A dual-hub route network optimization method and system

Abstract

The present invention discloses a dual-hub route network optimization method and system, which belongs to the field of civil aviation flight technology. By obtaining input indicators, output indicators and environmental variables for evaluating the efficiency of the dual-hub routes to be optimized, a dual-hub route efficiency evaluation index system is established, the efficiency of the dual-hub routes is evaluated, and the technical efficiency value of each dual-hub route to be optimized is obtained. In order to analyze the operating characteristics of the dual-hub airports, the principles of reducing the overlap rate, efficient operation of the route network, passenger convenience and minimum route adjustment are proposed. With the goals of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection cost and minimizing route flight adjustment, a dual-hub route network optimization model is constructed and solved, and the network layout of the dual-hub routes is optimized to obtain the optimization results. The method evaluates efficiency before optimization, improves the overall route efficiency of the dual-hub, and can achieve differentiation and efficiency of the dual-hub route network.

Description

Technical Field

[0001] The present invention relates to the field of civil aviation flight technology, and more particularly to a dual-hub route network optimization method and system based on route efficiency evaluation. Background Art

[0002] my country's total number of civil airports has begun to take shape, airport density has gradually increased, airport service capabilities have gradually improved, a civil transport airport system has been initially established, and several major airport cluster systems have begun to take shape. In particular, more and more cities have begun to develop dual hub airports, such as Beijing, Shanghai, and Chengdu. However, the domestic dual hub model is in its infancy, and work on differentiated and efficient development is still in the initial exploratory stage. Some routes between the two airports are inefficient and the route network layout is irrational, which does not effectively achieve functional complementarity and coordinated development between the airports.

[0003] At present, domestic and international technical solutions for route network optimization methods are mainly concentrated at the level of a single airport or the entire country. There are few methods for optimizing route networks for multiple airports, especially dual hubs. Research on multi-airport systems and route network optimization based on multiple airports is gradually becoming a research hotspot in the civil aviation industry. Foreign research on multi-airport development models, especially dual hub development models, is relatively mature. However, research on dual hubs in my country mostly remains at the macro level. Research on dual hub route layout is just beginning. In addition, most existing route network optimization models are traditional hub-and-spoke models. Research on route network optimization based on the operating characteristics of dual hub airports is relatively scarce, and no feasible improvement plans have been proposed for the route network of airport clusters. Existing technical solutions for multi-airport route optimization rarely comprehensively consider the overall efficiency of the multi-airport route network and the differentiated development of each airport from the perspectives of route operation efficiency and route overlap, resulting in low efficiency of some routes and waste of resources due to route network overlap. Summary of the Invention

[0004] In response to the problems existing in the above-mentioned fields, the present invention proposes a dual-hub route network optimization method and system, which can solve the technical problems that the existing technical solutions for multi-airport route optimization rarely comprehensively consider the overall efficiency of the multi-airport route network and the differentiated development of each airport from the perspective of route operation efficiency and route overlap, resulting in low efficiency of some routes and waste of resources due to route network overlap.

[0005] To solve the above technical problems, the present invention discloses a dual-hub route network optimization method, comprising the following steps:

[0006] Conduct characteristic analysis on the dual-hub routes to be optimized, and obtain input indicators, output indicators, and environmental variables for evaluating the efficiency of the dual-hub routes to be optimized;

[0007] Based on the input indicators, output indicators and environmental variables of dual-hub route efficiency, a dual-hub route efficiency evaluation index system is established to evaluate the efficiency of dual-hub routes and obtain the technical efficiency value of each dual-hub route to be optimized;

[0008] Based on the dual-hub route efficiency evaluation index system and technical efficiency values, the operational characteristics of dual-hub airports were analyzed, and principles were proposed for reducing overlap rates, ensuring efficient route network operation, facilitating passengers, and minimizing route adjustments. Based on these principles, a dual-hub route network optimization model was constructed with the goals of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection costs, and minimizing route and flight adjustments.

[0009] The dual-hub route network optimization model is solved, the network layout of the dual-hub route is optimized, and the optimization results are obtained.

[0010] Preferably, obtaining input indicators, output indicators and environmental variables for evaluating the efficiency of the dual-hub route to be optimized comprises the following steps:

[0011] The input and output indicators of route efficiency evaluation are based on dual-hub passenger routes. Based on the availability and quantification of data, the input indicators, output indicators and environmental variables in the indicator system are constructed.

[0012] Input indicators include flight frequency, fuel cost, available seats and the airfield grade of the airport at the point of access. Flight frequency, fuel cost and available seats represent the airline's investment cost and investment level for each route at the airport. The higher the flight frequency, fuel cost and available seats, the higher the investment cost for the route. The airfield grade of the airport at the point of access reflects the capacity and scale of the airport and the amount of transport capacity invested in the route. The higher the airfield grade, the larger the aircraft types used for take-off and landing at the airport, and the higher the transport capacity invested in the route.

[0013] Output indicators include route passenger volume, route load factor, and revenue per passenger kilometer (RPK). These reflect the return on a route after a certain investment. The higher the route passenger volume, route load factor, and revenue per passenger kilometer (RPK), the higher the efficiency and return on the route.

[0014] Environmental variables include per capita GDP of cities with air routes, proportion of flights during peak hours, and route distance.

[0015] Preferably, obtaining the technical efficiency value of each route of the dual hub to be optimized includes the following steps:

[0016] A three-stage data envelopment analysis (DEA) was used to evaluate the efficiency of the dual-hub routes to be optimized. The DEA consists of three stages:

[0017] The first stage: the traditional DEA model, which measures the efficiency value by selecting the non-radial and non-angular Super-SBM method;

[0018] Phase II: SFA model construction. By extracting the input slack from the evaluation results of the first phase as the dependent variable and selecting environmental factors as the independent variables, the SFA model is constructed as follows:

[0019] S in =f i (z i ,β n )+V in +U in (i=1,2,...,I; n=1,2,...,N)

[0020] Among them, S in is the slack of the ith input of the nth evaluation object, f i (z i ,β n ) is the environmental impact function, z i is an environmental variable, β n is the coefficient of the environmental variable, V in represents the random error term, which is assumed to obey the standard normal distribution; U in To manage inefficiency, a truncated normal distribution is assumed;

[0021] The SFA model regression results can separate V in +U in By deriving and estimating U in Part, obtain the random error term estimation results;

[0022] Taking the most efficient decision-making unit input as the benchmark, the other decision-making units are adjusted to the input under the same operating environment. The adjusted SFA model is:

[0023]

[0024] Among them, x in and are the results before and after adjustment of the i-th input of the n-th evaluation object, and They represent the same external environment and the same luck level after adjustment;

[0025] The third stage: the adjusted DEA model uses the adjusted input data to replace the original input data, and the efficiency value is recalculated using the non-radial and non-angular Super-SBM method. The calculated result is the efficiency value after eliminating environmental factors and random errors;

[0026] Based on the calculation results of the adjusted DEA model, each route of the dual hub is evaluated and the technical efficiency value of each route of the dual hub is obtained.

