CN111209679A - Genetic algorithm-based soil heavy metal content spatial interpolation method - Google Patents

Genetic algorithm-based soil heavy metal content spatial interpolation method Download PDF

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CN111209679A
CN111209679A CN202010031083.6A CN202010031083A CN111209679A CN 111209679 A CN111209679 A CN 111209679A CN 202010031083 A CN202010031083 A CN 202010031083A CN 111209679 A CN111209679 A CN 111209679A
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尹光彩
宋小旺
陶琳
肖荣波
林亲铁
陈幸玲
吴雄
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Guangdong University of Technology
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Abstract

The invention discloses a soil heavy metal content spatial interpolation method based on a genetic algorithm, which comprises the following steps: carrying out gene coding on the content of the soil heavy metal observation points, and acquiring an observation point clustering center and an initial population by adopting a k-means clustering algorithm; pairwise pairing individuals in the population and determining paired individuals px,pyThe new individuals p producednewObtaining soil related attribute parameter values of the new individual; and p for paired individualsx,pyPerforming gene crossover operation to generate new individuals pnewI.e. the heavy metal content value of the determined geographical location; for new individual pnewPerforming genetic variation operation to obtain new population
Figure DDA0002364317970000011
And for new population
Figure DDA0002364317970000012
Carrying out adaptability evaluation; updating iteration is carried out in the new population, and population merging is carried out on the new population after iteration.

Description

Genetic algorithm-based soil heavy metal content spatial interpolation method
Technical Field
The invention relates to the technical field of computers, soil science and ecology, in particular to a method for carrying out spatial data interpolation analysis on soil heavy metal content.
Background
The method is a common problem in the field of soil heavy metal research. At present, 3 types of methods are mainly used for solving the problem of spatial interpolation analysis of the heavy metal content in soil. The method of type 1 is an interpolation method represented by a common kriging method based on geostatistics, and is characterized by geospatial correlation, including a kriging method, a pan-kriging method and the like; the 2 nd type of methods are non-geostatistical methods represented by inverse distance weighted interpolation, which are remarkably characterized in that the influence of observation points on interpolation points is gradually weakened along with the increase of distance, and comprise an RBF (radial basis function) method and the like; the 3 rd type is the combination of the former two, and different methods are applied to solve the local problem of data interpolation from different sides, and finally a surround is formed to realize the data interpolation.
The genetic algorithm simulates the natural evolution and biological genetic process of the biological world, carries out biological evolution and population reproduction operations such as selection, crossing, variation and the like among biological individuals, and searches the optimal solution in the global range. Genetic algorithms have found wide application in the numerical optimization problem in many research areas. The soil heavy metal observation points are used as initial individuals of the biological community to form an initial biological population, the individuals multiply, good individuals are reserved, inferior individuals are eliminated, and the population scale is gradually enlarged. And (4) when the algorithm is finished, performing adaptability evaluation on the population, wherein the new individual reserved by the population is new interpolation point data.
The invention provides a soil heavy metal content spatial interpolation method based on genetic algorithm based on bionics in computational intelligence.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a soil heavy metal content spatial interpolation method based on a genetic algorithm.
The purpose of the invention is realized by the following technical scheme:
carrying out gene coding on the content of the soil heavy metal observation points, and acquiring an observation point clustering center and an initial population by adopting a k-means clustering algorithm;
pairwise pairing individuals in the population and determining paired individuals px,pyThe new individuals p producednewObtaining soil related attribute parameter values of the new individual; and
for paired individuals px,pyPerforming gene crossover operation to generate new individuals pnewI.e. the heavy metal content value of the determined geographical location;
for new individual pnewPerforming genetic variation operation to obtain new population
Figure BDA0002364317950000021
And for new population
Figure BDA0002364317950000022
Carrying out adaptability evaluation;
updating iteration is carried out in the new population, and population merging is carried out on the new population after iteration.
One or more embodiments of the present invention may have the following advantages over the prior art:
the method searches the data of the interpolation point in the global data space range, evaluates and controls the quality of a new individual at each stage of population evolution, namely the quality of the interpolation point data.
