CN102542051B - Design method for multi-target cooperative sampling scheme of randomly-distributed geographic elements - Google Patents

Abstract

The invention relates to a design method for a multi-target cooperative sampling scheme of randomly-distributed geographic elements, which includes the steps: 1 selecting multiple geographic elements with random distribution characteristics as sampling targets, and acquiring pre-sampling sample point data of the targets; 2 exploring spatial variation structures of the pre-sampling data by an ordinary Kriging method, fitting and generating a theory semi-variable function of each target, and obtaining a spatial distribution integral of all the targets by a Gaussian sequential random simulation method according to the theory semi-variable functions and the pre-sampling sample point data in the step 1; 3 computing the minimum cooperative sample size according to the precision requirements of the targets and prior variance, and setting a cooperative particle swarm optimization parameter; and 4 optimizing a current pre-sampling sample point scheme by means of cooperative particle swarm optimization, so that the multi-target cooperative sampling scheme is obtained. By the aid of the method, on-site sampling cost can be saved, self-organization and optimization during distribution of thesampling sample points are improved, and the design efficiency of the multi-target cooperative sampling scheme of the geographic elements is enhanced.

Description

A kind of multiple goal of stochastic distribution type geographic element is worked in coordination with the sampling plan method for designing

Technical field

The present invention relates to the collaborative sampling plan method for designing of a kind of multiple goal, especially relate to a kind of collaborative sampling plan method for designing of multiple goal of stochastic distribution type geographic element.

Background technology

Geographic element comprises landform, weather, the hydrology, biology and soil etc., it is implemented to investigate accurately is the key of explaining geographic element space distribution rule and evolution process, also is the needs of resource management, disaster management, ecological environment treatment and global change research due.In actual mechanical process, the researchist is in order to save the sampling cost and to improve sampling efficiency, usually only design the spacing sampling investigation task that a cluster scheme is implemented multiple geographic element index simultaneously, therefore how to design the sampling precision that sampling plan guarantees many indexs and require to become the focus that scholars pay close attention to.

At present in the two space-like Sampling Strategies that exist, be applicable to the multisampling object sample of large scale, large sample amount based on the Sampling Strategies (Design based sampling) of design, and exist not enough in problems such as deal with data disappearance (Missing data) and data analyses; Sampling Strategies (Model based sampling) based on model can avoid the data disappearance to the influence of sampling results, the single index of more concern in actual applications by making up overall model of fit.Stochastic distribution type physical geography essential factors space has randomness and space structure on distributing simultaneously, therefore be fit to application geo-statistic relative theory and method and explore its space distribution rule, make up the overall model of space distribution, assist and carry out space sampling plan design.As seen, improve based on the model sampling strategy, the method that makes up the collaborative sampling of a kind of many key elements has become a kind of development trend of the physical geography essential factors space methods of sampling.

From in essence, the sampling of multisampling target cooperative need be satisfied different indexs simultaneously to the requirement of sampling precision, therefore belongs to the problem in the multiple-objection optimization category.Tradition multiple goal Synergistic method carries out combination with method of weighted mean or minimum threshold method and simulated annealing derivation algorithm, and effect is remarkable.(Weighted Average method, core concept WA) is to adopt the mode of weighted sum that multi-objective problem is converted to the single goal problem to method of weighted mean, unites with many indexs that golden variance reaches minimum basis for estimation as optimal sampling plan in the gram.When weighted sum, for golden variance yields in the gram that guarantees different indexs has identical dimension, assist the base station value ways and means of semivariation variance function that it is carried out standardization by golden variance in will restraining divided by corresponding index.Minimum threshold method (Minimum Threshold Method, MT) core concept is to be golden variance desired value in the suitable minimum of each target setting gram, and will guarantee in the change of each sampling point position the gram of all indexs that golden variance is lower than or as far as possible near this desired value.If golden variance equals its desired value and shows that current sample plan can accurately describe the spatial variability rule of this index in the gram of a certain index; And if be lower than its desired value, show that then there is certain redundancy in current sample plan.But above-mentioned classic method exists certain not enough, be difficult to obtain as the weights for the multi-objective problem method of weighted mean of complexity, and the weight of setting can cause some target to reach optimum and the relatively poor extreme case of other targets usually; The minimum threshold method requires all desired values all will reach predetermined optimal value, therefore may search for less than optimum solution, and may be than the difficult optimal value of setting for some targets; In addition, existing searching algorithm more efficiently can be used for substituting simulated annealing.