[0027] Preferably, the construction of the dual-hub route network optimization model includes making assumptions, specifically including:

[0028] It mainly optimizes routes from the perspective of airports and passengers, without considering the differences in operating costs and benefits between airlines. It also believes that if airlines follow the advice, there will be fewer scheduling obstacles.

[0029] Regardless of the impact of schedules on routes and transfers, as long as two airports outside the dual hubs both have routes to one of the dual hubs, these two airports are considered to have the opportunity to transfer at the dual hub airport.

[0030] There will be no air routes between the two hubs;

[0031] Only passenger routes are considered, and stopover / transfer routes outside the dual hubs are not considered. Only direct routes are optimized;

[0032] The allocation of flight operations by airline to each route is not considered;

[0033] The flight frequency of the route is only the flight frequency of the route departing from the dual hub airports.

[0034] Preferably, the construction of the dual-hub route network optimization model further includes establishing an objective function, specifically including:

[0035] By analyzing the operational characteristics of dual-hub airports, the principles of reducing overlap, ensuring efficient route network operation, passenger convenience, and minimizing route adjustments are proposed. An objective function is established to minimize route overlap, minimize route efficiency mismatch, minimize passenger departure airport selection costs, and minimize route and flight adjustments. The objective functions are:

[0036] Objective 1: Minimize route overlap, which means the smaller the number of overlaps of the same route between the two hubs, the lower the probability of homogenization; The sum of the weekly flights that overlap between the dual hubs and airport i. Since only the number of overlapping flights at one of the dual hubs is counted, it needs to be multiplied by 2 to represent the weekly overlap of all flights on the dual hubs. The sum of the weekly flights on all routes of the dual hubs is:

[0037]

[0038] Where I is the set of dual-hub external airports that have routes with the dual-hub airports, i∈I; f ij (j=1,2) is a non-negative integer variable, which represents the weekly flight frequency of the route between airport i and dual hub airport j after optimization;

[0039] Goal 2: Minimize the route efficiency mismatch, which means that the smaller the efficiency mismatch of route ij, the more it conforms to the functional positioning of the dual hub airport; among them, the first part It represents the mismatch degree of route efficiency when route ij is opened. The higher the efficiency of the opened route, the lower the mismatch degree. The second part It represents the route efficiency mismatch when route ij is not opened. If those routes with higher efficiency are not opened, the route efficiency mismatch will be higher.

[0040]

[0041] Among them, ij is the technical efficiency of route ij, o ij The higher the value, the higher the operating efficiency of the route, which is more in line with the functional positioning of the airport. The value is obtained based on the route efficiency evaluation of the DEA model after the three-stage adjustment in the first part, 0≤o ij ≤1;x ij (j=1,2) is a 0-1 variable, which is 1 when route ij is opened, otherwise it is 0;

[0042] Objective 3: Minimize the cost of passengers choosing their departure airport, which means that the cost of passengers choosing their departure airport due to route adjustments is minimized. The first term c·[(1-x i1 )f i2 w i2 +(1-x i2 )f i1 w i1 ]·(1-x i1 x i2 ) represents the inter-airport access cost incurred by passengers who are forced to choose another airport when the routes do not overlap; the second term c·|f i1 w i1 -f i2 w i2 |(x i1 x i2 ) represents the cost incurred due to the difference in flight frequency between the two routes when the routes overlap;

[0043]

[0044] Where c is the average cost per passenger traveling to the dual hubs; w ij(j=1,2) is the average weekly passenger volume of each flight on route ij;

[0045] Objective 4: Minimize the amount of flight adjustments on each route, meaning that the difference between the weekly flight frequency of each route after optimization and the weekly flight frequency in the original pre-planned flight schedule is minimized:

[0046]

[0047] Among them, f ij '(j=1,2) is the weekly flight frequency of route ij before optimization.

[0048] Preferably, the construction of the dual-hub route network optimization model further includes setting constraints on the objective function, specifically including:

[0049] Route flight constraint: represents the relationship between two optimization variables, namely the route frequency f ij With the decision variable x ij The relationship between them is that only when route ij is opened, there can be flights between airport i and airport j. Similarly, when the number of flights between airport i and airport j is zero, f ij = 0, route ij is not open, x ij =0:

[0050]

[0051] Dual-hub airport capacity constraints: After optimization, the weekly outbound flights of the dual-hub airports cannot exceed half of the inbound and outbound flights of each airport:

[0052]

[0053] Among them, F j is the weekly inbound and outbound flight capacity of dual-hub airport j;

[0054] Route opening constraints: If an airport outside the dual hubs has opened routes with the dual hub airports before optimization, it must open a route with at least one of the dual hub airports after optimization:

[0055]

[0056] Among them, 1 j Indicates that airport j among the dual hub airports has opened a route;

[0057] Flight capacity constraint: For any non-dual hub airport i, the flight frequency of the route between it and dual hub airport j cannot be higher than the total flight frequency of the two airports, and at least one flight must be opened:

[0058]

[0059] Decision variable constraints:

[0060]

[0061] Wherein, N is a set of non-negative integers.

[0062] Preferably, solving the dual-hub route network optimization model comprises the following steps:

[0063] A non-dominated sorting genetic algorithm based on reference points is used to solve the dual-hub route network optimization model. The algorithm process of the non-dominated sorting genetic algorithm based on reference points is divided into three stages, including crossover and mutation of the population, fast non-dominated sorting, and selection based on reference points.

[0064] Construct a set of reference points;

[0065] Randomly generate an initial population P containing N individuals t , then perform crossover and mutation of the population, and use binary crossover and polynomial mutation to generate a new population Q t , and with the population P t Combine to generate a new population R t ;

[0066] For population R t Perform fast non-dominated sorting and sort the population R t Small populations divided into multiple nondominant castes;

[0067] Select N individuals to enter the next generation population P t+1 , divided into two cases, one is to enter P according to the non-dominated level t+1 , the other is that if non-dominated level selection cannot be used, it is necessary to select individuals with sparse distribution around them to enter the population P through the reference point mechanism t+1 , when P t+1 The process stops when the number of individuals in is equal to N.

