Double-hub airline network optimization method and system

Abstract

The invention discloses a dual-hub airline network optimization method and system, and belongs to the technical field of civil aviation flight, and the method comprises the steps: building a dual-hub airline efficiency evaluation index system through obtaining an input index, an output index and an environment variable for evaluating the efficiency of a to-be-optimized dual-hub airline, and carrying out the efficiency evaluation of the dual-hub airline. The technical efficiency value of each route of the to-be-optimized dual hub is obtained to analyze the operation characteristics of the dual hub airport, and the principles of reduction of the coincidence rate, efficient operation of the route network, convenience of passengers and minimum route adjustment amplitude are put forward. And establishing a dual-hub airline network optimization model by taking the minimum airline overlap ratio, the minimum airline efficiency mismatching degree, the minimum passenger departure airport selection cost and the minimum airline flight adjustment amount as targets, performing solving, and optimizing the network layout of the dual-hub airline to obtain an optimization result. According to the method, the efficiency is evaluated before optimization, the double-hub overall route efficiency is improved, and differentiation and high efficiency of a double-hub route network can be achieved.

Description

Technical Field

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

[0002] The total number of civil airports in my country has taken shape, the airport density has gradually increased, the airport service capacity has gradually improved, the civil transport airport system has been initially established, and several major airport cluster systems have taken shape, especially more and more cities have begun to develop dual hub airports, such as Beijing, Shanghai and Chengdu. However, the domestic dual hub model is just starting, and the work on differentiation and efficient development is still in the initial exploration stage. There are some routes between the two airports that are inefficient and the route network layout is unreasonable, which cannot achieve the effect of functional complementarity and coordinated development between airports.

[0003] At present, the technical solutions for route network optimization methods at home and abroad are mainly concentrated on the level of a single airport or the entire country. There are few methods for optimizing route networks of multiple airports, especially dual hubs. The 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 the development model of multiple airports, especially dual hubs, is relatively mature. However, most of my country's research on dual hubs remains at the macro level. Research on dual hub route layout has just started, and most of the existing route network optimization models are traditional hub-and-spoke models. There is a lack of research on route network optimization based on the operating characteristics of dual hub airports, and no feasible improvement plan has been proposed for the route network of airport clusters. 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 caused by 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] In order 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] According to 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 values ​​of each dual-hub route to be optimized;

[0008] According to the dual-hub route efficiency evaluation index system and technical efficiency value, the operating characteristics of dual-hub airports are analyzed, and the principles of reducing overlap rate, efficient operation of route network, passenger convenience and minimum route adjustment are proposed; according to the principles of reducing overlap rate, efficient operation of route network, passenger convenience and minimum route adjustment, 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 cost and minimizing route and flight adjustment;

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

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

[0011] The input and output of route efficiency evaluation refers to the dual-hub passenger routes, based on the availability and quantifiability of data, to construct input indicators, output indicators and environmental variables in the indicator system, among which:

[0012] The input indicators include flight frequency, fuel cost, number of available seats and the level of airfield at the airport. Flight frequency, fuel cost and number of available seats indicate the investment cost and level of the airline for each route of the airport. The larger the values ​​of flight frequency, fuel cost and available seats, the higher the investment cost of the route. The level of airfield at the airport reflects the capacity and scale of the airport and the amount of transport capacity invested in the route. The higher the level of the airfield, 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 passenger load factor and passenger-kilometer revenue; route passenger volume, route passenger load factor and passenger-kilometer revenue reflect the revenue of the route after a certain cost is invested. The higher the route passenger volume, route passenger load factor and passenger-kilometer revenue, the higher the efficiency and return of 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] The three-stage data envelopment analysis is used to evaluate the efficiency of the dual-hub routes to be optimized. The three-stage data envelopment analysis includes 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] The second stage: SFA model construction, by extracting the input slack from the evaluation results of the first stage as the dependent variable, selecting environmental factors as independent variables, and constructing the SFA model 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 environment 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, 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 of the i-th input of the n-th evaluation object before and after adjustment, and They represent the same external environment and the same luck level after adjustment respectively;

