicators. The experimental results show that the method proposed in the present invention has good advantages in terms of diversity and convergence.

[0179] The technical solution of the present invention is not limited to the limitations of the above specific embodiments. Any technical deformation made according to the technical solution of the present invention falls within the protection scope of the present invention.

Claims

1. A multi-objective apron allocation method based on a multi-strategy fast non-dominated sorting genetic algorithm, characterized in that It includes the following steps: S1. Establish a multi-objective airport apron allocation optimization model with the minimum apron idle time and the shortest passenger walking distance; S2. Based on the NSGA-II algorithm, design the EPINSGA-II algorithm to solve the multi-objective apron allocation model to obtain an apron allocation plan: S21. Design an initialization strategy with real number coding to improve the feasibility of the initial solution of the multi-objective airport apron allocation optimization model and the algorithm efficiency; S22. Design a multi-crossover strategy to improve the convergence of the solution set; S23. Design an external archive evolution strategy to increase the diversity of algorithm solutions; S24. Design a multi-objective apron allocation based on the multi-strategy fast non-dominated sorting genetic algorithm to achieve effective apron allocation; It is characterized in that the multi-crossover strategy in step S22 is a multi-strategy crossover method that combines the SBX crossover strategy with better diversity distribution ability and the BLX-α strategy with Pareto solution set ability, and its algorithm pseudo-code: The external archive evolution strategy in step S23 specifically includes: S231. External archive update strategy By setting an external archive to save all non-dominated solutions searched during the evolution process, the best individual in each generation is stored in the external archive matrix. When the scale is greater than the set scale, it will be updated according to the following mechanism, and the relatively poor individuals will be eliminated; S232. Utilize the excellent individuals searched by the algorithm stored in the external archive. In order to make full use of the excellent genetic characteristics of the non-dominated solutions in the external archive, by selecting several non-dominated solutions among them and participating in the crossover and mutation of the next generation to generate excellent offspring individuals, the purpose of accelerating the algorithm convergence is achieved.

2. The multi-objective apron allocation method based on the multi-strategy fast non-dominated sorting genetic algorithm according to claim 1, characterized in that Step S1 specifically includes: Describe the multi-objective optimization problem, and its definition is as follows: s.t. X ∈ Ω g(x) = [g1(x), g2(x),... g d (x)] ≤ 0 h(x) = [h1(x) h2(x) ...h k (x)] = 0 where, Ω is the decision variable space, represents the n-dimensional decision variable, f n (x) represents the nth sub-function, m is the total number of optimization objectives; g(x) represents d inequality constraint conditions; h(x) represents k equality constraint conditions; the constraint conditions constitute the feasible region; Determine the optimization objectives: (1) Take the total passenger walking distance as the optimization objective: (2) Total apron idle time The idle time of the jth apron consists of three parts, namely the start idle time, the end idle time, and the flight idle time; the start idle time refers to the time between the opening time of the airport and the arrival time of the first flight at this apron; the end idle time refers to the time between the closing time of the airport and the departure time of the last flight at this apron; the flight idle time refers to the time between the arrival time of the latter flight and the departure time of the former flight among two adjacent flights at this apron: Among them The constraint conditions are as follows: (1) Flight uniqueness The same flight can only be parked at one near apron or far apron, that is, it satisfies: (2) Apron uniqueness At most one flight is allowed to be parked at one apron at the same time, that is, it satisfies: NI j,t ≤ 1; (3) Aircraft type matching The type of the apron should conform to the type of the flight. That is, small aircraft are allowed to be parked at small aprons, medium aprons, and large aprons; medium aircraft are allowed to be parked at medium aprons and large aprons; large aircraft are only allowed to be parked at large aprons, that is, it satisfies: GT j ∈AT i , if s i,j = 1; (4) Time interval between adjacent flights at the same apron For safety reasons, it is required that the push-out time of the previous flight and the push-in time of the next flight on the same apron are greater than a certain time interval, that is, it satisfies: LE p -AR q ≥T cur ; p, q ∈ A i , flight p is the next flight of flight q; (5) Push-in and push-out interval time between adjacent aprons For adjacent aircraft positions, for safety considerations, it is generally required that adjacent aircraft positions do not push in and out flights simultaneously, that is, the push-in and push-out times of flights on adjacent aircraft positions are greater than a certain time interval, that is, it satisfies: (6) Special flights must satisfy For flights in some special situations, such as VIP flights, etc., it is required that they must be assigned to near aircraft positions, that is, it satisfies:

3. The multi-objective apron allocation method based on the multi-strategy fast non-dominated sorting genetic algorithm according to claim 2, characterized in that, The specific steps of step S21 include: Assuming there are three types of aircraft positions and flights, namely S, M, and L, the following real number initialization method is proposed: First, process flights with L-type attributes, store the L-type aircraft position numbers among 30 aircraft positions in the list_L string, and encode it with rand(list_L). Secondly, process M-type flights, store the L-type and M-type aircraft position numbers in list_M, and encode it with rand(list_M). Finally, process S-type flights, which can be parked at any of the 30 aircraft positions, and random encoding can be used.

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