[0068] Preferably, a dual-hub route network optimization system is further included, comprising:

[0069] An evaluation index acquisition module is used to perform feature analysis on the dual-hub route to be optimized and obtain input indicators, output indicators, and environmental variables for evaluating the efficiency of the dual-hub route to be optimized;

[0070] The route efficiency evaluation module is used to establish a dual-hub route efficiency evaluation index system based on the input indicators, output indicators and environmental variables of the dual-hub route efficiency, evaluate the efficiency of the dual-hub routes, and obtain the technical efficiency value of each dual-hub route to be optimized;

[0071] The dual-hub route network optimization model construction module is used to analyze the operating characteristics of dual-hub airports based on the dual-hub route efficiency evaluation index system and technical efficiency values, and propose principles for reducing overlap rates, ensuring efficient route network operation, passenger convenience, and minimizing route adjustments. Based on these principles, a dual-hub route network optimization model is established with the goals of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection costs, and minimizing route and flight adjustments.

[0072] The route layout optimization module is used to solve the dual-hub route network optimization model, optimize the network layout of the dual-hub routes, and obtain optimization results.

[0073] Compared with the prior art, the present invention has the following beneficial effects:

[0074] The dual-hub route network optimization method based on route efficiency evaluation proposed in this invention can break through the existing technical solutions for multi-airport route optimization, which rarely comprehensively consider the overall efficiency of the multi-airport route network and the differentiated development of each airport from the perspective of route operation efficiency and route overlap, resulting in low efficiency of some routes and resource waste caused by route network overlap. By constructing a route efficiency evaluation index system and a dual-hub route network optimization model, the method optimizes the network layout of dual-hub routes. While meeting the airport operation capacity constraints and controlling the flight adjustment volume to be small, it can effectively reduce the route overlap, route efficiency mismatch and passenger departure airport selection cost of the dual-hub airports. The optimized routes are more in line with the design positioning of efficient dual-hub operation, and can effectively solve the problem of hindered operational efficiency of dual-hubs due to unreasonable route layout, solve the problem of resource waste caused by route overlap at dual-hub airports, alleviate the current situation of serious homogeneity of dual-hubs, improve the overall operational efficiency of the dual-hub route network, and provide a theoretical basis and decision-making reference for the route network optimization strategy of dual-hub airports to achieve efficient and differentiated operation, which has important practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] Figure 1 Schematic diagram of the overall method flow of the present invention;

[0076] Figure 2 The route efficiency evaluation index system constructed for the present invention;

[0077] Figure 3 This is a flow chart of the reference point-based non-dominated sorting genetic algorithm adopted by the present invention. DETAILED DESCRIPTION

[0078] The following is a combination of the embodiments of the present invention Figure 1-Figure 3, the technical solutions in the embodiments of the present invention are clearly and completely described. It should be understood that the terms used in the present invention are only used to describe specific implementation methods and are not intended to limit the present invention.

[0079] At present, the technical solutions for route network optimization methods at home and abroad are mainly concentrated at the level of a single airport or the entire country. There are few methods for route network optimization with multiple airports, especially dual hubs. Most of the current technical solutions adopt the following methods: 1) Research on the single hub network optimization problem with capacity constraints, and use the Lagrangian relaxation method combined with branch and bound and heuristic algorithms to solve the model; 2) Research on the hub network design problem without capacity constraints, establish a quadratic integer programming model and design a genetic algorithm for solution; 3) Use a time window-based route network model with capacity constraints to study non-strict hub route networks, take capacity constraints as constraints, and use a hybrid algorithm of taboo search and branch and bound to solve the problem; Method to solve; 4) From the perspective of complex networks, the layout characteristics and evolution laws of aviation networks are studied based on network evolution theory; 5) From the perspective of airlines, an airline network optimization model in a competitive environment is established with the goal of minimizing airline operating costs and maximizing passenger transportation volume; 6) Considering hub construction costs and congestion costs, while taking into account the limitations of hub number and capacity, a hub airport route network optimization model with the minimum total network cost is established; 7) Taking the hub airport radial route network as the research object, a route network model with uncertain traffic demand and capacity constraints is established, and a genetic algorithm is designed to solve it; 8) A hub airport-based airport route collaborative optimization model is constructed. The model is customized The hub airports within the airport cluster and the small and medium-sized airports within the airport cluster connect to the hub airport to realize the transfer of passengers and cargo. The optimized route network constitutes a multi-hub radiation network; 9) The study found that the routes of the 9 airports in Jiangsu Province are seriously homogeneous. Therefore, the p-hub median problem method is used to construct a regional multi-airport system route network model, optimize the routes with serious homogeneity, and use the taboo search algorithm and the shortest path algorithm to solve it; 10) It is found that the airport routes in the region are insufficient and the resource allocation is unreasonable. For this reason, a route network optimization model of the regional multi-airport system is constructed with the goal of minimizing the total transportation cost of all air transport passenger flows in the region. The Jiangsu Province airport cluster is used as an example to solve the model using the particle swarm optimization algorithm; 1 1) The congestion cost of hub airports is taken into account in the network cost, and a non-strict hub route network structure optimization model for congestion is established, and the SA-PSO algorithm is designed to solve it; 12) In view of the route network layout problem when dual hub airports are competing, from the perspective of airports, a dual hub route network optimization model is proposed to reduce passenger delay costs and route overlap costs, and the impact of different route overlap costs on the optimization results is studied; 13) From the perspective of airlines and airport clusters, the functional positioning of each airport is taken into account, and the relationship between airport subsidy strategies and airline route adjustments is studied. A two-tier game model between passengers, airlines and airports is constructed to determine the optimal route network and the best pricing strategy for airlines within the airport cluster.

[0080] In order to overcome the shortcomings of the existing technology, the present invention takes the actual needs of differentiated and efficient development of dual-hub airports as the background, takes the dual-hub route network as the technical object, and based on route efficiency evaluation and multi-objective integer programming methods, proposes a dual-hub route network optimization method with the goals of improving route operation efficiency and reducing route overlap. In order to eliminate the influence of environmental factors and random errors on route efficiency, a three-stage Data Envelopment Analysis (DEA) is used to evaluate the efficiency of dual-hub routes, and an efficiency evaluation index system for dual-hub routes is established. From the perspectives of reducing the overlap of dual-hub routes, improving operational efficiency, and reducing the unnecessary costs brought to airports and passengers by route adjustments, a dual-hub route network optimization model is constructed with the goals of minimizing route overlap, route efficiency mismatch, passenger departure airport selection cost, and route and flight adjustment. A non-dominated sorting genetic algorithm (NSGA-III) based on reference points is designed to optimize the model, and then an optimal layout of the dual-hub route network is proposed, which provides a theoretical basis and a reference for the application of model methods for practical work, in order to vigorously promote the construction of dual-hub airports in my country and make them more efficient and differentiated.

