Airport cluster spatial layout optimization method based on reachability

Abstract

This invention relates to a method for optimizing the spatial layout of airport clusters based on accessibility, comprising the following steps: Step 1, dividing a predetermined area into regional grids; Step 2, randomly generating m feasible airport cluster layout strategies P based on the grid division results of area A. m Step 3: Establish an airport cluster spatial satisfaction model and construct an objective function Z based on airport distance satisfaction; Step 4: Model calculation; Step 5: Layout optimization and iterative adjustment; Step 6: Obtain the airport cluster spatial layout strategy P. m and the global optimal solution P g The system outputs the maximum spatial satisfaction value of the airport cluster, max Z, which can rationally plan the structure and spatial distribution of the airport cluster, break through the bottleneck of the overall service quality of the airport cluster, improve operational efficiency, and provide support for improving the service quality of the airport cluster system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of optimization methods. Specifically, it relates to an airport cluster spatial layout optimization method based on accessibility. BACKGROUND

[0002] In the field of existing traffic planning and major project management, related research on the uneven development of airport cluster systems mostly focuses on coordinated operation and management of airport clusters, and there is little research on spatial planning and layout of airport cluster systems. However, compared with coordinated operation and management methods, reasonable spatial planning and layout of airport cluster systems are the basic prerequisite for breaking the bottleneck of overall service quality and operational efficiency of airport clusters, and are an important support for optimizing airport airspace flow and operation management methods. In order to analyze the influence of spatial layout of airport cluster systems on overall service quality and accessibility, an airport cluster spatial layout analysis model based on accessibility is established, considering multiple constraint conditions such as total construction cost, coverage range and airport carrying capacity, exploring different spatial layout forms of airport clusters and analyzing their spatio-temporal accessibility, which can provide support for optimizing the spatial structure of airport clusters and improving airport service quality. SUMMARY

[0003] In view of the problems in the prior art, the present application aims to provide an airport cluster spatial layout optimization method based on accessibility, which can reasonably plan the structure and spatial distribution of airport cluster systems, break the bottleneck of overall service quality of airport clusters and improve operational efficiency. Another purpose of the present application is to establish an airport cluster spatial layout model based on accessibility, and based on the nonlinear characteristics of the model, a fast solution method based on the particle swarm algorithm is proposed. At the same time, considering the aggregation and randomness of demand distribution, as well as the coverage range, construction cost and support capacity of different types of airports, the influence of spatial layout of airport cluster systems on overall service quality is analyzed. In addition, the change trend of overall satisfaction of airport cluster systems under the condition of resource change is discussed, which provides support for improving the service quality of airport cluster systems.

[0004] The technical solution of the present application is as follows:

[0005] An airport cluster spatial layout optimization method based on accessibility comprises:

[0006] Step 1: regional grid division is performed for a predetermined area;

[0007] Step 2: m feasible airport cluster layout strategies P are randomly generated based on the grid division results of region A m ;

[0008] Step 3: an airport cluster spatial satisfaction model is established, and an objective function Z is constructed according to airport distance satisfaction;

[0009] Step 4: model calculation;

[0010] Step five: layout optimization iterative adjustment;

[0011] Step six: get the airport cluster spatial layout strategy P m , and the global optimal solution P g , output the maximum airport cluster spatial satisfaction max Z.

[0012] Preferably, for the predetermined area A, the area A is covered with a square grid, which divides the area A into n1 rows and n2 columns of sub-areas, and each sub-area covers the entire area A.

[0013] Preferably, any sub-area can be represented as (i,j):

[0014]

[0015] Wherein: N1={1,2,3,…,n1-1,n1} represents a set of position numbers i;

[0016] N2={1,2,3,…,n2-1,n2} represents a set of position numbers j.

[0017] Preferably, a set of initial solutions of the airport cluster layout P={P1,P2,…,P m} is randomly generated, m≥1.

[0018] If P m satisfies:

[0019]

[0020] Preferably, in order to facilitate the optimization of the initial feasible solution P m , a dynamic factor V m is introduced:

[0021]

[0022] Wherein, r ij is a random number, and the value range is 0≤r ij ≤1, which can be randomly generated.

[0023] Preferably, in order to improve the service capacity of the airport cluster, a target function Z is constructed according to the airport cluster spatial satisfaction, the target function Z is solved, and the maximum airport cluster spatial satisfaction Z in the area A is realized.

