CN112528359A - City expansion simulation method based on bargaining model and ant colony optimization algorithm - Google Patents

City expansion simulation method based on bargaining model and ant colony optimization algorithm Download PDF

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CN112528359A
CN112528359A CN202010783897.5A CN202010783897A CN112528359A CN 112528359 A CN112528359 A CN 112528359A CN 202010783897 A CN202010783897 A CN 202010783897A CN 112528359 A CN112528359 A CN 112528359A
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汤弟伟
刘恒
孙毅
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Abstract

The invention provides a city expansion simulation method based on a bargaining model and an ant colony optimization algorithm, which comprises the following steps of: firstly, judging whether all pixels capable of being converted into cities are added into a city expansion candidate area or not by utilizing a dynamic bargaining model of a government and a farmer which considers fair preference; and setting an urban expansion target by utilizing an ant colony optimization algorithm in the candidate region, and simulating an urban expansion process. The method has the advantages that the method can accurately simulate the land acquisition process in the urban expansion process by utilizing the preference-considering dynamic bargaining model of both the government and the peasant, thereby protecting the basic benefits of the peasants; meanwhile, the ant colony optimization algorithm is utilized to perform optimization simulation on the whole city expansion result in the expansion candidate area in the land acquisition game result, the simulation result is more in line with the city development direction under the control of the objective function, land acquisition conflict events in the city expansion process can be reduced or avoided, and smooth implementation of city expansion or planning is guaranteed.

Description

City expansion simulation method based on bargaining model and ant colony optimization algorithm
Technical Field
The invention belongs to the technical field of urban planning, and particularly relates to an urban expansion simulation method based on a bargaining model and an ant colony optimization algorithm.
Background
China, the largest developing country in the world, is undergoing a rapid urbanization process with a dramatic increase in urban land demand. Land collection is a main means for meeting the land requirement of city construction, the rapid advance of urbanization enables the land collection quantity to be increased sharply, and in the land collection process, because of conflict of interests of all parties, a large amount of land collection conflicts occur, so that the process and the direction of city expansion are influenced to a certain extent, and even certain negative effects are brought to the harmony and stability of the whole society. Therefore, the urban expansion simulation should be based on the smooth implementation of land collection.
The game theory is the most common method for analyzing and solving the problem of land collection conflict, but the existing land collection playing model has the following characteristics: (1) multiple microscopic land investigation cases are subjected to static analysis modeling, and the model is difficult to apply to other cases or other areas, particularly large-scale land collection problems; (2) most of the single-side government quotation models are government single-side quotation models, and farmers can only adopt an acceptance or rejection strategy, which is inconsistent with the actual invisible negotiation; (3) interactions between farmers and governments, such as the ubiquitous fairness preferences of farmers and governments, are not considered. The bargaining model is a complete information dynamic game model, is a game process for the participants who have common benefits to try to reach an agreement when facing conflict, and is a practical implementation process matched with Chinese character areas; compared with a static game model, the dynamic bargaining model has stronger expanding applicability.
The existing city expansion simulation method mainly takes Cellular Automata (CA) and Agent-based modeling (ABM) as main components, and both CA and ABM belong to methods from bottom to top, namely, the global situation is deduced through the change of cells or Agent individuals, the adjustment and control of global simulation results are lacked, meanwhile, researchers generally think that the acquisition of CA conversion rules is difficult, and the simulation of decision processes and behaviors of people is lacked, so that the use of the method is limited; while the ABM can simulate the interaction and decision between people and ground, the problem of city expansion is very complex, the main body involved in city expansion and the relationship between people and ground are difficult to accurately express through the category, knowledge and behavior definition of an agent, and only the main body and environment are simplified, and the simplification necessarily influences the simulation precision of the ABM.
The ant colony optimization algorithm proposed by Dorigo et al in the early 90 s of the 20 th century solves various optimization problems by simulating the foraging behavior of ants. The algorithm has better robustness due to an information positive feedback mechanism. Meanwhile, the method is based on an evaluation mechanism of an objective function, can adjust and control the overall effect of a solution scheme, and is successfully applied to the related fields of ecological protection area planning, land utilization optimization layout, city expansion simulation and the like.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a city expansion simulation method based on a bargaining model and an ant colony optimization algorithm.