[0081] Example

[0082] like Figure 1 As shown, an embodiment of the present invention provides a dual-hub route network optimization method, including the following steps:

[0083] S1: Analyze the characteristics of the dual-hub route to be optimized and obtain the input indicators, output indicators and environmental variables for evaluating the efficiency of the dual-hub route to be optimized;

[0084] S2: Based on the input indicators, output indicators and environmental variables of the dual-hub route efficiency, establish a dual-hub route efficiency evaluation index system, evaluate the efficiency of the dual-hub routes, and obtain the technical efficiency value of each dual-hub route to be optimized;

[0085] S3: Based on the dual-hub route efficiency evaluation index system and technical efficiency values, analyze the operational characteristics of dual-hub airports and propose principles for reducing overlap, ensuring efficient route network operation, facilitating passengers, and minimizing route adjustments. Based on these principles, establish a dual-hub route network optimization model with the goals of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection costs, and minimizing route and flight adjustments.

[0086] S4: Solve the dual-hub route network optimization model, optimize the network layout of the dual-hub route, and obtain the optimization results.

[0087] In step S1, obtaining input indicators, output indicators, and environmental variables for evaluating the efficiency of the dual-hub route to be optimized includes the following steps:

[0088] The input and output indicators of route efficiency evaluation take dual-hub passenger routes as the object, take the availability and quantification of data as the starting point, and construct the input indicators, output indicators and environmental variables in the indicator system, such as Figure 2 As shown, where:

[0089] Input indicators include flight frequency, fuel cost, available seats and the airfield grade of the airport at the point of access. Flight frequency, fuel cost and available seats represent the airline's investment cost and investment level for each route at the airport. The higher the flight frequency, fuel cost and available seats, the higher the investment cost for the route. The airfield grade of the airport at the point of access reflects the capacity and scale of the airport and the amount of transport capacity invested in the route. The higher the airfield grade, the larger the aircraft types used for take-off and landing at the airport, and the higher the transport capacity invested in the route.

[0090] Output indicators include route passenger volume, route load factor, and revenue per passenger kilometer (RPK). These reflect the return on a route after a certain investment. The higher the route passenger volume, route load factor, and revenue per passenger kilometer (RPK), the higher the efficiency and return on the route.

[0091] Environmental variables include per capita GDP of cities with air routes, proportion of flights during peak hours, and route distance.

[0092] In step S2, the technical efficiency value of each route of the dual hub to be optimized is obtained, which includes the following steps:

[0093] A three-stage data envelopment analysis (DEA) model is used. DEA is a traditional nonparametric calculation method primarily used to evaluate input-output efficiency. This method uses linear programming and statistical data to determine a relatively efficient frontier. The statistical data does not require preprocessing, making it relatively simple to operate. Therefore, this method has a wide range of applications.

[0094] The efficiency of the dual-hub routes to be optimized is evaluated. The three-stage data envelopment analysis includes three stages:

[0095] Phase 1: The traditional DEA model uses input and output indicator data to calculate the efficiency value of the decision-making unit. Considering that the large number of input indicators makes it difficult to fully participate in the efficiency value evaluation, this paper uses the non-radial and non-angular Super-SBM method to calculate the efficiency value;

[0096] The second stage: SFA model construction. The main purpose of this stage is to adjust the original input variables to achieve a relatively consistent external environment for multiple decision-making units, so as to reflect the actual efficiency level gap. First, the input slack in the evaluation results of the first stage is extracted as the dependent variable, and the environmental factors are selected as the independent variables to construct the SFA model as shown in formula (1):

[0097] S in =f i (z i ,β n )+V in +U in (i=1,2,...,I; n=1,2,...,N) (1)

[0098] Among them, S in is the slack of the ith input of the nth evaluation object, f i (z i ,β n ) is the environmental impact function, z i is an environmental variable, β n is the coefficient of the environmental variable, V in represents the random error term, which is assumed to obey the standard normal distribution, U in To manage inefficiency, a truncated normal distribution is assumed;

[0099] The SFA model regression results can separate V in +U in Item, using the Roden jump method to estimate U in Part, obtain the random error term estimation results.

[0100] In order to eliminate the influence of the external environment and random errors, the present invention takes the most efficient decision-making unit input as the benchmark, adjusts the input of other decision-making units to the input under the same operating environment, adjusts the SFA model, and obtains the adjusted SFA model as shown in formula (2):

[0101]

[0102] Among them, x in and are the results before and after adjustment of the i-th input of the n-th evaluation object, and They represent the same external environment and the same luck level after adjustment;

[0103] The third stage: the adjusted DEA model uses the adjusted input data to replace the original input data, and the efficiency value is recalculated using the non-radial, non-angular Super-SBM method. At this time, the calculated result is the efficiency value after eliminating environmental factors and random errors, which can more accurately reflect the technical efficiency level of the evaluation object.

[0104] Based on the calculation results of the adjusted DEA model, each dual-hub route is evaluated and the technical efficiency value of each dual-hub route is obtained, which will be used in the subsequent dual-hub route network optimization research.

[0105] A city's per capita GDP determines its level of economic development and, to a certain extent, reflects its size. Although this factor has a significant impact on air transportation, it needs to be excluded when evaluating route efficiency. This is because dual-hub airports pursue differentiated development. Their routes not only serve developed regions but, as hub airports, they also need to focus on the accessibility of routes to underdeveloped regions. If this factor is not used as an environmental variable, subsequent optimization will result in only routes to developed cities with high efficiency, while routes to underdeveloped cities will be restricted, which is not in line with the diversified development of dual-hub routes. Similarly, the proportion of peak-hour flights and route distance are also true. Due to limited airport capacity, it is impossible to concentrate all high-efficiency flights within peak hours. As an international hub airport, its route types include short-haul, long-haul, and intercontinental routes of various distances. Whether a route's flights fall within peak hours or the length of the route cannot affect the evaluation of route efficiency. Therefore, the proportion of peak-hour flights and route distance are used as environmental variables.

[0106] In step S3, a dual-hub route network optimization model is constructed, including making conditional assumptions on the optimization model, constructing an objective function, and setting constraints on the objective function.