Collaborative particle swarm optimization (Coorperative Particle Swarm Optimization, CPSO) can influencing each other and cooperating with each other by individuality, spontaneously orderly group behavior on deadline, space and the function is widely used in the multiple-objection optimization field.This algorithm has improved the global convergence ability of algorithm widely by adopting the independent and collaborative mode of evolution that combines.Therefore, introducing the collaborative particle swarm optimization of scale-of-two carries out the collaborative sampling of many geographic elements and has bigger operability and application space.

Summary of the invention

The present invention solves the existing in prior technology technical matters; Provide a kind of and can save the cost of sampling on the spot, can improve the collaborative sampling plan design efficiency of the many indexs of geographic element, sampling sampling point laying process has the collaborative sampling plan method for designing of multiple goal of self-organization, the property optimized and intelligent a kind of stochastic distribution type geographic element.

Above-mentioned technical matters of the present invention mainly solves by the following technical programs:

A kind of multiple goal of stochastic distribution type geographic element is worked in coordination with the sampling plan method for designing, it is characterized in that, may further comprise the steps:

Step 1, select a plurality of geographic elements with random distribution characteristic as the sampling index, obtain the pre-sampling sampling point data of index, the zone of will sampling is carried out graticule mesh and is divided, the grid cell that forms is as sampling unit, and the sampling unit set in the sampling zone is as the sampling frame;

Step 2, utilize common gram Li Jinfa to explore the spatial variability structure of pre-sampled data, match generates the theoretical semivariable function of each index, according to the pre-sampling sampling point data in theoretical semivariable function and the step 1, it is overall to adopt the sequential Method of Stochastic of Gauss to obtain the space distribution of each index;

Step 3 is calculated minimum collaborative sample size according to accuracy requirement and the prior variance of index, and collaborative particle swarm optimization parameter is set;

Step 4 utilizes collaborative particle swarm optimization that pre existing sampling sampling point scheme is optimized, and obtains the collaborative sampling plan of many indexs, and described pre existing sampling sampling point scheme is the described pre-sampling sampling point data of obtaining index of step 1.

The present invention adopts the collaborative sampling plan in multiple goal space that generates stochastic distribution type physical geography key element based on the collaborative particle swarm optimization of the scale-of-two of " doughnut model ", be applicable under the prerequisite of the representativeness that effectively keeps each index sampling point and sampling precision and by making up a cluster scheme many indexs carried out the space sampling simultaneously, can save the cost of sampling on the spot; Be the weighing criteria of particulate fitness with golden variance and information entropy in the average gram, the constraint that adopts minimum collaborative sample size, sampling accessibility and cost of sampling to lay as the sampling point space, dynamically seek the optimum combination scheme of variable sample size and variable sampling point layout, improved the sampling sampling point and laid the self-organization of process and the property optimized; The inventive method has been inherited the characteristic of collaborative particle swarm optimization, and self-organization self-learning capability strong, intelligent degree height has improved the design efficiency of the collaborative sampling plans of the many indexs of physical geography key element.

In the collaborative sampling plan method for designing of the multiple goal of above-mentioned a kind of stochastic distribution type geographic element, in the described step 3, the step of calculating minimum collaborative sample size is as follows: definition sampling sample space A, the sampling unit number is N, sampling index quantity is V, if there is the sampling design of an optimum in index i, its accuracy requirement is p _i, the corresponding sample capacity is n _i

Step 3.1, the accuracy requirement p of setting index 1 ₁, population mean μ ₁, index 1 sampling mean

And standard deviation s ₁, adopt the smallest sample amount computing formula in traditional arbitrary sampling method to determine that the smallest sample capacity of index 1 is n ₁, the sampling sample of formation is ξ ₁

Wherein, ${\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">n</figure-callout>}}_1=\frac{{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}^2{{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">s</figure-callout>}}_1}^2}{{(\stackrel{\&OverBar;}{x_{1n}}-{\mathrm{\&mu;}}_1)}^2}$ Formula one;