The invention is realized by the following technical scheme: a city expansion simulation method based on bargaining models and ant colony optimization algorithms is characterized by comprising the following steps:
the method comprises the following steps: collecting study area Y1Year, Y2Year, Y3Annual land use data, infrastructure data, land acquisition compensation standards, reference land prices, Digital Elevation Models (DEMs) and administrative zoning data; wherein the infrastructure data comprises railway, highway, national road, provincial road, subway, city main road and river data; carrying out format conversion, resampling, reclassification, unified projection processing and information extraction processing on the data;
step two: for Y1Year and Y2Performing superposition operation on reclassified data of annual land utilization to obtain Y3All picture element layer Y capable of being converted into city by year1-2And randomly sampling together with the distance grid pattern layer, establishing a city expansion logistic regression model, and calculating Y1-2The city conversion probability P of each pixel in the image;
step three: predicting Y using Markov Chain (MC) and correlation data3Year to planning target year Y4Dividing the area by the size of the pixel, thereby converting the expanded area into the number N of the expanded pixels;
step four: establishing a dynamic bargaining model of both the government and the peasant considering the fair preference: determining a bargaining order and a maximum bargaining round, determining government and farmer gaming strategies, bargaining functions (C, F) and expected earnings (G, R), and determining an unconventional conflict condition; for Y1-2Calculating the expected income of each round of government and peasants according to the established government and peasant dynamic bargaining model considering the fair preference, and judging whether the pixel can be added into the urban expansion candidate area C or not according to the condition of no land acquisition conflict1(ii) a If C1The number of the pixels in the step (C) is less than the number N of the expanded pixels obtained by calculation in the step (three), and the maximum bargaining turns, the current factor of the government and farmers and the fair preference parameter are adjusted to ensure that the current factor of the government and the farmers is equal to the fair preference parameter1The number of the middle pixels is greater than N;
step five: setting city expanding objective function and utilizing ant colony optimization algorithm in step C1Middle simulation Y3Urban expansion in year: each ant from C1Randomly selecting N pixels as urban land according to the state transition probability, thereby constructing an urban expansion simulation scheme, and evaluating the constructed scheme according to a target function; after all ants complete the construction of the scheme, the pheromone is updated according to a pheromone release and update mechanism; after the maximum iteration times are reached, selecting a scheme with the optimal objective function evaluation score from the schemes constructed by the ants as a final simulation result;
step six: comparison Y3Annual simulation of results and Y3Carrying out precision evaluation on simulation results within the actual urban land range; if the simulation precision is low, adjusting ant colony optimization algorithm parameters and the weight of each optimization target in the objective function;
step seven: if the simulation precision reaches the simulation requirement, synchronizing two to four steps, and utilizing Y2And Y3Year data, obtaining Y3To the planned target yearY4City expansion candidate area C of2And then using the ant colony optimization algorithm at C2Middle simulation Y4Urban expansion of the year.
Preferably, the specific step of the first step comprises the following substeps:
1-1: collecting study area Y1Year, Y2Year, Y3Annual land use data, infrastructure data, land acquisition compensation standards, reference land prices, Digital Elevation Models (DEMs) and administrative zoning data; wherein the infrastructure data comprises railway, highway, national road, provincial road, subway, city main road and river data;
1-2: rasterizing the collected non-raster data, resampling the non-raster data into the non-raster data with the same size, and unifying a coordinate system;
1-3: will Y1Year, Y2Year, Y3Reclassifying annual land utilization data, wherein the current situation is that the pixel value of the city is reclassified as 2, the pixel value which can be converted into the city is classified as 1, and the other pixels are background areas and are classified as 0;
1-4: extracting elevation and gradient data of a research area from the DEM to obtain an elevation and gradient map layer;
1-5: calculating the distance between the pixel which can be converted into urban land and the railway, the expressway, the national road, the provincial road, the subway, the urban main road and the river to form a distance grid image layer;
preferably, the specific steps of the second step include the following substeps:
2-1: for Y in steps 1-31Year and Y2Reclassifying data for annual land utilization to perform logic difference operation and extracting Y2Deduction of Y from classified data of annual land utilization1Other pixel data Y after annual urban land1-2；
2-2: from Y1-2Randomly sampling points in the pixel and assigning values to Y1-2Using pixel values of the medium sampling points as dependent variables, using pixel values of the sampling points in the elevation and gradient layers in the 1-4 and the grid layers in the 1-5 distances as observation variables, establishing a city expansion logistic regression model, calculating the city conversion probability of the pixels, and calculating the city conversion probability of the pixelsAnd verifying the validity of the model. The formula of the urban expansion logistic regression model is as follows:
Figure BDA0002621219630000041
in the formula, Pi,jIs Y1-2City conversion probability, x, of pixel element in ith row and jth column in layer and with value of 1kIs the kth variable (normalized to [0, 1 ]])，βkIs xkCoefficient of regression of, betaoIs a constant;
preferably, the specific step of step four includes the following substeps:
4-1: establishing a dynamic bargaining model of both the government and the peasant considering the fair preference:
(1) the game main body: the model comprises two types of game main bodies of peasants and governments, wherein the two types of main bodies are rational, can adopt an optimal strategy to maximize the income of the peasants, and have the intention of reaching an agreement, and meanwhile, the bargaining parties are assumed to have the same complete information, namely the government and the peasants mutually know the expectation and the benefit of each other, so that the bargaining model of complete information alternate bidding (trading offers) is formed;