[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] According to the calculation results of the adjusted DEA model, each route of the dual hubs is evaluated and the technical efficiency value of each route of the dual hubs 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 route costs and benefits between airlines, and believes that if airlines follow advice, there will be fewer scheduling obstacles;

[0029] Regardless of the impact of the schedule on routes and transfers, as long as two airports outside the dual hubs have opened 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 are no 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 airlines to each route is not taken into account;

[0033] The flight frequency of a 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 operating characteristics of dual hub airports, the principles of reducing overlap rate, efficient operation of route network, passenger convenience and minimum route adjustment are proposed, and the objective function of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection cost and minimizing route and flight adjustment is established, among which:

[0036] Objective 1: Minimize the overlap of routes, which means that the smaller the overlap of the same route between the two hubs, the smaller the probability of homogenization; It represents the sum of the weekly flights that overlap with the dual hubs and airport i. Since only the number of overlapping flights at one airport in the dual hubs is calculated, it needs to be multiplied by 2 to represent the number of overlapping flights on all routes of the dual hub airports in one week. The sum of the weekly flights of 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 indicates the weekly flight frequency of the route between airport i and dual hub airport j after optimization;

[0039] Objective 2: Minimize the route efficiency mismatch, which means that the smaller the efficiency mismatch of route ij is, the more it conforms to the functional positioning of the dual hub airport; the first part It represents the mismatch degree of route efficiency when opening route ij. 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 the departure airport, which means that the cost of passengers choosing the departure airport due to route adjustment 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 there is overlap in routes;

[0043]

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

[0045] Goal 4: Minimize the amount of flight adjustments on routes, which means that the difference between the weekly flight frequency of each route after optimization and the weekly flight frequency in the original pre-flight schedule is minimal:

[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 decision variables 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 number of outbound flights per week at dual-hub airports cannot exceed half of the number of inbound and outbound flights at each airport:

[0052]

[0053] Among them, F j is the capacity of inbound and outbound flights at dual hub airport j in one week;

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

[0055]

[0056] Among them, 1 j It means that airport j in the dual hub airport has opened a route;

[0057] Flight volume constraint: For any non-dual hub airport i, the flight frequency of the route opened between it and the dual hub airport j shall not be higher than the total of the known flight frequencies at 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] The dual-hub route network optimization model is solved by using a non-dominated sorting genetic algorithm based on reference points. 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, the population is crossovered and mutated, and a new population Q is generated using binary crossover and polynomial mutation. 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 If non-dominated rank selection cannot be used, the reference point mechanism is used to select individuals with sparse distribution around them to enter the population P. t+1 , when P t+1 Stop when the number of individuals in is equal to N.

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

[0069] An evaluation index acquisition module is used to perform feature analysis on the dual-hub routes to be optimized, and to obtain input indicators, output indicators and environmental variables for evaluating the efficiency of the dual-hub routes 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 value, and propose principles for reducing overlap rates, efficient route network operation, passenger convenience, and minimal route adjustment; based on the principles of reducing overlap rates, efficient route network operation, passenger convenience, and minimal route adjustment, 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 the present 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 the problem of low efficiency of some routes and resource waste caused by route network overlap. The method optimizes the network layout of dual-hub routes by constructing a route efficiency evaluation index system and a dual-hub route network optimization model. It can effectively reduce the route overlap, route efficiency mismatch and passenger departure airport selection cost of dual-hub airports while satisfying the airport operation capacity limit 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 of dual hub airports, alleviate the current situation of serious homogeneity of dual hubs, improve the overall operation efficiency of dual hub route networks, 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 It is a 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 will be combined with the attached embodiment 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 described in the present invention are only used to describe specific implementation methods and are not used 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 optimizing route networks with multiple airports, especially dual hubs. At present, most technical solutions adopt the following methods: 1) Research on the optimization problem of a single hub network 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 solving it; 3) Use a route network model with capacity constraints based on a time window 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 according to 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 the hub construction cost and congestion cost, 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 cluster route collaborative optimization model is constructed. This model is customized The hub airports in the airport cluster, the small and medium-sized airports in the airport cluster connect to the hub airport to realize the transfer of passengers and cargo, and 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, so the p-hub median problem method is used to construct a regional multi-airport system route network model, and the routes with serious homogeneity are optimized, and the taboo search algorithm and the shortest path algorithm are combined to solve the problem; 10) It is found that there are insufficient airport routes and unreasonable resource allocation in the region. 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, and 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, 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, the relationship between airport subsidy strategy and airline route adjustment is studied, and a two-layer game model between passengers, airlines and airports is constructed to determine the optimal route network and the best pricing strategy for airlines in the airport cluster.