[0107] At present, there are serious problems of route network homogeneity and low route operation efficiency between dual hub airports. The most important manifestation of route homogeneity is route overlap. In order to reduce the route homogeneity of dual hub airports and improve the operation efficiency of dual hub airports, and based on the operation characteristics of dual hub airports, considering the departure airport selection cost for passengers and the adjustment cost for airport operations brought by route adjustments, a route network optimization model is established with minimizing route overlap, route efficiency mismatch, passenger departure airport selection cost and route flight adjustment amount as objective functions. The model aims to take into account the cost of route adjustment while adjusting the dual hub routes with high overlap and low route efficiency, so as to optimize the overall route network of the dual hub.

[0108] To address the above issues, a capacity-constrained and strict multi-allocation dual-hub route network optimization model is constructed. The model assumes the following:

[0109] It mainly optimizes routes from the perspective of airports and passengers, without considering the differences in operating costs and benefits between airlines. It also believes that if airlines follow the advice, there will be fewer scheduling obstacles.

[0110] Regardless of the impact of schedules on routes and transfers, as long as two airports outside the dual hubs both have routes to one of the dual hubs, these two airports are considered to have the opportunity to transfer at the dual hub airport.

[0111] There will be no air routes between the two hubs;

[0112] Only passenger routes are considered, and stopover / transfer routes outside the dual hubs are not considered. Only direct routes are optimized;

[0113] The allocation of flight operations by airline to each route is not considered;

[0114] The flight frequency of the route is only the flight frequency of the route departing from the dual hub airports.

[0115] In step S3, constructing the objective function includes the following steps:

[0116] By analyzing the operational characteristics of dual-hub airports, the principles of reducing overlap, ensuring efficient route network operation, passenger convenience, and minimizing route adjustments are proposed. An objective function is established to minimize route overlap, minimize route efficiency mismatch, minimize passenger departure airport selection costs, and minimize route and flight adjustments. The objective functions are:

[0117] Objective 1: Minimize route overlap, which means the smaller the number of overlaps of the same route between the two hubs, the lower the probability of homogenization; The sum of the weekly flights that overlap between the dual hubs and airport i. Since only the number of overlapping flights at one of the dual hubs is counted, it needs to be multiplied by 2 to represent the weekly overlap of all flights on the dual hubs. The sum of the weekly flights on all routes of the dual hubs is:

[0118]

[0119] Where I is the set of dual-hub external airports that have routes with the dual-hub airports, i∈I; f ij (j=1,2) is a non-negative integer variable, which represents the weekly flight frequency of the route between airport i and dual hub airport j after optimization;

[0120] Goal 2: Minimize the route efficiency mismatch, which means that the smaller the efficiency mismatch of route ij, the more it conforms to the functional positioning of the dual hub airport. It represents the mismatch degree of route efficiency when route ij is opened. The higher the efficiency of the opened route, the lower the mismatch degree. The second part It represents the route efficiency mismatch when route ij is not opened. If those routes with higher efficiency are not opened, the route efficiency mismatch will be higher:

[0121]

[0122] Among them, ij is the technical efficiency of route ij. The higher the value, the higher the operational efficiency of the route, which is more in line with the functional positioning of the airport. Its value is obtained based on the route efficiency evaluation of the DEA model after three-stage adjustment in the first part, 0≤o ij ≤1;x ij It is a 0-1 variable, which is 1 when the route ij is opened, otherwise it is 0;

[0123] Objective 3: Minimize the cost of passengers choosing their departure airport, which means that the cost of passengers choosing their departure airport due to route adjustments is minimized. The first term c·[(1-x i1 )f i2 w i2 +(1-x i2 )f i1 w i1 ]·(1-x i1 x i2 ) represents the inter-airport access cost incurred by passengers who are forced to choose another airport when the routes do not overlap; the second term c·|f i1 w i1 -f i2 w i2 |(x i1 x i2 ) indicates that the cost incurred due to the difference in flight frequency between the two routes when the routes overlap:

[0124]

[0125] Where c is the average cost per passenger traveling to the dual hubs; w ij (j=1,2) is the average weekly passenger volume of each flight on route ij;

[0126] Objective 4: Minimize the amount of flight adjustments on each route, meaning that the difference between the weekly flight frequency of each route after optimization and the weekly flight frequency in the original pre-planned flight schedule is minimized:

[0127]

[0128] Among them, f ij ' is the weekly flight frequency of route ij before optimization.

[0129] In step S3, constraints are set on the objective function of the dual-hub route network optimization model, including:

[0130] Route flight constraint: represents the relationship between two optimization variables, namely the route frequency f ij With the decision variable x ij The relationship between them is that only when route ij is opened, there can be flights between airport i and airport j. Similarly, when the number of flights between airport i and airport j is zero, f ij = 0, route ij is not open, x ij =0:

[0131]

[0132] Dual-hub airport capacity constraints: After optimization, the weekly outbound flights of the dual-hub airports cannot exceed half of the inbound and outbound flights of each airport:

[0133]

[0134] Among them, F j is the weekly inbound and outbound flight capacity of dual-hub airport j;

[0135] Route opening constraints: If an airport outside the dual hubs has opened routes with the dual hub airports before optimization, it must open a route with at least one of the dual hub airports after optimization:

[0136]

[0137] Among them, 1 j Indicates that airport j among the dual hub airports has opened a route;

[0138] Flight capacity constraint: For any non-dual hub airport i, the flight frequency of the route between it and dual hub airport j cannot be higher than the total flight frequency of the two airports, and at least one flight must be opened:

[0139]

[0140] Decision variable constraints:

[0141]

[0142] Wherein, N is a set of non-negative integers.

[0143] In step S4, the dual-hub route network optimization model is solved using the reference point-based non-dominated sorting genetic algorithm (NSGA-III), where:

[0144] The principle of the NSGA-III algorithm is that in 1994, Srinivas and Deb proposed the non-dominated sorting genetic algorithm (NSGA), a genetic algorithm based on the concept of Pareto optimality. However, NSGA suffers from issues such as high computational complexity, lack of an elitist strategy, and the requirement for a specified sharing radius. In 2010, Deb designed the second-generation non-dominated sorting genetic algorithm (NSGA-II), building on NSGA. This algorithm addressed the shortcomings of NSGA and significantly improved its performance. While NSGA-II demonstrates excellent performance for solving bi-objective optimization problems, it is prone to falling into local optima when solving multi-objective optimization problems with three or more objectives. This is because the resulting solutions are unevenly distributed across the non-dominated layers. Therefore, to solve multi-objective optimization problems with more than three objectives, Deb improved the selection mechanism of NSGA-II, switching from a congestion-based selection mechanism to a reference point-based selection mechanism. This resulted in the design of the NSGA-III algorithm, which improves the algorithm's convergence and solution diversity.