(2) game strategy and expected revenue: the model is a two-party unlimited rotation bidding bargaining model, according to the actual land acquisition process, the government bids firstly, the first price of the government is the land acquisition compensation standard, the later price is influenced by the counter-offer of a farmer and the price of the surrounding farmland, the new counter-offer of the farmer is compared with the last counter-offer, if the counter-offer is reduced, the government considers that the farmer cooperates with the land acquisition, the farmer can be treated more fairly, the fair and positive effects of the two parties are generated, the price is increased to promote the land acquisition, the government is used as a public department, the fairness of the whole can be emphasized besides the fairness of a certain farmer is considered, the neighborhood fairness is generated, meanwhile, the farmer can pay more attention to the social fairness compared with the government, the fairness strength is greater than that of the farmer, and based:
Figure RE-GDA0002668235770000042
in which n is an even number, alphagIs a fair strength of both sides of the government, betagIs the neighborhood fairness strength of government, 0 is less than or equal to betag<αg1 or less, when n is 3, F0＝I；
For the farmer subjects, the counter-offer considers the maximization of the respective benefits (the self-profit preference), and also expresses the attention on fairness, for example, the farmers consider to obtain a certain degree of fairness treatment in the face of the improvement of government quotations, and under the action of the fairness preference, the counter-offer may be compromised, and the expected income is properly reduced; similarly, if the compensation received by the surrounding farmers is low, the expected profit is also reduced appropriately under the fair bias, so the bargaining function of the farmers is:
Figure BDA0002621219630000052
wherein n is bargaining round, FnCounter-offer to the certified plot for the n (even) th turn of the farmer, Cn-1Compensating quotes for the government's n-1 th round, CmExpropriate compensation for neighborhoods to other farmers, alphafIs fair strength between both sides of the farmer, betafIs the neighborhood fair strength of farmers, wherein beta is more than or equal to 0f<αf≤1， βf<βg，αf<αgU is the initial expected income of farmers, the value is 0.4V, and V is the standard land price of the residence;
if the land acquisition is successful, the income function of the peasant has 2 cases, namely that the peasant receives the quoted price of the government and that the government receives the quoted price of the peasant, so that the income function of the peasant is as follows:
Figure BDA0002621219630000053
in the formula, deltaf(0＜δfLess than 1) is a discount factor of the farmer after considering negotiation time cost;
there are also 2 cases of government revenue functions:
Figure BDA0002621219630000061
wherein e is a government development cost coefficient, V is a reference land price, and deltag(0＜δg< 1) is a discount factor of the government after considering the negotiation time cost;
in the model, the pixels without land acquisition conflict need to satisfy the following conditions:
Figure BDA0002621219630000062
in the formula, E is the land economic value and is calculated in the following way:
Figure BDA0002621219630000063
wherein I is the basic economic benefit (land acquisition compensation standard) of farmers' cultivation, PiFor the possibility of land i developing into a city, NiThe number of the city pixels in the neighborhood range of the land i is N; wherein P isiThe urbanization probability of the pixels in the step two is represented by i, which is the number of the pixels and can be mapped into the row and column numbers of the pixels;
if the pixel meets the above conditions, adding the pixel into the urban expansion candidate area C1If not, not adding;
4-2: for Y1-2All pixels with category 1 in the total number are processed according to 4-1, and in order to reasonably control the bargaining process, the maximum negotiation number N can be setmaxObtaining a city expansion candidate area C by bargaining all pixels with the category of 11；
4-3: if city expands candidate area C1If the number of the middle pixels is less than the number N of the city expansion pixels, the maximum bargaining turns, the current factor of the government and farmers and the fair strength are properly adjusted to ensure that C1The number of the medium pixels is more than N;
preferably, the specific steps of the step five comprise the following substeps:
5-1: according to the city development target, setting a city expansion target function as follows:
Figure BDA0002621219630000071
wherein k is ant number, n is optimized target number, and wiThe ith optimization objective weight, the sum of all the optimization objective weights is 1,
Figure BDA0002621219630000072
evaluating the ith optimization target value of the kth ant optimization scheme;
5-2: calculating urban expansion candidate area C by using Logistic regression model in 4-11Urbanization probability P of each image elementiTaking the value as a heuristic value of an ant colony optimization algorithm;
5-3: using ant colony optimization algorithm at C1The method simulates urban expansion and comprises the following steps:
(1) algorithm initialization: initializing parameters required by an ant colony optimization algorithm for simulating city expansion, wherein the parameters comprise algorithm parameters, such as ant number, iteration times, alpha, beta, pheromone volatilization rate, heuristic value data, and city expansion related parameters, such as city expansion candidate area data, expansion pixel number, neighborhood size and output file path;
(2) judging whether the iteration is finished, if so, turning to (10), otherwise, continuing to execute downwards;
(3) judging whether all ants finish simulation, if so, turning to (8), otherwise, selecting one ant from the ants which do not finish simulation as the current working ant, and executing operation downwards by the ant;
(4) judging whether the pixel number in the ant simulation result reaches the expanded pixel number N, if so, turning to (7), otherwise, continuing to execute downwards;
(5) the ant calculates the transfer probability of the pixel in each city expansion candidate area in the following way:
Figure BDA0002621219630000073
in the formula, PosijRefers to the picture element located in the ith row and the jth column,
Figure BDA0002621219630000074
indicates being located at PosijThe pheromone content of the picture element above,
Figure BDA0002621219630000075
indicates being located at PosijHeuristic value of the above pel, allowedkIndicating that the pixel set which can be selected by the kth ant needs to be excluded when the pixel is selected, wherein alpha and beta are an pheromone factor and a heuristic factor respectively;
(6) selecting a randomly selected pixel by roulette: calculating the contribution probability according to the transition probability calculated in the step (5), wherein the calculation mode is as follows:
Figure BDA0002621219630000081