[0024] Preferably, there are airport clusters N3 in the area A, and for each k∈N3, the spatial accessibility a ijk of the residents in the sub-area (i,j) to the kth airport is calculated:

[0025]

[0026] wherein: N3={1,2,3,…,n3-1,n3} represents the set of airports; q k,max represents the maximum passenger service capacity of the kth airport; d k,max represents the maximum service coverage radius of the kth airport, respectively. and represent the average distance and average speed from the sub-area (i,j) to the kth airport, respectively.

[0027] Preferably, the actual time required to reach the airport is t ijk :

[0028]

[0029] Preferably, let the demand of the sub-area (i,j) be w ij , then according to the accessibility a ijk of the airport, the flow w ijk from the sub-area (i,j) to the kth airport can be calculated.

[0030] Preferably, the distance satisfaction function of the sub-area (i,j) to the kth airport is :

[0031]

[0032] Compared with the prior art, the advantages of the present application are:

[0033] The present application establishes an airport cluster spatial layout model based on accessibility, and according to the nonlinear characteristics of the model, a fast solving method based on particle swarm algorithm is proposed, which reasonably plans the airport cluster system structure and spatial distribution, breaks the bottleneck of overall service quality of the airport cluster, improves the operation efficiency, and solves the difficult problems urgently needed to be solved in the fields of traffic planning and major project management. BRIEF DESCRIPTION OF DRAWINGS

[0034] The advantages of the above and / or additional aspects of the present application will become apparent and easy to understand from the following description of embodiments with reference to the drawings, in which:

[0035] Figure 1 is a flow chart of the airport cluster spatial layout optimization method based on accessibility according to the present application. DETAILED DESCRIPTION

[0036] In order to enable the above-mentioned objects, features and advantages of the present application to be more clearly understood, the present application will be further described below with reference to the drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0037] An airport cluster spatial layout optimization method based on accessibility, as Figure 1As shown, it includes:

[0038] Step 1: Divide the predetermined area into grids.

[0039] For a predetermined region A, a square grid of m×n km (n>0) is used to fill region A, dividing region A into n1 rows and n2 columns of subregions, that is, completely covering region A. Any subregion can be represented as (i,j):

[0040]

[0041] Where: N1 = {1, 2, 3, ..., n1-1, n1} represents the set of position numbers i;

[0042] N2 = {1, 2, 3, ..., n2-1, n2} represents the set of position numbers j.

[0043] If the center of the square grid at position (i,j) is within region A, then the square grid is a sub-region; if the center of the square grid at position (i,j) is not within region A, then the square grid is not a sub-region.

[0044] Step 2: Based on the grid division results of region A, randomly generate m feasible airport cluster layout strategies P m

[0045] Based on the total construction investment C and the estimated construction cost c of each sub-region (i,j) airport. ij The set of initial solutions for the randomized airport cluster layout is P = {P1, P2, ..., P...}. m}, m≥1. Where, the initial solution P m It can be represented as:

[0046]

[0047] δ ij ∈{0,1} (3)

[0048] Where, any initial solution P m δ ij The independent variable is either 0 or 1.

[0049] δ ij Indicates whether an airport is built in sub-region (i,j), δ ij A value of 0 indicates that no airport will be built in sub-region (i,j), δ ij A value of 1 indicates that an airport is built in sub-region (i,j). δ ij A random number ζ between 0 and 1 can be generated; if ζ ≥ 0.5, then δ ij =1, if ζ < 0.5 then δ ij =0.

[0050] If P m satisfies:

[0051]

[0052] then P m is the initial feasible solution, otherwise randomly select the existing delta ij =1 sub-region to change to delta ij =0 until P m satisfies formula (4). At this time, m feasible airport cluster layout strategies P={P1, P2, …, P m} can be obtained.

[0053] then in the initial feasible solution P m , the total number of airports in the airport cluster within the predetermined area A is n3:

[0054]

[0055] At the same time, in order to facilitate the optimization of the initial feasible solution P m , a dynamic factor V m is introduced:

[0056]

[0057] where r ij is a random number, and the value range is 0 ij ≤r ij ≤1, which can be randomly generated.

[0058] Step three: establish an airport cluster space satisfaction model, and construct an objective function Z

[0059] In order to improve the service capacity of the airport cluster, an objective function Z is constructed according to the airport cluster space satisfaction, and the objective function Z is solved to realize the maximum space satisfaction Z of the airport cluster in the area A. Z can be expressed as:

[0060]

[0061] where w ij represents the demand of the sub-region (i,j); w ijk represents the flow of the calculable sub-region (i,j) to the kth airport; represents the sub-region (i,j) to the kth airport distance satisfaction function; N3={1,2,3,…,n3-1,n3} represents the set of sub-regions (i,j) with delta m =1 in the initial feasible solution P ij .