Drawings
FIG. 1 is a flow chart of a soil heavy metal content spatial interpolation method;
FIG. 2 is a schematic diagram of the selection range of individual population when selection, crossover and variation are performed;
FIG. 3 is a schematic diagram of a new individual geographic location distribution area;
FIG. 4 is one embodiment of a spatial interpolation method for heavy metal content in soil;
FIG. 5 is a second embodiment of the spatial interpolation method for heavy metal content in soil.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the following embodiments and accompanying drawings.
As shown in FIG. 1, a process of a spatial interpolation method for heavy metal content in soil comprises
Obtaining k clustering centers, k initial populations and member individuals thereof by gene coding and k-means clustering analysis of a certain heavy metal content observed value of soil and soil environment parameters thereof; carrying out selective pairing in the population, determining the position of a new individual, carrying out gene crossing and gene mutation operations to obtain a new population, and carrying out adaptability evaluation on the new population; and carrying out population merging operation on the new population after iteration. The algorithm is ended using the following strategy.
Algorithm end strategy one: the whole population is iterated and accumulated to the appointed number of times;
and (5) algorithm ending strategy two: the total number of individuals of the new population reaches the expected number;
and (3) algorithm ending strategy three: the adaptability evaluation is not obviously improved, and even the population quality is reduced.
Carrying out gene coding on the content of the soil heavy metal observation points, and acquiring an observation point clustering center and an initial population by adopting a k-means clustering algorithm; dividing all observation point individuals into k initial populations according to pairwise adjacent distances, wherein piFor individual observation point, lon and lat are longitude and latitude of the observation point, n is number of individual observation point, PkK initial populations and their member individuals,
Figure BDA0002364317950000031
is a population
Figure BDA0002364317950000032
The number of individuals.
pi＝＜lon，lat，...＞
P0＝{p1，p2，...，pn}，1≤k≤n/2
P1＝P0
Figure BDA0002364317950000033
Figure BDA0002364317950000034
Figure BDA0002364317950000035
All individuals are divided into k initial populations and satisfy the condition (1) to obtain k clustering centers and k initial populations Pk。
Figure BDA0002364317950000036
And (3) carrying out gene coding on the soil heavy metal content of the observation point by adopting a binary system, wherein the gene coding comprises the gene coding of an integer part and a decimal part, and the formula (2) is shown. The gene sequences with the same growth degree (n + m) are coded by the heavy metal content codes of the soil of all the observation points and the estimation points, and the insufficient positions are filled with 0.
an-1an-2…a0·a-1a-2…a-mai＝0or1-m≤i≤n-1 (2)
For any one population
Figure BDA0002364317950000037
Implementing pairwise individual pairing selection exerciseDo this. Population
Figure BDA0002364317950000038
The scope of the pair selection is all individuals within the population, if the population is
Figure BDA0002364317950000039
With other populations
Figure BDA00023643179500000310
Is close (less than a certain threshold), the population will be formed
Figure BDA00023643179500000311
Is included in the population adjacent to the individual
Figure BDA00023643179500000312
See fig. 2 for a range of pairing selections. Individuals selected by pairing are denoted < px，py>. the strategy for pairing selection can be the following principle:
the principle of the approach is as follows: preferentially selecting 2 individuals with close distance;
random principle: randomly selecting 2 individuals;
the combination principle is as follows: a hybrid selection of the 2 selection principles described above.
For paired individuals<px,py>The new individual to be generated is determined to be geographically located. Setting the influence range of the parent individuals on the new individuals as radius r, 2 parents<px,py>The radius of the circumscribed circle of the influence range is R, and the geographical position range of the new individual is a region formed by 2 parent circular regions and 2 circumscribed circles, which is shown in figure 3. Determining paired individuals with uniformly distributed probability in the region<px,py>New individual p ofnewA geographic location. After the geographical position of the new individual is determined, the soil related attribute parameter values of the individual can be obtained, wherein the soil related attribute parameter values comprise soil type, elevation, organic matter content, soil pH value, soil cation exchange capacity, distance from a parent body, pollution source and the like.