Step 3.2 is according to the sampling precision requirement test samples ξ of index 2 ₁, rejecting does not form one group of new sample after meeting the sampling point of index 2 sampling designing requirements

Step 3.3 according to the accuracy requirement of index 2, is extrapolated sample

The maximum subsample space A that can represent ₂And residue sample space

Step 3.4 is in the residue sample space

Adopt arbitrary sampling method to determine that capacity is n according to the sampling designing requirement of index 2 ₂A sample ξ ₂, then capacity is n ₁+ n ₂Sample ξ ₁∪ ξ ₂It is the one group of smallest sample that satisfies index 1 and index 2 sampling designs simultaneously;

Step 3.5, repeated execution of steps 3.1 are to step 3.4, and repeating number of times is V-1 time, wherein, and N ₀=n ₁+ n ₂+ ... + n _v, and ξ ₁, ξ ₂, Λ, ξ _vSeparate, N then ₀Satisfy the smallest sample capacity of the collaborative sampling design of many indexs exactly.

In the collaborative sampling plan method for designing of the multiple goal of above-mentioned a kind of stochastic distribution type geographic element, described step 4 concrete operations step is as follows:

Step 4.1 makes up particulate and the regional mapping relations of sampling, according to mapping relations initialization particulate group S;

Step 4.2, according to branch particulate groups such as index quantity V, when population scale P is divided exactly by V, sub-particulate group S then _vPopulation scale P _v=P/V; When population scale P is not divided exactly by V, lose for fear of particulate group particle information, at first determine the basic particulate number that each subgroup comprises

Before then remaining particulate being distributed to successively

Individual subgroup then from wherein selecting a particulate to copy at random, guarantees each sub-particulate group S for the subgroup of additional allocation particulate not _vPopulation scale be

Wherein Be bracket function;

Step 4.3 makes up the ring-type synergetic structure of sub-population, is the head end of ring texture with a sub-population at random, adopts the mode of picked at random to determine the sub-population of its neighborhood, repeats this step and is combined into the ring-type synergetic structure up to all sub-populations;

Step 4.4 is a collaborative period T _CoorIn, setting Flag identifies sub-population and independently evolves whether finish t _CoorThe sign algebraically that in the collaborative cycle evolve in the subgroup, initial value is 1, sub-particulate group S _vIndependently seek the optimal sampling scheme of a soil attribute respectively, wherein, (1≤t _Coor≤ T _Coor);

Step 4.5 is obtained the current global history optimal location of all subgroups and is formed the Pareto disaggregation as optimum solution, if Flag=true enters step 4.6, distributes to adjacent sub-population S otherwise Pareto is separated the optimum solution i that concentrates _I+1As S _I+1Step 4.4 is also returned in the initial global optimum position in next collaborative cycle, when i=V, then optimum solution i is distributed to sub-population S ₁

Step 4.6 selects an optimum solution as the collaborative sampling plan output of the multiple goal of stochastic distribution type geographic element from the Pareto solution is concentrated at random.

In the collaborative sampling plan method for designing of the multiple goal of above-mentioned a kind of stochastic distribution type geographic element, in the described step 4.4, independent evolutionary step is as follows:

Step 4.4.1 calculates S _vIn each particulate S _Vi(t) fitness;

Step 4.4.2 determines the individual historical optimum position of particulate and global history optimal location;

Step 4.4.3 judges whether to satisfy end condition, if satisfy then set Flag=true and execution in step 4.5, simultaneously with the Sg that generates among the step 4.4.1 _v(t) export as the optimal sampling plan of subgroup, otherwise will enter step 4.4.4;

Step 4.4.4 judges whether to finish a collaborative cycle t _Coor=T _CoorIf, finish then set Flag=false skipping to step 4.5, and with the Sg that generates among the step 4.4.1 _v(t) export as the optimal sampling plan of subgroup, otherwise enter step 4.4.5;

Step 4.4.5 is according to the position of the historical optimum position of the current individuality of particulate and current global history optimal location renewal particulate, t _CoorAutomatically add 1, and return step 4.4.1.