[0080] In order to overcome the shortcomings of the prior art, 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 operating 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 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 my country's dual-hub airports and make them more efficient and differentiated.

[0081] Example

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

[0083] S1: 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;

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

[0085] S3: Based on the dual-hub route efficiency evaluation index system and technical efficiency values, the operating characteristics of dual-hub airports are analyzed, and the principles of reducing overlap rate, efficient operation of route network, passenger convenience and minimum route adjustment are proposed; based on the principles of reducing overlap rate, efficient operation of route network, passenger convenience and minimum route adjustment, 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 cost and minimizing route and flight adjustment;

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

[0087] In step S1, the input index, output index and environmental variables for evaluating the efficiency of the dual-hub route to be optimized are obtained, including the following steps:

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

[0089] The input indicators include flight frequency, fuel cost, number of available seats and the level of airfield at the airport. Flight frequency, fuel cost and number of available seats indicate the investment cost and level of the airline for each route of the airport. The larger the values ​​of flight frequency, fuel cost and available seats, the higher the investment cost of the route. The level of airfield at the airport reflects the capacity and scale of the airport and the amount of transport capacity invested in the route. The higher the level of the airfield, 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 passenger load factor and passenger-kilometer revenue; route passenger volume, route passenger load factor and passenger-kilometer revenue reflect the revenue of the route after a certain cost is invested. The higher the route passenger volume, route passenger load factor and passenger-kilometer revenue, the higher the efficiency and return of 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, including the following steps:

[0093] The three-stage data envelopment analysis, i.e. the three-stage DEA model, is adopted. DEA is a traditional non-parametric calculation method, which is mainly used to evaluate the input-output efficiency. This method uses linear programming and statistical data to determine the relatively effective frontier, in which the statistical data does not need to be preprocessed and the operation is relatively simple, so the application field and scope of this method are very wide.

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

[0095] The first stage: the traditional DEA model uses input and output indicator data to calculate the efficiency value of the decision-making unit. Considering that the input slack is difficult to fully participate in the efficiency value evaluation due to the large number of input indicators, the present invention 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 so that multiple decision-making units are in a relatively consistent external environment 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 environment variable, β n is the coefficient of the environmental variable, V in represents the random error term, which is assumed to follow 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, and 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 a benchmark, adjusts 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 of the i-th input of the n-th evaluation object before and after adjustment, and They represent the same external environment and the same luck level after adjustment respectively;

[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] According to 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, which will be used in the subsequent dual hub route network optimization research.

[0105] The per capita GDP of a city determines the level of economic development and reflects the size of the city to a certain extent. Although this factor has a great impact on air transportation, it is necessary to exclude the influence of this factor when evaluating route efficiency because dual-hub airports pursue differentiated development. Their routes are not only connected to developed areas. As a hub airport, they should also pay attention to the accessibility of routes to underdeveloped areas. If it is not used as an environmental variable, it will lead to the opening of only developed city routes with high efficiency in subsequent optimization, while underdeveloped city routes 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 distances are also the same. Due to limited airport capacity, it is impossible to concentrate all efficient flights within the peak hours. As an international hub airport, the route types include short-distance, long-distance and intercontinental routes of various distances. The evaluation results of route efficiency cannot be affected by whether the flights on the route are within the peak hours and the size of the route distance. 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 caused 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 as objective functions. This model aims to adjust the dual hub routes with high overlap and low efficiency while taking into account the cost of route adjustment, so as to optimize the overall route network of the dual hubs.