[0145] Later, some scholars compared the calculation results using multiple numerical cases and found that NSGA-III outperformed NSGA-II in both solution time and convergence speed in multi-objective optimization. Some scholars also compared the performance of NSGA-II and NSGA-III by using different numbers of objectives and found that NSGA-III is more suitable for solving multi-objective optimization problems with 3 or more objectives. The NSGA-III algorithm has the following advantages:

[0146] (1) By introducing a reference point-based selection mechanism, the convergence and population diversity can be greatly improved. At the same time, the search direction is guided in the iterative process, so that the algorithm can solve multi-objective optimization problems of different forms and with complex diversity.

[0147] (2) Fast non-dominated sorting and efficient selection strategy are adopted to improve the search efficiency and solution efficiency of the algorithm.

[0148] Based on this, the present invention selects NSGA-III to solve the multi-objective optimization problem of the dual-hub route network. The basic principles and framework of the NSGA-III algorithm are similar to those of NSGA-II. The difference lies in the elite population retention strategy, that is, the use of a reference point-based selection mechanism. For the NSGA-III algorithm, the core of the reference point mechanism is the adaptive normalization of the population. Its main process includes ideal point calculation, translation of target values, calculation of each target extreme point, and population normalization. The calculation formula is as follows:

[0149]

[0150] Where M is the dimension of the multi-objective optimization problem, is the normalized value of the target for each individual in the population, Translate the target value for the population, y i (x) is the original target value of the population, a i is the intercept of the constructed linear hyperplane, is the minimum value of the population among N objective functions.

[0151] The overall process of the NSGA-III algorithm is as follows Figure 3 As shown, the algorithm process can be roughly divided into three stages, including crossover and mutation of the population, fast non-dominated sorting, and reference point-based selection;

[0152] Construct a set of reference points;

[0153] Randomly generate an initial population P containing N individuals t , then perform crossover and mutation of the population, and use binary crossover and polynomial mutation to generate a new population Q t , and with the population P t Combine to generate a new population R t ;

[0154] For population R t Perform fast non-dominated sorting to sort the population R t Small populations divided into multiple nondominant castes;

[0155] Select N individuals to enter the next generation population P t+1 , divided into two cases, one is to enter P according to the non-dominated level t+1 , the other is that if non-dominated level selection cannot be used, it is necessary to select individuals with sparse distribution around them to enter the population P through the reference point mechanism t+1 , when P t+1 The process stops when the number of individuals in is equal to N.

[0156] The present invention also proposes a dual-hub route network optimization system, comprising:

[0157] An evaluation index acquisition module is used to perform feature analysis on the dual-hub route to be optimized and obtain input indicators, output indicators, and environmental variables for evaluating the efficiency of the dual-hub route to be optimized;

[0158] The route efficiency evaluation module is used to establish a dual-hub route efficiency evaluation index system based on the input indicators, output indicators and environmental variables of the dual-hub route efficiency, evaluate the efficiency of the dual-hub routes, and obtain the technical efficiency value of each dual-hub route to be optimized;

[0159] The dual-hub route network optimization model construction module is used to analyze the operating characteristics of dual-hub airports based on the dual-hub route efficiency evaluation index system and technical efficiency values, and propose principles for reducing overlap rates, ensuring efficient route network operation, passenger convenience, and minimizing route adjustments. Based on these principles, a dual-hub route network optimization model is established with the goals of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection costs, and minimizing route and flight adjustments.

[0160] The route layout optimization module is used to solve the dual-hub route network optimization model, optimize the network layout of the dual-hub routes, and obtain optimization results.

[0161] The dual-hub route network optimization method based on route efficiency evaluation proposed in the present invention can effectively reduce the route overlap, route efficiency mismatch and passenger departure airport selection cost of dual-hub airports while meeting the airport operation capacity constraints and controlling the flight adjustment amount to be small. The optimized routes are more in line with the design positioning of efficient operation of dual hubs, and can effectively solve the problem of hindered operation efficiency of dual hubs due to unreasonable route layout, solve the problem of resource waste caused by route overlap in dual hub airports, alleviate the current situation of serious homogeneity of dual hubs, improve the overall operation efficiency of the dual-hub route network, and provide a theoretical basis and decision-making reference for the route network optimization strategy of dual hub airports to achieve efficient and differentiated operation, which has important practical value.

[0162] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

[0163] In addition, unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those skilled in the art to which the present invention belongs. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods related to the documents. In the event of any conflict with any incorporated document, the content of this specification shall prevail.