In the collaborative sampling plan method for designing of the multiple goal of above-mentioned a kind of stochastic distribution type geographic element, in the described step 3, the parameter of particulate clustering class algorithm comprises population scale P, maximum iteration time, inertia weight w, stray parameter r ₁And r ₂, individual information aceleration pulse c ₁, the aceleration pulse c of social information ₂, the collaborative period T of converging factor x and sub-population _Coor, adopt maximum iteration time as the algorithm end condition.

In the collaborative sampling plan method for designing of the multiple goal of above-mentioned a kind of stochastic distribution type geographic element, in the mapping relations that described step 4.1 makes up, a scale-of-two particulate is the set of sampling unit, represent a kind of sampling plan, each dimension in the particulate represents a sampling unit, dimension values is that the corresponding sampling unit of 1 expression is chosen as sampling point, and dimension values is that the corresponding sampling unit of 0 expression is not chosen as sampling point.

In the collaborative sampling plan method for designing of the multiple goal of above-mentioned a kind of stochastic distribution type geographic element, among the described step 4.4.1, golden variance and sampling point information entropy were weighed in the fitness of particulate adopted and on average restrains, and determined particulate S _ViAt individual historical optimum position Sb of the t moment _Vi(t) with particulate group overall situation optimum position Sg _v(t) step is as follows:

When the fitness of t+1 moment particulate was better than the fitness of its historical optimum, then that particulate is current position was recorded as individual historical optimum position, otherwise remains unchanged;

As subgroup S _vWhen t+1 is in a first generation in the new collaborative cycle constantly, t wherein _Coor=1, then subgroup global optimum position equals subgroup S _V-1Last collaborative end cycle the time position Sg of global optimum that obtains _V-1(t), thereby for the message exchange that guarantees between the subgroup, otherwise, contrast the historical global optimum in optimum individual position and the subgroup position in the current subgroup, will be subgroup S than the superior _vCurrent global optimum position:

${\mathrm{Sb}}_{\mathrm{vi}}(t+1)=\left\{\begin{array}{cc}{\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)& \mathrm{if}[f_v\left(S_{\mathrm{vi}}(t+1)\right)\&GreaterEqual;f_v\left({\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)\right)]\\ S_{\mathrm{vi}}(t+1)& \mathrm{otherwise}\end{array}\right.$ Formula two

${\mathrm{Sg}}_v\left(t\right)=\left\{\begin{array}{cc}{\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)& \mathrm{if}[f_v\left({\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)\right)={\min }_{1_S{i}_{S}N}{\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)]\mathrm{and}[t_{\mathrm{coor}}\&NotEqual;1]\\ {\mathrm{Sg}}_{v-1}\left(t\right)& \mathrm{if}[t_{\mathrm{coor}}=1]\end{array}\right.$ Formula three.

In the collaborative sampling plan method for designing of the multiple goal of above-mentioned a kind of stochastic distribution type geographic element, among the described step 4.4.5, the particulate position is upgraded namely according to subgroup S _vMiddle particulate S _Vi(t) the historical optimum position Sb of current individuality _Vi(t) and current global history optimal location Sg _v(t) determine its t+1 value x of dimension j constantly _{Vi, j}(t+1):

$\left\{\begin{array}{c}{V}_{\mathrm{vi},j}(t+1)=\mathrm{\&chi;}({\mathrm{wV}}_{\mathrm{vi},j}\left(t\right)+c_1{r}_1({\mathrm{Sb}}_{\mathrm{vi},j}\left(t\right)-S_{\mathrm{vi},j}\left(t\right))+c_2{r}_2({\mathrm{Sg}}_{v,j}\left(t\right)-S_{\mathrm{vi},j}\left(t\right)))\\ x_{\mathrm{vi},j}(t+1)=\left\{\begin{array}{cc}0& \mathrm{if}[r\&GreaterEqual;\mathrm{sig}\left(V_{\mathrm{vi},j}(t+1)\right)]\\ 1& \mathrm{otherwise}\end{array}\right.\end{array}\right.$ Formula four;

Minimum collaborative sample size, sampling accessibility and 3 factors of sampling expense of being subject to are upgraded in the particulate position, and wherein minimum collaborative sample size is calculated by step 3, the number of sampling point in the restriction sampling plan; The restriction of sampling accessibility comprises buildings, waters scope or the zone, abrupt slope in the sampling zone, the locus of restriction sampling point; The number of sampling costs constraints sampling point, comprise that total sampling expense is that FT, basic sampling expense are FB and single sampling point sampling expense three parts, single sampling point sampling expense is divided into I level difficult region, II level difficult region and III level difficult region by the sampling zone, and establishing I level difficult region sampling point sampling expense is FS ₁, sampling point quantity is N ₁, each sampling point sampling expense of II level is FS ₂, sampling point quantity is N ₂, III level zone is FS ₃, sampling point quantity is N ₃, sampling costs constraints condition can be expressed as:

FS ₁* N ₁+ FS ₂* N ₂+ FS ₃* N ₃≤ FT-FB formula five.