[0108] Aiming at the above problems, a dual-hub route network optimization model with strict multi-allocation and capacity constraints is constructed. The model assumptions are as follows:

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

[0110] Regardless of the impact of the schedule on routes and transfers, as long as two airports outside the dual hubs have opened 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 are no 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 airlines to each route is not taken into account;

[0114] The flight frequency of a 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 operating characteristics of dual hub airports, the principles of reducing overlap rate, efficient operation of route network, passenger convenience and minimum route adjustment are proposed, and the objective function of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection cost and minimizing route and flight adjustment is established, among which:

[0117] Objective 1: Minimize the overlap of routes, which means that the smaller the overlap of the same route between the two hubs, the smaller the probability of homogenization; It represents the sum of the weekly flights that overlap with the dual hubs and airport i. Since only the number of overlapping flights at one airport in the dual hubs is calculated, it needs to be multiplied by 2 to represent the number of overlapping flights on all routes of the dual hub airports in one week. The sum of the weekly flights of 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 indicates the weekly flight frequency of the route between airport i and dual hub airport j after optimization;

[0120] Objective 2: Minimize the route efficiency mismatch, which means that the smaller the efficiency mismatch of route ij is, the more it conforms to the functional positioning of the dual hub airport. It represents the mismatch degree of route efficiency when opening route ij. 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 operating 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 is a 0-1 variable, which is 1 when route ij is opened, otherwise it is 0;

[0123] Objective 3: Minimize the cost of passengers choosing the departure airport, which means that the cost of passengers choosing the departure airport due to route adjustment 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 routes overlap but the cost is incurred due to the difference in flight frequency between the two sides:

[0124]

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

[0126] Goal 4: Minimize the amount of flight adjustments on routes, which means that the difference between the weekly flight frequency of each route after optimization and the weekly flight frequency in the original pre-flight schedule is minimal:

[0127]

[0128] Among them, f ij 'To optimize the weekly flight frequency of route ij.

[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 decision variables 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 number of outbound flights per week at dual-hub airports cannot exceed half of the number of inbound and outbound flights at each airport:

[0133]

[0134] Among them, F j is the capacity of inbound and outbound flights at dual hub airport j in one week;

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

[0136]

[0137] Among them, 1 j It means that airport j in the dual hub airport has opened a route;

[0138] Flight volume constraint: For any non-dual hub airport i, the flight frequency of the route opened between it and the dual hub airport j shall not be higher than the total of the known flight frequencies at 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 a reference point-based non-dominated sorting genetic algorithm (NSGA-III), where:

[0144] The principle of NSGA-Ⅲ algorithm is that in 1994, Srinivas and Deb proposed the non-dominated sorting genetic algorithm (NSGA), which is a genetic algorithm based on the concept of Pareto optimality. However, the NSGA algorithm has problems such as high computational complexity, no elite strategy, and the need to specify a shared radius. In 2010, Deb designed the second generation non-dominated sorting genetic algorithm (NSGA-II) based on NSGA, improved the defects of NSGA, and greatly improved the performance of the algorithm. NSGA-II algorithm shows excellent performance in solving dual-objective optimization problems, but it is easy to fall into local optimality when solving multi-objective optimization with three or more objectives, because the obtained solutions will be unevenly distributed on the non-dominated layer. Therefore, in order to solve multi-objective optimization problems with more than three objectives, Deb improved the selection mechanism of NSGA-II, changed the congestion selection mechanism to the reference point-based selection mechanism, and designed the NSGA-III algorithm, which increased the convergence of the algorithm and the diversity of solutions.