[0062] In the airport cluster space satisfaction model, the airport cluster space satisfaction Z is related to w ijk , and is affected by the distance satisfaction function Influence.

[0063] Step 4: Model Calculation

[0064] For the initial feasible solution P m P can be calculated in the following order. m The corresponding objective function value Z m We obtain m initial feasible solutions P m Airport cluster spatial satisfaction Z m .

[0065] ①Spatial accessibility calculation of airport clusters

[0066] Within region A, there exists a cluster of airports N3. For each k ∈ N3, calculate the spatial reachability a of residents within sub-region (i,j) to the k-th airport. ijk :

[0067]

[0068] Where: N3 = {1, 2, 3, ..., n3-1, n3} represents the set of airports; q k,max d represents the maximum passenger capacity of the k-th airport; k,max Let represent the maximum service coverage radius of the k-th airport; and Let represent the average distance and average speed from subregion (i,j) to the kth airport, respectively.

[0069] The spatial accessibility a of the k-th airport can be obtained by analyzing the spatial accessibility of the airport cluster. ijk The actual time t required to travel from sub-region (i,j) to the airport ijk The relationship.

[0070] Furthermore, the actual time required for region (i,j) to travel to the airport is t. ijk :

[0071]

[0072] ② Calculation of traffic flow from sub-region to any airport

[0073] Let w be the demand for subregion (i,j). ij Then, based on the airport's accessibility a ijk It can calculate the flow w from sub-region (i,j) to the kth airport. ijk for:

[0074]

[0075] ③ Calculation of the satisfaction function for the distance from the sub-region to any airport

[0076] The distance satisfaction function of the sub-region (i, j) to the kth airport is:

[0077]

[0078] It can be seen that, within the airport service range, is linearly reduced with the distance between the sub-region (i, j) and the kth airport increases.

[0079] Through formula (7), combined with formulas (8)-(11), the airport group space satisfaction Z under m feasible airport group layout strategies can be obtained m . Select the maximum airport group space satisfaction max{Z1, Z2, …, Z m} corresponding to the initial feasible solution of the airport group as the global optimal solution P g .

[0080] Set the number of iterations to t, at this time t = 1, set the maximum number of iterations t max .

[0081] Step five: layout optimization iteration adjustment

[0082] When t = 1, for all m initial feasible solutions P m , set m individual optimal solutions P lm , let the individual optimal solution P lm = P m .

[0083] Let t = t + 1, adjust the dynamic factor V m according to the following formula for m feasible solutions:

[0084]

[0085] wherein, represents the inertia weight, which balances the degree of movement of the dynamic factor V m according to the speed inertia of the previous moment; b1 and b2 respectively represent the learning factor of the dynamic factor V m absorbing experience from the feasible solution individual and solution set; two independent random numbers λ1 and λ2 respectively represent the randomness of the dynamic factor V m moving with the individual and solution set, and the value range is between 0 and 1.

[0086] After adjustment, if r ij exceeds its own value range, it is corrected according to the following formula:

[0087]

[0088] At this time, the initial solution Pm The iterative update is:

[0089] P m = P m + V m (14)

[0090] and the updated δ ij is modified according to the following formula:

[0091]

[0092] At this time, if the constraint of formula (4) is met, P m is a feasible solution, otherwise a random existing δ ij = 1 is changed to δ ij = 0 until P m satisfies formula (4). At this time, the updated m feasible airport group layout strategies P = {P1, P2, …, P m} can be obtained.

[0093] According to step four, the airport group space satisfaction Z m (t) under the m updated airport group layout strategies at the current time is calculated, if Z m (t) is greater than Z m (t-1), the individual optimal solution P lm = P m ; otherwise the individual optimal solution P lm is unchanged.

[0094] If max{Z1(t), Z2(t), …, Z m (t)} is higher than max{Z1(t-1), Z2(t-1), …, Z m (t-1)}, the global optimal solution P g is updated to the airport group layout strategy corresponding to the maximum airport group space satisfaction max{Z1(t), Z2(t), …, Z m (t)}, otherwise the global optimal solution P g is unchanged.

[0095] If t < t max , repeat step five; otherwise, go to the next step.

[0096] Step six: obtain the airport group space layout strategy P m and the global optimal solution P g , output the calculation of the maximum airport group space satisfaction maxZ.

[0097]

[0098]

[0099] Each of the examples is provided by way of explanation of the application but is not meant as a limitation of the application. Indeed, various modifications and changes can be made thereto without departing from the scope or spirit of the application as set forth in the claims. For example, features from one embodiment can be incorporated into another embodiment. Accordingly, it is contemplated that the application will encompass modifications and variations as fall within the scope of the appended claims and their equivalents.