in the formula, n is the number of candidate pixels;
generating a random number, sequentially calculating the cumulative probability of each pixel, and selecting a pixel as an urban expansion unit to be added into a simulation result when the cumulative probability of the pixel is greater than the random number; the cumulative probability is calculated as follows:
Figure BDA0002621219630000082
wherein m is PosijThe serial number of the pixel when the selection probability is calculated;
adding the randomly selected pixel into the simulation result of the ant, and then turning to the step (4);
(7) evaluating the simulation result of the ants by using the objective function of 5-1, calculating the score of the objective function, updating the population optimal simulation result, and turning to the step (3) after the calculation is finished;
(8) updating pheromones on the paths;
(9) after the pheromone is updated, emptying simulation results of all ants, and turning to the step (2);
(10) after the algorithm is finished, outputting the optimal simulation result in all ants;
the invention has the beneficial effects that: the city expansion simulation method based on the bargaining model and the ant colony optimization algorithm establishes a dynamic bargaining game model of both the government and the peasant considering the fairness preference so as to simulate the land collection process in city expansion and find out a candidate area for city expansion. And in the candidate area, simulating urban expansion by using an ant colony optimization algorithm so as to provide decision reference for urban planning management. The method has the advantages that from the view point of land acquisition, the decision-making behaviors of governments and farmers in the process of land acquisition can be accurately simulated, namely, areas where land acquisition can be smoothly carried out are found firstly, and then city expansion simulation is carried out, so that the possibility of land acquisition conflict caused by city expansion is avoided or reduced; meanwhile, the invention can effectively control the city expansion simulation result according to the city development target, so that the simulation result is more in line with the city development direction. In summary, the simulation precision of the city expansion simulation result of the invention is greatly improved compared with the simulation precision of the traditional CA and ABM methods.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a 2006 land use reclassification diagram of an embodiment of the invention;
fig. 3 is a 2011 re-classification diagram of land use according to an embodiment of the present invention;
FIG. 4 is a 2016 land use reclassification diagram of an embodiment of the present invention;
FIG. 5 is a 2016 number expansion candidate area map according to one embodiment of the present invention;
FIG. 6 is a 2016 city expansion simulation diagram according to an embodiment of the present invention;
FIG. 7 is a diagram of candidate regions for expansion in 2021 according to an embodiment of the present invention;
fig. 8 is a diagram of a simulation of urban expansion in 2021 according to an embodiment of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.
Referring to fig. 1 to 8, the present invention provides a technical solution: a city expansion simulation method based on bargaining models and ant colony optimization algorithms comprises the following steps:
the method comprises the following steps: collecting and processing data; the method comprises the following specific steps:
1-1: collecting Landsat images, basic facility data, land acquisition compensation standards, reference land prices, a Digital Elevation Model (DEM) and administrative division data of research areas in 2006, 2011 and 2016; wherein the infrastructure data comprises railway, highway, national road, provincial road, subway, city main road and river data;
1-2: classifying the images in ENVI to obtain land utilization data of three years, converting the collected non-grid data into grids in ArcGIS, resampling all the grids to 30 mx 30m resolution by a resampling tool, and unifying a data coordinate system by a projection transformation tool;
1-3: in ArcGIS, a reclassification tool is utilized to reclassify the soil utilization data in 2006, 2011 and 2016, the current situation is that the pixel value of a city is reclassified to be 2, the pixel value which can be converted into the city is classified to be 1, and the other pixels are background areas and are classified to be 0, which is shown in the attached figures 2-4;
1-4: extracting elevation and gradient data of a research area from the DEM in ArcGIS for calculating urban conversion probability;
1-5: calculating the distance between the pixel which can be converted into urban land and railways, expressways, national roads, provincial roads, subways, urban arterial roads and rivers in the ArcGIS to form a distance grid layer;
step two: performing superposition operation on the reclassified data of the land utilization in 2006 and 2011, randomly sampling the reclassified data and the distance grid pattern layer, and establishing an urban expansion logistic regression model; the method comprises the following specific steps:
2-1: performing logical difference operation on the binary data of the 2006-year and 2011-year land utilization in the step 1-3, and extracting other pixel data Y of the 2011-year land utilization classification data with 2006-year urban land deduction1-2；
2-2: in ArcGIS, using a tool for generating random points, from Y1-28000 sampling points are randomly extracted from the pixels, then a target point extracting tool is used for assigning values to the sampling points, and the assignment layer comprises Y1-2Pattern layers, elevation and gradient pattern layers in 1-4, and distance raster pattern layers in 1-5, where Y is1-2Taking the pixel values of the middle sampling points as dependent variables, taking the pixel values of the sampling points in the elevation and gradient image layers and the distance raster image layer as observation variables, establishing a city expansion logistic regression model in the SPSS, and verifying the effectiveness of the model;
step three: prediction of urban expanse of 2016 years to planned target years 2021 using Markov Chain (MC) and related data, about 5.82km2Dividing the area by the pixel size (30m x 30m) to expand the number of pixels to about 6467;
step four: for Y1-2Judging whether the pixels with the category of 1 in the image layer can be added into the city expansion candidate area C according to the following game process of the two-party dynamic bargaining model considering fairness preference1(ii) a The method comprises the following specific steps:
4-1: establishing a bargaining model considering fairness preference:
(1) the game main body: the model comprises two types of game main bodies of peasants and governments, wherein the two types of main bodies are rational, can adopt an optimal strategy to maximize the income of the peasants, and have the intention of reaching an agreement, and meanwhile, the bargaining parties are assumed to have the same complete information, namely the government and the peasants mutually know the expectation and the benefit of each other, so that the bargaining model of complete information alternate bidding (trading offers) is formed;
(2) game strategy and expected revenue:
the model is a bargaining model for two parties to offer alternately in unlimited turns, according to the actual land acquisition process, the government offers first, the first offer of the government is a land acquisition compensation standard, the offer is influenced by the counter-offer of farmers and the price of the surrounding farmlands, the new counter-offer of the farmers is compared with the last counter-offer, if the counter-offer is reduced, the government considers that the farmers cooperate with land acquisition, the farmers can treat the farmers more fairly, the fair and fair effects of the two parties are generated, the offer is increased to promote land acquisition, the government is used as a public department, the fairness of a certain farmer is considered, the whole fairness is emphasized, the neighborhood fair and fair effects are generated, meanwhile, the farmers can pay more attention to the social fairness compared with the government, the equity strength is greater than that of the farmers, and based on the bargaining function:
Figure RE-GDA0002668235770000101
in which n is an even number, alphagThe strength of the two sides of the government is equal to 0.7, betagThe strength of the neighborhood fairness of the government is 0.65, and when n is 3, F0＝I；
For the farmer subjects, the counter-offer considers the maximization of the respective benefits (the self-profit preference), and also expresses the attention on fairness, for example, the farmers consider to obtain a certain degree of fairness treatment in the face of the improvement of government quotations, and under the action of the fairness preference, the counter-offer may be compromised, and the expected income is properly reduced; similarly, if the compensation received by the surrounding farmers is low, the expected profit will also be reduced appropriately under fair preference;
therefore, the counter-offer of each bargaining turn of the farmers is as follows:
Figure BDA0002621219630000112
wherein n is bargaining round, FnCounter-offer to the certified plot for the n (even) th turn of the farmer, Cn-1Compensating quotes for the government's n-1 th round, CmExpropriate compensation for neighborhoods to other farmers, alphafThe strength is equal to 0.6, betafThe neighborhood fair strength of the peasant is taken as 0.4, U is the initial expected income of the peasant, the value is 0.4V, and V is the standard land price of the residence;
if the land acquisition is successful, the income function of the peasant has 2 cases, namely that the peasant receives the quoted price of the government and that the government receives the quoted price of the peasant, so that the income function of the peasant is as follows:
Figure BDA0002621219630000121
in the formula, deltafIn order to consider the current factor of the farmers after the negotiation time cost, the value is 0.95;
there are also 2 cases of government revenue functions:
Figure BDA0002621219630000122
in the formula, e is a development cost coefficient of the government and takes a value of 0.2; v is a reference land price; deltagPasting a factor for the government, wherein the value is 0.9;
in the model, the pixels without land acquisition conflict need to satisfy the following conditions:
Figure BDA0002621219630000123
in the formula, E is the land economic value and is calculated in the following way:
Figure BDA0002621219630000124
wherein I is the basic economic benefit (land acquisition compensation standard) of farmers' cultivation, PiFor the possibility of land i developing into a city, NiIs the city pixel in the neighborhood range of land i, N is the number of neighborhoods, wherein P isiCalculating by using a Logistic regression model, wherein the formula is as follows:
Figure BDA0002621219630000125
in the formula, xkIs the kth variable (normalized to [0, 1 ]])，βkIs xkCoefficient of regression of, betaoIs a constant;
if the pixel meets the above conditions, adding the pixel into the urban expansion candidate area C1If not, not adding;
4-2: for Y1-2All pixels with the category of 1 in the city expansion candidate area C are processed according to the step 4-1, in order to reasonably control the bargaining process, the maximum negotiation can be set to be 5, and finally the city expansion candidate area C is obtained1The number of candidate pixels is 31441, which is much larger than the expansion number 6467, so as to satisfy the expansion requirement, see fig. 5;
step five: setting city expanding objective function and utilizing ant colony optimization algorithm in step C1Medium simulation 2016 city expansion; the method comprises the following specific steps:
5-1: according to the city development goal, setting a city expansion objective function, such as setting the objective function as:
Funck＝w1×fcpt(k)+w2×fcost(k)
wherein w1 and w2 are target weights respectively set to 0.5 and 0.5; f. ofcptSpace gathering is encouraged for space compactness; f. ofcostIn order to reduce land acquisition cost and land acquisition development cost, each target calculation formula is as follows:
Figure BDA0002621219630000131
Figure BDA0002621219630000132
wherein A is the perimeter of the patch, P represents the area of the patch, the compactness is between 0 and 1, and the compactness is higher when the patch is closer to a circle; i is a land acquisition compensation standard;
5-2: calculating urban expansion candidate area C by using Logistic regression model in 4.11Urbanization probability P of each image elementiAs it isHeuristic values of an ant colony optimization algorithm;
5-3: using ant colony optimization algorithm at C1The method simulates urban expansion and comprises the following steps:
(1) algorithm initialization: initializing parameters required by the ant colony optimization algorithm for simulating urban expansion, and setting algorithm parameters as follows: the number of ants is 50, the iteration number is 100, alpha is 2, beta is 3, the pheromone volatilization rate is 0.2, and heuristic value data is the city conversion probability; the city expansion related parameters are set as follows: c is the data of the city expansion candidate area1The number of the expansion pixels is 6467, the size of the neighborhood is 1 order, and the path of the output file is a certain path of the computer;
(2) judging whether the iteration is finished, if so, turning to (10), otherwise, continuing to execute downwards;
(3) judging whether all ants finish simulation, if so, turning to (8), otherwise, selecting one ant from the ants which do not finish simulation as the current working ant, and executing operation downwards by the ant;
(4) judging whether the pixel number in the ant simulation result reaches the expanded pixel number N, if so, turning to (7), otherwise, continuing to execute downwards;