[0145] Later, some scholars compared the calculation results using multiple numerical cases and found that NSGA-III is superior to NSGA-II in solution time and convergence speed in multi-objective optimization. Some scholars 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 can be 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 strategies 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 principle and framework of the NSGA-III algorithm are approximately the same as those of NSGA-II. The difference is the elite population retention strategy, that is, the reference point-based selection mechanism is adopted. 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 target value, 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 selection based on reference points;

[0152] Construct a set of reference points;

[0153] Randomly generate an initial population P containing N individuals t Then, the population is crossovered and mutated, and a new population Q is generated using binary crossover and polynomial mutation. 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 If non-dominated rank selection cannot be used, the reference point mechanism is used to select individuals with sparse distribution around them to enter the population P. t+1 , when P t+1 Stop 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 routes to be optimized, and to obtain input indicators, output indicators and environmental variables for evaluating the efficiency of the dual-hub routes 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 value, and propose principles for reducing overlap rates, efficient route network operation, passenger convenience, and minimal route adjustment; based on the principles of reducing overlap rates, efficient route network operation, passenger convenience, and minimal route adjustment, 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 for dual hub airports to achieve efficient and differentiated operation, which has important practical value.

[0162] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

[0163] In addition, unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings 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; According to 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 values ​​of each dual-hub route to be optimized; According to the dual-hub route efficiency evaluation index system and technical efficiency value, the operating characteristics of dual-hub airports are analyzed, and the principles of reducing overlap rate, efficient operation of route network, passenger convenience and minimum route adjustment are proposed; according to the principles of reducing overlap rate, efficient operation of route network, passenger convenience and minimum route adjustment, 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 cost and minimizing route and flight adjustment; The dual-hub route network optimization model is solved, the network layout of the dual-hub routes is optimized, and the optimization results are obtained.

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 routes to be optimized includes the following steps: The input and output of route efficiency evaluation refers to the dual-hub passenger routes, based on the availability and quantifiability of data, to construct input indicators, output indicators and environmental variables in the indicator system, among which: The input indicators include flight frequency, fuel cost, number of available seats and the level of airfield at the airport. Flight frequency, fuel cost and number of available seats indicate the investment cost and level of the airline for each route of the airport. The larger the values ​​of flight frequency, fuel cost and available seats, the higher the investment cost of the route. The level of airfield at the airport reflects the capacity and scale of the airport and the amount of transport capacity invested in the route. The higher the level of the airfield, 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 passenger load factor and passenger-kilometer revenue; route passenger volume, route passenger load factor and passenger-kilometer revenue reflect the revenue of the route after a certain cost is invested. The higher the route passenger volume, route passenger load factor and passenger-kilometer revenue, the higher the efficiency and return of 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: The three-stage data envelopment analysis is used to evaluate the efficiency of the dual-hub routes to be optimized. The three-stage data envelopment analysis includes 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; The second stage: SFA model construction, by extracting the input slack from the evaluation results of the first stage as the dependent variable, selecting environmental factors as independent variables, and constructing the SFA model as follows: S in =f i (z i ,β n )+V in +U in (i=1,2,...,I;n=1,2,...,N) 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 environment 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; 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; Taking the most efficient decision-making unit input as the benchmark, other decision-making units are adjusted to the input under the same operating environment. The adjusted SFA model is: Among them, x in and are the results of the i-th input of the n-th evaluation object before and after adjustment, and They represent the same external environment and the same luck level after adjustment respectively; 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. According to the calculation results of the adjusted DEA model, each route of the dual hubs is evaluated and the technical efficiency value of each route of the dual hubs is obtained.

4. The dual-hub route network optimization method according to claim 3, characterized in that: The construction of the dual-hub route network optimization model includes making assumptions, specifically including: It mainly optimizes routes from the perspective of airports and passengers, without considering the differences in operating route costs and benefits between airlines, and believes that if airlines follow advice, there will be fewer scheduling obstacles; Regardless of the impact of the schedule on routes and transfers, as long as two airports outside the dual hubs have opened routes to one of the dual hubs, these two airports are considered to have the opportunity to transfer at the dual hub airport; There are no routes between the two hubs; Only passenger routes are considered, and stopover / transfer routes outside the dual hubs are not considered. Only direct routes are optimized; The allocation of flight operations by airlines to each route is not taken into account; The flight frequency of a route is only the flight frequency of the route departing from the dual hub airports.