Claims

1. A dual-hub route network optimization method, characterized in that: The following steps are involved: Conduct characteristic analysis on the dual-hub routes to be optimized, and obtain input indicators, output indicators, and environmental variables for evaluating the efficiency of the dual-hub routes to be optimized; Based on the input indicators, output indicators and environmental variables of dual-hub route efficiency, a dual-hub route efficiency evaluation index system is established to evaluate the efficiency of dual-hub routes and obtain the technical efficiency value of each dual-hub route to be optimized; Based on the dual-hub route efficiency evaluation index system and technical efficiency values, the operational characteristics of dual-hub airports were analyzed, and principles were proposed for reducing overlap rates, ensuring efficient route network operation, facilitating passengers, and minimizing route adjustments. Based on these principles, a dual-hub route network optimization model was constructed with the goals of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection costs, and minimizing route and flight adjustments. Solve the dual-hub route network optimization model, optimize the network layout of the dual-hub routes, and obtain the optimization results; The construction of the dual-hub route network optimization model includes making assumptions, specifically: optimizing routes from the perspectives of airports and passengers, not considering the differences in operating route costs and benefits between airlines, and assuming that airlines follow suggestions and have fewer scheduling obstacles; not considering the impact of time slots on routes and transfers, and as long as two airports outside the dual hubs both open routes to one of the dual hubs, these two airports are considered to have the opportunity to transfer at the dual hub airport; no routes are opened between the dual hubs; only passenger routes are considered, and stopover / transfer routes outside the dual hubs are not considered, and only direct routes are optimized; not considering the airline's allocation of flight operations to each route; the flight frequency of a route is only the frequency of flights departing from the dual hub airport; The construction of the dual-hub route network optimization model also includes establishing an objective function, specifically including: by analyzing the operational characteristics of the dual-hub airports, proposing principles for reducing overlap, ensuring efficient route network operation, passenger convenience, and minimizing route adjustments, and establishing an objective function that minimizes route overlap, minimizes route efficiency mismatch, minimizes passenger departure airport selection costs, and minimizes route and flight adjustments, wherein: Objective 1: Minimize route overlap, which means the smaller the number of overlaps of the same route between the two hubs, the lower the probability of homogenization; Indicates dual hubs and airports i The sum of the weekly flights with overlapping routes. Since only the number of overlapping flights at one airport in the dual hub is calculated, it needs to be multiplied by 2 to express the number of overlapping flights on all routes of the dual hub airports in a week; The sum of the weekly flights on all routes of the dual hubs is: in, A collection of dual-hub external airports that have routes with the dual-hub airports. i =1,2,... I , Is a non-negative integer variable, representing the optimized airport and dual hub airports Weekly flight frequency between j =1,2; Goal 2: The route efficiency mismatch is minimal, indicating that the route ij The smaller the efficiency mismatch, the more it conforms to the functional positioning of the dual hub airport; among them, the first part Indicates the opening of routes ij The higher the efficiency of the opened route, the lower the mismatch; the second part Indicates that the route is not open ij If the routes with higher efficiency are not opened, the route efficiency mismatch will be higher. in, For routes ij technical efficiency, The higher the value, the higher the operating efficiency of the route, which is more in line with the functional positioning of the airport. The value is obtained based on the route efficiency evaluation of the DEA model after the three-stage adjustment in the first part, 0≤ ≤1; It is a 0-1 variable. When the route is opened ij 1 when it is, otherwise 0; Objective 3: Minimize the cost of passengers choosing their departure airport, which means that the cost of passengers choosing their departure airport due to route adjustments is minimized; the first The second term represents the inter-airport access cost incurred by passengers who are forced to choose another airport when the routes do not overlap; It indicates the cost incurred due to the difference in flight frequency between the two sides when the routes overlap; in, is the average cost per passenger traveling to the dual hubs; For routes ij The average weekly passenger volume of each flight; Objective 4: Minimize the amount of flight adjustments on each route, meaning that the difference between the weekly flight frequency of each route after optimization and the weekly flight frequency in the original pre-planned flight schedule is minimized: in, To optimize the previous route ij Weekly flight frequency; The construction of the dual-hub route network optimization model also includes setting constraints on the objective function, specifically including: route flight constraint: represents the relationship between the two optimization variables, namely, route frequency and decision variables The relationship between ij When it opened, the airport i and airports j There are flights between, and similarly, when the airport i and airports j There are zero flights between Time, route ij Not open, : Dual-hub airport capacity constraints: After optimization, the weekly outbound flights of the dual-hub airports cannot exceed half of the inbound and outbound flights of each airport: in, Dual hub airport j The capacity of flights arriving and departing during the week; Route opening constraints: If an airport outside the dual hubs has opened routes with the dual hub airports before optimization, it must open a route with at least one of the dual hub airports after optimization: Among them, 1 j Indicates the airport in a dual hub airport The route was opened; Flight capacity constraints: For any airport outside the dual hub i , which is a dual hub airport j The flight frequency of the route opened between them shall not be higher than the total of the known flight frequencies at the two airports, and at least one flight shall be opened: Decision variable constraints: in, , is a set of non-negative integers.

2. The dual-hub route network optimization method according to claim 1, characterized in that: The step of obtaining input indicators, output indicators, and environmental variables for evaluating the efficiency of the dual-hub route to be optimized includes the following steps: The input and output indicators of route efficiency evaluation are based on dual-hub passenger routes. Based on the availability and quantification of data, the input indicators, output indicators and environmental variables in the indicator system are constructed. Input indicators include flight frequency, fuel cost, available seats and the airfield grade of the airport at the point of access. Flight frequency, fuel cost and available seats represent the airline's investment cost and investment level for each route at the airport. The higher the flight frequency, fuel cost and available seats, the higher the investment cost for the route. The airfield grade of the airport at the point of access reflects the capacity and scale of the airport and the amount of transport capacity invested in the route. The higher the airfield grade, the larger the aircraft types used for take-off and landing at the airport, and the higher the transport capacity invested in the route. Output indicators include route passenger volume, route load factor, and revenue per passenger kilometer (RPK). These reflect the return on a route after a certain investment. The higher the route passenger volume, route load factor, and revenue per passenger kilometer (RPK), the higher the efficiency and return on the route. Environmental variables include per capita GDP of cities with air routes, proportion of flights during peak hours, and route distance.

3. The dual-hub route network optimization method according to claim 1, characterized in that: The step of obtaining the technical efficiency value of each route of the dual hub to be optimized includes the following steps: A three-stage data envelopment analysis (DEA) was used to evaluate the efficiency of the dual-hub routes to be optimized. The DEA consists of three stages: The first stage: the traditional DEA model, which measures the efficiency value by selecting the non-radial and non-angular Super-SBM method; Phase II: SFA model construction. By extracting the input slack from the evaluation results of the first phase as the dependent variable and selecting environmental factors as the independent variables, the SFA model is constructed as follows: in, For the n Evaluation object i The amount of slack in the input, n =1,2,..., N , i =1,2,... I， is the environmental impact function, z i For environment variables, is the coefficient of the environmental variable, represents the random error term, which is assumed to obey the standard normal distribution; To manage inefficiency, a truncated normal distribution is assumed; The SFA model regression results can be separated into Item, estimated by derivation Part, obtain the random error term estimation results; Taking the most efficient decision-making unit input as the benchmark, the other decision-making units are adjusted to the input under the same operating environment. The adjusted SFA model is: in, and Respectively n evaluation object i The results before and after the input adjustment, and They represent the same external environment and the same luck level after adjustment; The third stage: the adjusted DEA model uses the adjusted input data to replace the original input data, and the efficiency value is recalculated using the non-radial and non-angular Super-SBM method. The calculated result is the efficiency value after eliminating environmental factors and random errors; Based on the calculation results of the adjusted DEA model, each route of the dual hub is evaluated and the technical efficiency value of each route of the dual hub is obtained.

4. The dual-hub route network optimization method according to claim 1, characterized in that: The construction of the dual-hub route network optimization model also includes setting constraints on the objective function, specifically including: Route flight constraint: represents the relationship between two optimization variables, namely route frequency and decision variables The relationship between ij When it opened, the airport i and airports j There are flights between, and similarly, when the airport i and airports j There are zero flights between Time, route ij Not open, : Dual-hub airport capacity constraints: After optimization, the weekly outbound flights of the dual-hub airports cannot exceed half of the inbound and outbound flights of each airport: in, Dual hub airport j The capacity of flights arriving and departing during the week; Route opening constraints: If an airport outside the dual hubs has opened routes with the dual hub airports before optimization, it must open a route with at least one of the dual hub airports after optimization: Among them, 1 j Indicates the airport in a dual hub airport The route was opened; Flight capacity constraints: For any airport outside the dual hub i , which is a dual hub airport j The flight frequency of the route opened between them shall not be higher than the total of the known flight frequencies at the two airports, and at least one flight shall be opened: Decision variable constraints: in, is a set of non-negative integers.