(5) the ant calculates the transfer probability of the pixel in each city expansion candidate area in the following way:
Figure BDA0002621219630000141
in the formula, PosijRefers to the picture element located in the ith row and the jth column,
Figure BDA0002621219630000142
indicates being located at PosijThe pheromone content of the picture element above,
Figure BDA0002621219630000143
indicates being located at PosijHeuristic value of the above pel, allowedkWhen the k-th ant selects the pixel, the optional pixel set needs to be excluded from the simulation resultWherein, alpha and beta are pheromone factors and heuristic factors respectively;
(6) selecting a randomly selected pixel by roulette: firstly, calculating contribution probability according to the transition probability calculated in the step (5), wherein the calculation method is as follows:
Figure BDA0002621219630000144
in the formula, n is the number of candidate pixels;
generating a random number, sequentially calculating the cumulative probability of each pixel, and selecting a pixel as an urban expansion unit to be added into a simulation result when the cumulative probability of the pixel is greater than the random number;
the cumulative probability is calculated as follows:
Figure BDA0002621219630000145
wherein m is PosijThe serial number of the pixel when the selection probability is calculated;
adding the randomly selected pixel into the simulation result of the ant, and then turning to the step (4);
(7) evaluating the simulation result of the ants by using the objective function in the step 5-1, calculating the objective function score, updating the population optimal simulation result, and turning to the step (3) after the calculation is finished;
(8) and updating the pheromone on the path in the following way:
Figure BDA0002621219630000151
wherein ρ is the pheromone volatilization rate,
Figure BDA0002621219630000152
the kth ant is in PosijThe pheromone content released on the pixel is calculated as follows:
Figure BDA0002621219630000153
(9) after the pheromone is updated, emptying simulation results of all ants, and turning to the step (2);
(10) after the algorithm is finished, outputting the optimal simulation result in all ants, and referring to the attached figure 6;
step six: comparison Y3Annual simulation of results and Y3Carrying out precision evaluation on simulation results within the range of actual urban land, wherein the total precision reaches 93.02%, and the Kappa coefficient is 0.67;
step seven: in the same steps of two to four, acquiring the city expansion candidate area C from 2016 to 2021 years of the planning target year2See fig. 7; reuse of ant colony optimization algorithm in C2Middle simulation 2021 year city expansion, see fig. 8.
While there have been shown and described what are at present considered the fundamental principles of the invention and its essential features and advantages, it will be apparent to those skilled in the art that the invention is not limited to the details of the foregoing exemplary embodiments, but is capable of other specific forms without departing from the spirit or essential characteristics thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description of the embodiments is for clarity only, and those skilled in the art should make the description as a whole, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (5)

1. A city expansion simulation method based on a bargaining model and an ant colony optimization algorithm is characterized by comprising the following specific steps:
the method comprises the following steps: collecting study area Y1Year, Y2Year, Y3Annual land use data, infrastructure data, land acquisition compensation standards, reference land prices, Digital Elevation Models (DEMs) and administrative zoning data; wherein the infrastructure data comprises railway, highway, national road, provincial road, subway, city main road and river data; carrying out format conversion, resampling, reclassification, unified projection processing and information extraction processing on the data;
step two: for Y1Year and Y2Performing superposition operation on reclassified data of annual land utilization to obtain Y3All picture element layers Y capable of being converted into city in year1-2And randomly sampling together with the distance grid layer, establishing a city expansion logistic regression model, and calculating Y1-2The city conversion probability P of each pixel in the image;
step three: predicting Y using Markov Chain (MC) and correlation data3Year to planning target year Y4Dividing the area by the size of the pixel, thereby converting the expanded area into the number N of the expanded pixels;
step four: establishing a dynamic bargaining model of both the government and the peasant considering the fair preference: determining a bargaining order and a maximum bargaining round, determining government and farmer gaming strategies, bargaining functions (C, F) and expected earnings (G, R), determining unobtrusive conflict conditions; for Y1-2Calculating the expected income of each round of government and peasants according to the established government and peasant dynamic bargaining model considering the fair preference, and judging whether the pixel can be added into the urban expansion candidate area C or not according to the condition of no land acquisition conflict1(ii) a If C1The number of the pixels in the step (C) is less than the number N of the expanded pixels obtained by calculation in the step (III), and the maximum bargaining turns, the current factor of the government and farmers and the fair preference parameter are adjusted to ensure that the current factor C is equal to the maximum bargaining turn number1The number of the middle pixels is more than N;
step five: setting city expanding objective function and utilizing ant colony optimization algorithm in step C1Middle simulation Y3Urban expansion of year: each ant from C1Randomly selecting N pixels as urban land according to the state transition probability, thereby constructing an urban expansion simulation scheme, and evaluating the constructed scheme according to a target function; after all ants complete the construction of the scheme, the pheromone is updated according to a pheromone release and update mechanism; after the maximum iteration times are reached, selecting a scheme with the optimal objective function evaluation score from the schemes constructed by the ants as a final simulation result;
step six: comparison Y3Annual simulation of results and Y3Carrying out precision evaluation on simulation results within the actual urban land range; if the simulation precision is low, adjusting ant colony optimization algorithm parameters and the weight of each optimization target in the objective function;
step seven: if the simulation precision reaches the simulation requirement, synchronizing two to four steps, and utilizing Y2And Y3Annual data, get Y3To the planned target year Y4City expansion candidate area C of2And then using the ant colony optimization algorithm at C2Middle simulation Y4Urban expansion of the year.