For paired individuals<px,py>Performing gene crossover operation to generate new individuals pnewI.e. the heavy metal content value of the determined geographical location. Is provided with<px,py>Respectively expressed by the formula (3), calculating the gene crossing position N and satisfying the condition (4), and simultaneously determining the dominant parent.
Figure BDA0002364317950000041
Figure BDA0002364317950000042
n-1≤N≤0 (4)
Soil type: if the new individual pnewThe soil type and 2 matrixes<px,py>If the two parents are the same, the 2 parents participate in crossing with equal probability; if the new individual's soil type is associated with 1 parent (e.g. p)x) If the two genes are the same, the parent participates in crossing with higher probability, namely more genes of the parent are reserved; if the soil type of the new individual is different from that of the 2 parents, the 2 parents participate in crossing with equal probability, or the new individual is abandoned and the parents are reselected. Finally determining the contribution degrees of 2 parent soil types to new individuals, wherein the contribution degrees are respectively counted as
Figure BDA0002364317950000043
And
Figure BDA0002364317950000044
expressed as 2 percent, the sum of 2 is 1.
Elevation: under the influence of gravity and precipitation, the heavy metals in the soil have the characteristic of migrating from high to low topography along with the water flow direction. If the 2 parents have the same elevation, the parents participate in crossing with equal probability; if the parent is pxWith high topography, it participates in the crossing with higher probability; if the new individual has a higher profile than 2 parents, the elevation factor is ignored, or the new individual is discarded and the parents are reselected. Finally determining the contribution degree of the elevation of 2 parents to the new individual, respectively calculating as
Figure BDA0002364317950000045
And
Figure BDA0002364317950000046
the organic matter content of the soil is as follows: the soil with high organic matter content has stronger adsorption capacity to some heavy metals, thereby improving the fixation and accumulation of the soil to the heavy metals. If the 2 matrixes have the same soil organic matter content, the matrixes participate in crossing with equal probability; if the parent px has higher soil organic matter content, the parent px participates in crossing with higher probability; if the new individual has a higher soil organic content than the 2 parents, the organic content factor is ignored or the new individual is discarded and the parents are reselected. Finally determining the contribution degree of the soil organic matter content of 2 parent bodies to new individuals, and respectively calculating the contribution degree
Figure BDA0002364317950000051
And
Figure BDA0002364317950000052
the pH value of the soil is as follows: the heavy metal release potential increases as the soil pH decreases. If 2 parents have the same pH value, the parents participate in crossing with equal probability; if the parent px has a low pH, then it is more likely to participate in crossover; if the new individual has a lower pH than the 2 parents, the pH factor is ignored, or the new individual is discarded and the parents are reselected. Finally determining the contribution degree of the soil pH value of 2 parents to a new individual, and respectively calculating the contribution degree
Figure BDA0002364317950000053
And
Figure BDA0002364317950000054
soil Cation Exchange Capacity (CEC): the higher the CEC value of the soil, the higher the net negative charge amount of soil particles, so the more the adsorption points of cations are, especially the stronger the obligatory adsorption of heavy metal elements is, if 2 matrixes have the same CEC value, the matrixes participate in the crossing with equal probability;if parent px has a larger CEC value, then it is more likely to participate in the crossover; if the new individual has a greater CEC value than 2 parents, the CEC influencing factors are ignored or the new individual is discarded and the parents are reselected. Finally determining the contribution degree of CEC of 2 parents to new individuals, respectively calculating the contribution degree
Figure BDA0002364317950000055
And
Figure BDA0002364317950000056
distance from mother body: the new individuals are distributed in the blocks shown in FIG. 3, and the parents with close distances have large influence on the new individuals, have high relevance and participate in gene crossing with higher probability. Finally determining the contribution degree of the distance between the parent and the new individual to the new individual, respectively
Figure BDA0002364317950000057
And
Figure BDA0002364317950000058
according to the above influence factors, calculating the comprehensive contribution degree of 2 parents to the heavy metal content of the new individual, and expressing as wxAnd wyAnd determining the dominant parent, see formula (5) and formula (6).
Figure BDA0002364317950000059
Figure BDA00023643179500000510
Let the dominant parent be pxCalculating the gene crossing position N to generate a new individual pnewSee equations (7) and (8), where rand generates random perturbations.