5. The dual-hub route network optimization method according to claim 4, characterized in that: Solving the dual-hub route network optimization model includes the following steps: A non-dominated sorting genetic algorithm based on reference points is used to solve the dual-hub route network optimization model. The algorithm process of the non-dominated sorting genetic algorithm based on reference points is divided into three stages, including crossover and mutation of the population, fast non-dominated sorting, and selection based on reference points. Construct a set of reference points; Randomly generate a N The initial population of individuals P t , then perform crossover and mutation of the population, and use binary crossover and polynomial mutation to generate a new population Q t , and with the population P t Combine to form a new population R t ; For populations R t Perform fast non-dominated sorting and sort the population R t Small populations divided into multiple nondominant castes; choose N Individuals enter the next generation of the population P t+1 , divided into two cases, one is to enter according to the non-dominant level P t+1 If non-dominated hierarchical selection cannot be used, the reference point mechanism should be used to select individuals with sparse distribution around them to enter the population. P t+1 ,when P t+1 The number of individuals in is equal to N Then stop.

6. A dual-hub route network optimization system, characterized in that: include: An evaluation index acquisition module is used to perform feature analysis on the dual-hub route to be optimized and obtain input indicators, output indicators, and environmental variables for evaluating the efficiency of the dual-hub route to be optimized; The route efficiency evaluation module is used to establish a dual-hub route efficiency evaluation index system based on the input indicators, output indicators and environmental variables of the dual-hub route efficiency, evaluate the efficiency of the dual-hub routes, and obtain the technical efficiency value of each dual-hub route to be optimized; The dual-hub route network optimization model construction module is used to analyze the operating characteristics of dual-hub airports based on the dual-hub route efficiency evaluation index system and technical efficiency values, and propose principles for reducing overlap rates, ensuring efficient route network operation, passenger convenience, and minimizing route adjustments. Based on these principles, a dual-hub route network optimization model is established with the goals of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection costs, and minimizing route and flight adjustments. The route layout optimization module is used to solve the dual-hub route network optimization model, optimize the network layout of the dual-hub routes, and obtain the optimization results; The construction of the dual-hub route network optimization model includes making assumptions, specifically: optimizing routes from the perspectives of airports and passengers, not considering the differences in operating route costs and benefits between airlines, and assuming that airlines follow suggestions and have fewer scheduling obstacles; not considering the impact of time slots on routes and transfers, and as long as two airports outside the dual hubs both open routes to one of the dual hubs, these two airports are considered to have the opportunity to transfer at the dual hub airport; no routes are opened between the dual hubs; only passenger routes are considered, and stopover / transfer routes outside the dual hubs are not considered, and only direct routes are optimized; not considering the airline's allocation of flight operations to each route; the flight frequency of a route is only the frequency of flights departing from the dual hub airport; The construction of the dual-hub route network optimization model also includes establishing an objective function, specifically including: by analyzing the operational characteristics of the dual-hub airports, proposing principles for reducing overlap, ensuring efficient route network operation, passenger convenience, and minimizing route adjustments, and establishing an objective function that minimizes route overlap, minimizes route efficiency mismatch, minimizes passenger departure airport selection costs, and minimizes route and flight adjustments, wherein: Objective 1: Minimize route overlap, which means the smaller the number of overlaps of the same route between the two hubs, the lower the probability of homogenization; Indicates dual hubs and airports i The sum of the weekly flights with overlapping routes. Since only the number of overlapping flights at one airport in the dual hub is calculated, it needs to be multiplied by 2 to express the number of overlapping flights on all routes of the dual hub airports in a week; The sum of the weekly flights on all routes of the dual hubs is: in, A collection of dual-hub external airports that have routes with the dual-hub airports. i =1,2,... I ; Is a non-negative integer variable, representing the optimized airport and dual hub airports Weekly flight frequency between j =1,2; Goal 2: The route efficiency mismatch is minimal, indicating that the route ij The smaller the efficiency mismatch, the more it conforms to the functional positioning of the dual hub airport; among them, the first part Indicates the opening of routes ij The higher the efficiency of the opened route, the lower the mismatch; the second part Indicates that the route is not open ij If the routes with higher efficiency are not opened, the route efficiency mismatch will be higher. in, For routes ij technical efficiency, The higher the value, the higher the operating efficiency of the route, which is more in line with the functional positioning of the airport. The value is obtained based on the route efficiency evaluation of the DEA model after the three-stage adjustment in the first part, 0≤ ≤1; It is a 0-1 variable. When the route is opened ij 1 when it is, otherwise 0; Objective 3: Minimize the cost of passengers choosing their departure airport, which means that the cost of passengers choosing their departure airport due to route adjustments is minimized; the first The second term represents the inter-airport access cost incurred by passengers who are forced to choose another airport when the routes do not overlap; It indicates the cost incurred due to the difference in flight frequency between the two sides when the routes overlap; in, is the average cost per passenger traveling to the dual hubs; For routes ij The average weekly passenger volume of each flight; Objective 4: Minimize the amount of flight adjustments on each route, meaning that the difference between the weekly flight frequency of each route after optimization and the weekly flight frequency in the original pre-planned flight schedule is minimized: in, To optimize the previous route ij Weekly flight frequency; The construction of the dual-hub route network optimization model also includes setting constraints on the objective function, specifically including: route flight constraint: represents the relationship between the two optimization variables, namely, route frequency and decision variables The relationship between ij When it opened, the airport i and airports j There are flights between, and similarly, when the airport i and airports j There are zero flights between Time, route ij Not open, : Dual-hub airport capacity constraints: After optimization, the weekly outbound flights of the dual-hub airports cannot exceed half of the inbound and outbound flights of each airport: in, Dual hub airport j The capacity of flights arriving and departing during the week; Route opening constraints: If an airport outside the dual hubs has opened routes with the dual hub airports before optimization, it must open a route with at least one of the dual hub airports after optimization: Among them, 1 j Indicates the airport in a dual hub airport The route was opened; Flight capacity constraints: For any airport outside the dual hub i , which is a dual hub airport j The flight frequency of the route opened between them shall not be higher than the total of the known flight frequencies at the two airports, and at least one flight shall be opened: Decision variable constraints: in, , is a set of non-negative integers.

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