2. The city expansion simulation method based on bargaining model and ant colony optimization algorithm according to claim 1, wherein: the specific steps of the first step are as follows:
1-1: collecting study area Y1Year, Y2Year, Y3Annual land use data, infrastructure data, land acquisition compensation standards, reference land prices, Digital Elevation Models (DEMs) and administrative zoning data; wherein the infrastructure data comprises railway, highway, national road, provincial road, subway, city main road and river data;
1-2: rasterizing the collected non-raster data, resampling the non-raster data into the non-raster data with the same size, and unifying a coordinate system;
1-3: will Y1Year, Y2Year, Y3The annual land utilization data is reclassified, the current situation is that the pixel value of the city is reclassified as 2, the pixel value which can be converted into the city is classified as 1, and the others are background areasClassified as 0;
1-4: extracting elevation and gradient data of a research area from the DEM to obtain an elevation and gradient map layer;
1-5: and calculating the distance between the pixel of the urban land and the railway, the expressway, the national road, the provincial road, the subway, the urban main road and the river to form a distance raster image layer.
3. The city expansion simulation method based on bargaining model and ant colony optimization algorithm according to claim 1, wherein: the second step comprises the following specific steps:
2-1: for Y in steps 1-31Year and Y2Performing logic difference operation on reclassified data of annual land utilization, and extracting Y2Deduction of Y from classified data of annual land utilization1Other pixel data Y after annual urban land1-2；
2-2: from Y1-2Randomly sampling points in the pixel and assigning values to Y1-2And taking the pixel values of the intermediate sampling points as dependent variables, taking the pixel values of the sampling points in the elevation and gradient layers in the 1-4 and the distance grid layers in the 1-5 as observation variables, establishing a city expansion logistic regression model, calculating the city conversion probability of the pixels, and verifying the effectiveness of the model. The formula of the urban expansion logistic regression model is as follows:
Figure RE-FDA0002668235760000021
in the formula, Pi,jIs Y1-2City conversion probability, x, of pixel element in ith row and jth column in layer and with value of 1kIs the kth variable (normalized to [0, 1 ]])，βkIs xkCoefficient of regression of, betaoIs a constant.
4. The city expansion simulation method based on bargaining model and ant colony optimization algorithm according to claim 1, wherein: the fourth step comprises the following specific steps:
4-1: establishing a dynamic bargaining model of both the government and the peasant considering the fair preference:
(1) the game main body: the model comprises two types of game main bodies of peasants and governments, wherein the two types of main bodies are rational, can adopt an optimal strategy to maximize the income of the peasants, and have the intention of reaching an agreement, and meanwhile, the bargaining parties are assumed to have the same complete information, namely the government and the peasants mutually know the expectation and the income of the other party, so that the bargaining model of complete information alternate bidding (trading offers) is formed;
(2) game strategy and expected revenue: the model is a two-party unlimited rotation bidding bargaining model, according to the actual land acquisition process, the government bids first, the first price of the government is the land acquisition compensation standard, the later price is influenced by the counter-offer of a farmer and the price of the surrounding farmland, the new counter-offer of the farmer is compared with the last counter-offer, if the counter-offer is reduced, the government considers that the farmer cooperates with the land acquisition, the farmer can be treated more fairly, the fair and fair effects of the two parties are generated, the price is increased to promote the land acquisition, the government is used as a public department, the fairness of the whole can be emphasized besides the fairness of a certain farmer is considered, the neighborhood fair and fair effects are generated, meanwhile, compared with the government, the farmer can emphasize the fair and the fairness strength is greater than that of the farmer, and based:
Figure RE-FDA0002668235760000031
in which n is an even number, alphagIs a fair strength of both sides of the government, betagIs the neighborhood fairness strength of government, 0 is less than or equal to betag<αg1 or less, when n is 3, F0＝I；
For the farmer subjects, the counter-offers also show fair concerns except for considering respective benefit maximization (self-profit preference), for example, the farmers consider to obtain a certain degree of fair treatment in the face of government price improvement, and may be compromised under the action of fair preference to properly reduce expected income; similarly, if the compensation received by the surrounding farmers is low, the expected profit is also reduced appropriately under the fair bias, so the bargaining function of the farmers is:
Figure RE-FDA0002668235760000032
wherein n is bargaining round, FnCounter-offer to the certified plot for the n (even) th turn of the farmer, Cn-1Compensating quotes for the government's n-1 th round, CmExpropriate compensation for neighborhoods to other farmers, alphafIs fair strength between both sides of the farmer, betafIs the neighborhood fair strength of farmers, wherein beta is more than or equal to 0f<αf≤1，βf<βg，αf<αgU is the initial expected income of farmers, the value is 0.4V, and V is the standard land price of the residence;