N＝[n×(1-wx)×rand](7)
Figure BDA00023643179500000511
For new individual pnewPerforming gene mutation operation. Mutation operations may employ the following strategy.
Low probability strategy: the new individual is similar to 2 parents in the soil related attribute parameter value;
the medium probability strategy is as follows: the new individual is similar to 1 parent in the soil related attribute parameter value;
high probability strategy: the difference between the values of the soil-related attribute parameters was significant for 3 individuals.
The mutation probability of the gene determined according to the mutation strategy is pvarThe number of the mutated gene is pvarX (n + m) x rand, and occurs uniformly in the new individual pnewIn (c). Finally generated new individual pnewAdding into the population
Figure BDA0002364317950000061
In (1).
For new individual pnewA source of contamination strategy may be used in performing genetic variation manipulations.
High-order gene variation: new individual pnewIf the neighborhood has a pollution source and the elevation is lower than the pollution source, the new individual has variation in the high gene region according to a certain probability;
median genetic variation: new individual pnewIf a pollution source exists in the nearby area and the elevation is not higher than the pollution source, mutation occurs in the median gene area of the new individual according to a certain probability;
low-order gene variation: new individual pnewIf the gene is far from the source of pollution, the mutation will occur in the low-order gene region of the new individual with a certain probability.
Obtaining a new population after selection, crossing and mutation operations
Figure BDA0002364317950000062
The population was evaluated for fitness. New population
Figure BDA0002364317950000063
Is represented by formula (9), wherein
Figure BDA0002364317950000064
Representing a population
Figure BDA0002364317950000065
The initial individual of (a) or (b),
Figure BDA0002364317950000066
representing a population
Figure BDA0002364317950000067
A newborn subject of (1).
Figure BDA0002364317950000068
In the whole population
Figure BDA0002364317950000069
Is subjected to inverse distance weighting (or kriging)
Figure BDA00023643179500000610
Interpolation is carried out to obtain
Figure BDA00023643179500000611
Is estimated value of
Figure BDA00023643179500000612
Adaptation of new populations using a coefficient of determination (R)2) Root Mean Square Error (RMSE) and relative analytical error (RPD) as evaluation indices, R2And the larger the RPD and the smaller the RMSE, the stronger the adaptability of the new population, receiving the population and replacing the original population, otherwise giving up the new individual
Figure BDA00023643179500000613
The population returns to the original state
Figure BDA00023643179500000614
And re-evolved.
The merging between populations is examined and performed after update iterations occur within the populations.
One of the conditions for population merging is that the number of adjacent individuals of adjacent populations reaches a certain degree.
The second condition of population merging is that 2 and 1 clustering centers are respectively set by adopting a k-means clustering algorithm, and the evaluation index is set to be 1 clustering center
Figure BDA00023643179500000615
Does not increase significantly.
The third condition for population merging is that after merging, adaptability evaluation and evaluation index (R) are carried out2RMSE, RPD) to meet the requirements of reception. The populations are combined to form a new population.
One implementation of this embodiment is to implement the parallel implementation in a multi-thread manner, as shown in fig. 4.
Firstly, standardizing the soil heavy metal content observed value and soil environment parameters thereof into database records, wherein each record corresponds to 1 observation point, namely 1 original individual.
Gene coding is completed in the main thread, k-means clustering analysis is performed, and all database records are divided into k initial populations.
And starting k working threads for the k initial populations respectively, performing selection, crossing and mutation operations in the populations and the neighborhoods thereof, determining the geographic position of the new individual, and performing adaptive evaluation on the new populations.
And performing pairwise combination between the populations. And after finishing one round of population iteration updating, the working thread checks whether the condition of population merging is met. And when the population merging condition is met, waiting for another population to finish the iterative updating of the current round, and then implementing population merging. After merging, 1 of the working threads is terminated, and the other 1 of the working threads continues population evolution iteration.
And when all the populations are iterated to the appointed times, finishing the algorithm, and finally outputting all the individual data.
The second embodiment of the present invention is implemented serially by using a third-party tool and a custom plug-in.
Firstly, normalizing the soil heavy metal content observation value and the environment background data thereof into an ArcGis data format, and establishing a grid image.