Therefore, the present invention has following advantage: can improve the collaborative sampling plan design efficiency of the many indexs of geographic element, save the cost of sampling on the spot, sampling sampling point laying process has self-organization, the property optimized and intelligent.

Description of drawings

Fig. 1 is workflow synoptic diagram of the present invention.

Fig. 2 is particulate mapping relations synoptic diagram among the present invention.

Fig. 3 is the unreachable regional synoptic diagram of sampling among the present invention.

Fig. 4 is the linear relationship chart of employing expense and sample size among the present invention.

Fig. 5 is test regional location figure in the embodiment of the invention.

Fig. 6 is test site data plot in the embodiment of the invention.

Fig. 7 is the collaborative sampling plan design result figure of many soil index in the embodiment of the invention.

Fig. 8 is the convergence curve figure of collaborative particle swarm optimization in the embodiment of the invention.

Fig. 9 is that minimum is worked in coordination with sample size to the figure that influences of sample sampling precision in the embodiment of the invention.

Figure 10 is minimum the influence figure of sample size to the algorithm convergence time that work in coordination with in the embodiment of the invention.

Figure 11 is that the cycle of working in coordination with in the embodiment of the invention is to the figure that influences of particulate group convergence time.

Embodiment

Below by embodiment, and by reference to the accompanying drawings, technical scheme of the present invention is described in further detail.

Embodiment:

Theoretical foundation involved in the present invention is as follows:

The collaborative sampling plan design of many indexs needs to satisfy two conditions: golden interpolation result reaches minimum accuracy requirement in the gram that the sample size of (1) sampling and sampling point layout can make arbitrary index; (2) methods of sampling must be quantifiable (Vasat et al., 2010).This shows that the collaborative sampling in the space of the many indexs of physical geography key element belongs to the category of multi-objective optimization question.In sampling process, the accuracy limitations of each index is an optimization aim, because the space distribution structure of index is different, these optimization aim can't be met in same set of sampling point placement scheme simultaneously.Contradiction between the optimization aim shows as when sample plan makes the sample fitting precision of an index reach optimum, the precision of another index may descend, and also needs to consider restrictions such as smallest sample amount, sampling expense and sampling accessibility in addition in sample laying process.The collaborative space sampling of many indexs design process is exactly to seek one group of sampling point placement scheme to make all optimization aim reach Pareto (Pareto) optimum by suitable compromise under sampling constraint condition, also namely when this sampling plan rises the fitting precision of an index, can not cause the precise decreasing of other indexs at least.

(Coorperative Particle Swarm Optimization CPSO) comes from the swarm intelligence Study on Theory collaborative particle swarm optimization.The theoretical essence of swarm intelligence is that the gregarious type animal behavior of occurring in nature is simulated, exploring colony is having under the situation of material or energy exchange with the external world, how influencing each other and cooperating with each other, spontaneously orderly group behavior on deadline, space and the function by individuality.This Study on Theory has promoted Swarm Intelligent Computation method and collaborative theoretical combination.Core concept based on the colony intelligence computing method of working in coordination with thought is: if having N optimization aim in the optimizing process, then whole colony is divided into N sub-group, each sub-group is that individual suitability degree judgment criterion is launched parallel independently optimal solution search corresponding to an optimization aim and with this target, thereby the optimum individual that sub-group all can obtain it after each iterative process is shared as social information and instructed other sub-group completing places renewals.By this independence and the collaborative mode of evolution that combines, the global convergence ability of algorithm can access bigger raising.