if the land acquisition is successful, the income function of the peasant has 2 cases, namely that the peasant receives the quoted price of the government and that the government receives the quoted price of the peasant, so that the income function of the peasant is as follows:
Figure RE-FDA0002668235760000041
in the formula, deltaf(0＜δfLess than 1) is a discount factor of the farmer after considering negotiation time cost;
there are also 2 cases of government revenue functions:
Figure RE-FDA0002668235760000042
wherein e is a government development cost coefficient, V is a reference land price, and deltag(0＜δg< 1) is a government's discount factor after considering negotiation time costs;
in the model, the pixels without land acquisition conflict need to satisfy the following conditions:
Figure RE-FDA0002668235760000043
in the formula, E is the land economic value and is calculated in the following way:
Figure RE-FDA0002668235760000044
wherein I is the basic economic benefit (land acquisition compensation standard) of farmers' cultivation, PiFor the possibility of land i developing into a city, NiThe number of the city pixels in the neighborhood range of the land i is N; wherein P isiThe pixel city conversion probability obtained by calculation in the step two, i is the pixel number, and can be mapped into the pixel row number;
if the pixel meets the above conditions, adding the pixel into the urban expansion candidate area C1If not, not adding;
4-2: for Y1-2All pixels with category 1 in the total number are processed according to 4-1, and in order to reasonably control the bargaining process, the maximum negotiation number N can be setmaxObtaining a city expansion candidate area C by bargaining all pixels with the category of 11；
4-3: if city expands candidate area C1If the number of the middle pixels is less than the number N of the city expansion pixels, the maximum bargaining turns, the current factor of the government and the peasant and the fair strength are properly adjusted to ensure that C1The number of the middle pixels is larger than N.
5. The city expansion simulation method based on bargaining model and ant colony optimization algorithm according to claim 1, wherein: the concrete steps of the fifth step are as follows:
5-1: according to the city development target, setting a city expansion target function as follows:
Figure RE-FDA0002668235760000051
wherein k is ant number, n is optimized target number, and wiIs the ithOptimizing target weights, the sum of all the optimizing target weights is 1,
Figure RE-FDA0002668235760000052
evaluating the ith optimization target value of the kth ant optimization scheme;
5-2: calculating urban expansion candidate area C by using Logistic regression model in 4-11Urbanization probability P of each pixel iniTaking the value as a heuristic value of an ant colony optimization algorithm;
5-3: using ant colony optimization algorithm at C1The method simulates urban expansion and comprises the following steps:
(1) algorithm initialization: initializing parameters required by an ant colony optimization algorithm for simulating city expansion, wherein the parameters comprise algorithm parameters of ant number, iteration times, alpha, beta, pheromone volatilization rate, heuristic value data and city expansion related parameters comprising city expansion candidate area data, expansion pixel number, neighborhood size and output file path;
(2) judging whether the iteration is finished, if so, turning to (10), otherwise, continuing to execute downwards;
(3) judging whether all ants finish simulation, if so, turning to (8), otherwise, selecting one ant from the ants which do not finish simulation as the current working ant, and executing the operation downwards by the ant;
(4) judging whether the pixel number in the ant simulation result reaches the expanded pixel number N, if so, turning to (7), otherwise, continuing to execute downwards;
(5) the ant calculates the transfer probability of the pixel in each city expansion candidate area in the following way:
Figure RE-FDA0002668235760000053
in the formula, PosijRefers to the picture element located in the ith row and the jth column,
Figure RE-FDA0002668235760000054
representation positionAt PosijThe pheromone content of the picture element above,
Figure RE-FDA0002668235760000055
indicates being located at PosijHeuristic value of the above pel, allowedkIndicating that the pixel set which can be selected by the kth ant needs to be excluded when the pixel is selected, wherein alpha and beta are an pheromone factor and a heuristic factor respectively;
(6) selecting a randomly selected pixel by roulette: calculating the contribution probability according to the transition probability calculated in the step (5), wherein the calculation mode is as follows:
Figure RE-FDA0002668235760000061
in the formula, n is the number of candidate pixels;
generating a random number, sequentially calculating the cumulative probability of each pixel, and selecting a pixel as an urban expansion unit to be added into a simulation result when the cumulative probability of the pixel is greater than the random number; the cumulative probability is calculated as follows:
Figure RE-FDA0002668235760000062
wherein m is PosijThe serial number of the pixel when the selection probability is calculated;
adding the randomly selected pixel into the simulation result of the ant, and then turning to the step (4);
(7) evaluating the simulation result of the ants by using the objective function of 5-1, calculating the score of the objective function, updating the population optimal simulation result, and turning to the step (3) after the calculation is finished;
(8) updating pheromones on the paths;
(9) after the pheromone is updated, emptying simulation results of all ants, and turning to the step (2);
(10) and (5) finishing the algorithm and outputting the optimal simulation result in all ants.
CN202010783897.5A 2020-08-06 2020-08-06 City expansion simulation method based on bargaining model and ant colony optimization algorithm Pending CN112528359A (en)

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