And (3) carrying out clustering analysis on the grid image according to the geographical position by adopting a Pcluster tool in ArcGis to obtain k clustering centers and k initial populations.
In ArGis, an interpolation point grid, namely the geographical position of a new individual, is established for the whole interpolation area, and a configuration matrix is selected for each interpolation point and meets the conditions shown in FIG. 3. When population iteration is started, part of interpolation points may not be configured to the parent satisfying the condition, but are successfully configured in the middle and later stages of the iteration.
In ArcGis, 1 custom plug-in is created with Python, and population iterations are performed in a serial fashion, i.e., only 1 population is performing an iteration at a particular time, as shown in fig. 5.
And when all new individuals of the interpolation point grid are finished, or when all populations iterate to the specified times, finishing the algorithm, and finally outputting all individual data.
Although the embodiments of the present invention have been described above, the above descriptions are only for the convenience of understanding the present invention, and are not intended to limit the present invention. It will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (9)

1. A soil heavy metal content spatial interpolation method based on a genetic algorithm is characterized by comprising the following steps:
carrying out gene coding on the content of the soil heavy metal observation points, and acquiring an observation point clustering center and an initial population by adopting a k-means clustering algorithm;
pairwise pairing individuals in the population and determining paired individuals px,pyThe new individuals p producednewObtaining soil related attribute parameter values of the new individual; and
for paired individuals px,pyPerforming gene crossover operation to generate new individuals pnewI.e. the heavy metal content value of the determined geographical location;
for new individual pnewPerforming genetic variation operation to obtain new population
Figure FDA0002364317940000011
And for new population
Figure FDA0002364317940000012
Carrying out adaptability evaluation;
updating iteration is carried out in the new population, and population merging is carried out on the new population after iteration.
2. The genetic algorithm-based soil heavy metal content spatial interpolation method of claim 1, wherein binary coding is adopted to perform gene coding on soil heavy metal content data.
3. The soil heavy metal content spatial interpolation method based on the genetic algorithm as claimed in claim 1, wherein the k-means clustering algorithm is to perform clustering analysis according to the distance between the observation points, and take the minimum average value of the distance between the observation points as the optimal clustering.
4. The genetic algorithm-based soil heavy metal content spatial interpolation method of claim 1,
the range of the pairing selection is that all individuals in the population and other population individuals adjacent to the boundary, the circular area of the paired individuals and the area formed by the circumscribed circle of the circular area are used as the position range of the new individual, and the position of the new individual is determined by uniform distribution probability;
the strategy principle of the pairing selection is as follows: a proximity principle, a random principle, and a combination principle.
5. The genetic algorithm-based soil heavy metal content spatial interpolation method according to claim 1, wherein the soil-related attribute parameter values comprise soil type, elevation, soil organic matter content, soil pH value, soil cation exchange capacity, distance from parent body, and pollution source.
6. The genetic algorithm-based soil heavy metal content spatial interpolation method of claim 1, wherein the genetic variation operation is to perform the genetic variation operation on the interpolation point data according to the paired individuals, the soil type, the elevation, the soil organic matter content, the soil pH value, the soil cation exchange capacity, the distance from the parent body and the pollution source of the new individual to generate new interpolation point data.
7. The genetic algorithm-based soil heavy metal content spatial interpolation method of claim 1, wherein p is added to a new individualnewThe strategy for implementing gene variation operation is as follows: a low probability strategy, a medium probability strategy, and a high probability strategy; or
For new individual pnewThe gene variation operation is implemented by adopting a pollution source strategy, including high-order gene variation, medium-order gene variation and low-order gene variation.
8. The soil heavy metal content spatial interpolation method based on the genetic algorithm as claimed in claim 1, wherein the population adaptability evaluation is to interpolate observation point data by using observation point and interpolation point data in a population, and perform population adaptability evaluation by using original values and estimated values of the observation points.
9. The genetic algorithm-based soil heavy metal content spatial interpolation method according to claim 1, wherein the population merging condition is that the number of adjacent individuals of adjacent populations on the boundary reaches a certain degree, and the population clustering analysis and population adaptability evaluation are carried out.
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