[0100] In the description of the application, the terms "longitudinal", "lateral", "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", and the like are used to indicate the orientation or position relationship based on the orientation or position relationship shown in the drawings, and are only for the convenience of describing the application and do not require the application to be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation of the application. The terms "connected", "connected", "provided" used in the application should be understood broadly, for example, it can be fixed connection, can also be detachable connection; can be directly connected, can also be indirectly connected through intermediate components; can be wired electrical connection, wireless electrical connection, or wireless communication signal connection, and the specific meaning of the above terms can be understood by the person skilled in the art according to the specific circumstances.

[0101] The above is only the preferred embodiment of the application, and is not intended to limit the application. For those skilled in the art, the application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A method for optimizing the spatial layout of airport clusters based on accessibility, characterized in that, It includes: Step 1: Divide the predetermined area into a grid; For the designated area ,use The area is covered by a square grid. , will the area Divided into OK List several sub-regions, any sub-region is : ， in: Indicates location number A set; Indicates location number A set; Step 2: Region-based The mesh generation results are generated randomly. A feasible airport cluster layout strategy ; According to the total construction investment and each sub-region Airport estimated construction cost A set of initial solutions for the layout of a random airport cluster is generated. , where the initial solution It can be represented as ， To represent sub-regions Should an airport be built? A value of 0 indicates a sub-region. No airport to be built. A value of 1 indicates a sub-region. Airport construction satisfy: , available A feasible airport cluster layout strategy ; Step 3: Establish a spatial satisfaction model for the airport cluster, and construct an objective function based on airport distance satisfaction. ; Construct an objective function based on the spatial satisfaction of airport clusters. For the objective function Solve the problem to achieve the region Inland airport cluster space satisfaction maximum, Represented as: ， in: Subregion Demand; Represents a computable subregion To the Traffic volume at each airport; Subregion To the Airport distance satisfaction function; Indicates the initial feasible solution middle subregion gather; Step 4: Model Calculation; calculate Corresponding objective function value ,get An initial feasible solution Airport cluster space satisfaction ; area Memory in airport group For each , calculate sub-region Inner residents arrive at the Spatial accessibility of the airport : ， in: Indicates a group at the airport; Indicates the first The maximum passenger capacity of each airport; They represent the first The maximum service coverage radius of each airport; and Representing sub-regions respectively Reaching the Average distance and average speed of each airport; area The actual time required to reach the airport is : ， subregion To the Airport traffic for ， subregion To the Airport Distance Satisfaction Function for: ， get Airport cluster spatial satisfaction under feasible airport cluster layout strategies ; Select the highest airport cluster space satisfaction The corresponding initial feasible solution for the airport group is the global optimal solution. ; Step 5: Layout optimization and iterative adjustments; when At that time, for all An initial feasible solution ,set up The optimal solution for each individual Let the individual optimal solution ; To facilitate the initial feasible solution Optimization, introducing dynamic factors : ， in, It is a random number, and its value range is [value range missing]. , If after adjustment If the value exceeds its own range, it is corrected according to the following formula: ， make ,right One feasible solution, dynamic factor Adjust according to the following formula: ， in, Indicates inertia weight, which balances dynamic factors. The degree of inertia of the velocity from the previous moment; and Representing dynamic factors respectively Learning factors that draw experience from feasible solutions and the solution set; two independent random numbers. and Representing dynamic factors respectively The randomness of movement with individuals and solution sets; At this point, the initial solution Iterative updates are as follows: ， And after the update The following formula should be used for correction: ， At this point, if the conditions in step two are met... ,but This is a feasible solution; Updates are available A feasible airport cluster layout strategy ; Based on step four, the current time is obtained. Airport cluster space satisfaction under an updated airport cluster layout strategy ; like Higher than Then the global optimal solution Updated to the largest airport cluster space satisfaction The corresponding airport cluster layout strategy; otherwise, the globally optimal solution. constant; like If yes, repeat step five; otherwise, proceed to the next step. Step Six: Obtain the updated airport cluster spatial layout strategy and the global optimal solution Output the maximum spatial satisfaction of the airport cluster. ; ， ， 。 2. The airport cluster spatial layout optimization method based on accessibility as described in claim 1, characterized in that, Each sub-region will be a region Full coverage.

3. The airport cluster spatial layout optimization method based on accessibility as described in claim 2, characterized in that, To improve the service capacity of the airport cluster, an objective function is constructed based on the spatial satisfaction of the airport cluster. For the objective function Solve the problem to achieve the region Inland airport cluster space satisfaction maximum.

Images