5. The dual-hub route network optimization method according to claim 4, characterized in that: The construction of the dual-hub route network optimization model also includes establishing an objective function, specifically including: By analyzing the operating characteristics of dual hub airports, the principles of reducing overlap rate, efficient operation of route network, passenger convenience and minimum route adjustment are proposed, and the objective function of minimizing route overlap, minimizing route efficiency mismatch, minimizing passenger departure airport selection cost and minimizing route and flight adjustment is established, among which: Objective 1: Minimize the overlap of routes, which means that the smaller the overlap of the same route between the two hubs, the smaller the probability of homogenization; It represents the sum of the weekly flights that overlap with the dual hubs and airport i. Since only the number of overlapping flights at one airport in the dual hubs is calculated, it needs to be multiplied by 2 to represent the number of overlapping flights on all routes of the dual hub airports in one week. The sum of the weekly flights of all routes of the dual hubs is: 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 indicates the weekly flight frequency of the route between airport i and dual hub airport j after optimization; Objective 2: Minimize the route efficiency mismatch, which means that the smaller the efficiency mismatch of route ij is, the more it conforms to the functional positioning of the dual hub airport; the first part It represents the mismatch degree of route efficiency when opening route ij. 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; 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; Objective 3: Minimize the cost of passengers choosing the departure airport, which means that the cost of passengers choosing the departure airport due to route adjustment 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 there is overlap in routes; Where c is the average access cost per passenger to the dual hubs; w ij (j=1,2) is the average weekly passenger volume of each flight on route ij; Goal 4: Minimize the amount of flight adjustments on routes, which means that the difference between the weekly flight frequency of each route after optimization and the weekly flight frequency in the original pre-flight schedule is minimal: Among them, f ij '(j=1,2) is the weekly flight frequency of route ij before optimization.

6. The dual-hub route network optimization method according to claim 5, 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, the route frequency f ij With decision variables 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: Dual-hub airport capacity constraints: After optimization, the number of outbound flights per week at dual-hub airports cannot exceed half of the number of inbound and outbound flights at each airport: Among them, F j is the capacity of inbound and outbound flights at dual hub airport j in one week; Route opening constraints: If an airport other than the dual hub airport has opened routes with the dual hub airport before optimization, it must open routes with at least one of the dual hub airports after optimization: Among them, 1 j It means that airport j in the dual hub airport has opened a route; Flight volume constraint: For any non-dual hub airport i, the flight frequency of the route opened between it and the dual hub airport j shall not be higher than the total of the known flight frequencies at the two airports, and at least one flight must be opened: Decision variable constraints: Wherein, N is a set of non-negative integers.

7. The dual-hub route network optimization method according to claim 6, characterized in that: The method of solving the dual-hub route network optimization model comprises the following steps: The dual-hub route network optimization model is solved by using a non-dominated sorting genetic algorithm based on reference points. 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 an initial population P containing N individuals t Then, the population is crossovered and mutated, and a new population Q is generated using binary crossover and polynomial mutation. t , and with the population P t Combine to generate a new population R t ; For population R t Perform fast non-dominated sorting and sort the population R t Small populations divided into multiple nondominant castes; 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 If non-dominated rank selection cannot be used, the reference point mechanism is used to select individuals with sparse distribution around them to enter the population P. t+1 , when P t+1 Stop when the number of individuals in is equal to N.

8. 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 routes to be optimized, and to obtain input indicators, output indicators and environmental variables for evaluating the efficiency of the dual-hub routes 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 value, and propose principles for reducing overlap rates, efficient route network operation, passenger convenience, and minimal route adjustment; based on the principles of reducing overlap rates, efficient route network operation, passenger convenience, and minimal route adjustment, 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 optimization results.

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