Collaborative particle swarm optimization based on the population partition strategy is searched for the collaborative space sampling of many indexs of physical geography key element prioritization scheme.Its basic thought is divided into V sub-population for the optimization aim number according to multi-objective optimization question with the particulate group, each sub-population is carried out independently single goal optimization, can exchange between the optimizing process neutron population about the information of optimum solution separately, also can carry out sub-population reorganization operation, optimize the Pareto optimum solution of after finishing each sub-particulate group being obtained and be combined to form the Pareto optimal solution set also as optimizing result's output.

When N dimensional vector particulate group P was had the multi-objective optimization question F (p) of V target for optimization, population P at first was divided V sub-group, establishes S _vBe v sub-group, S _ViBe subgroup S _vIn i particulate, V _Vi(t) be particulate S _ViAt t flying speed constantly, S _Vi(t) be its t position constantly, Sb _Vi(t) the historical optimal location that experiences constantly at t for this particulate, Sg _v(t) be sub-particulate group under this particulate in t global optimum position constantly, Sg (t) is whole particulate group's global optimum position.

Be method flow step of the present invention below:

Implementation process of the present invention can be divided into macroscopical process, middle sight process and three parts of microprocess: macroscopical process mainly refers to co-operating between sub-population division, subgroup, and its minimum operation unit is sub-population; Middle sight process mainly comprises operations such as particulate evaluation, the renewal of sub-population, and its minimum operation unit is particulate; Microprocess mainly comprises operations such as particulate initialization, the renewal of particulate position, and its least unit is the particulate dimension.Specifically implementation step is as shown in Figure 1:

Step 1, selection has a plurality of geographic elements of random distribution characteristic as the sampling index, obtains the pre-sampling sampling point data of each index, and the zone of will sampling is carried out graticule mesh and divided, the grid cell that forms is as sampling unit, and the sampling unit set in the sampling zone is as the sampling frame;

Step 2, utilize in the common gram in ARCGIS 10 softwares of ESRI company metal working tool (Ordinary Kriging) to explore the spatial variability structure of pre-sampled data and the theoretical semivariable function that match generates each index, determine spatial variability structure fitting function and the function parameter base station value of each index, piece gold number and range, according to the pre-sampling sampling point data of theoretical semivariable function and index, it is overall to adopt the sequential Method of Stochastic of Gauss (Gaussian sequence randomly simulating method) in ARCGIS 10 softwares to obtain the space distribution of each index;

Step 3 arranges collaborative particle swarm optimization parameter, comprises population scale p, maximum iteration time, inertia weight w, stray parameter r ₁And r ₂, individual information aceleration pulse c ₁, the aceleration pulse c of social information ₂, the collaborative period T of converging factor x and sub-population _Coor, adopt maximum iteration time as the algorithm end condition; Accuracy requirement and prior variance according to the sampling index are calculated minimum collaborative sample size, and concrete steps are as follows:

For sampling sample space A, the sampling unit number is N, and sampling index quantity is V, establishes the sampling design that there is an optimum in index i, and its accuracy requirement is p _i, the corresponding sample capacity is n _i

Step (3.1) adopts single index smallest sample amount computing method and arbitrary sampling method to determine that the smallest sample capacity of index 1 is n ₁, minimum sampling sample is ξ ₁, concrete formula is as follows:

${\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">n</figure-callout>}}_1=\frac{{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}^2{{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">s</figure-callout>}}_1}^2}{{(\stackrel{\&OverBar;}{x_{1n}}-{\mathrm{\&mu;}}_1)}^2}$ Formula one;

The accuracy requirement p of index 1 in the formula ₁, population mean μ ₁, index 1 sampling mean

And standard deviation s ₁

Step (3.2) is according to the sampling precision requirement test samples ξ of index 2 ₁, rejecting does not form one group of new sample after meeting the sampling point of index 2 sampling designing requirements

Step (3.3) according to the accuracy requirement of index 2, is extrapolated sample

The maximum subsample space A that can represent ₂And residue sample space

Step (3.4) is in the residue sample space

Adopt arbitrary sampling method to determine that capacity is n according to the sampling designing requirement of index 2 ₂A sample ξ ₂, then capacity is n ₁+ n ₂Sample ξ ₁∪ ξ ₂It is the one group of smallest sample that satisfies index 1 and index 2 sampling designs simultaneously.

Step (3.5), so repeatedly, N ₀=n ₁+ n ₂+ ... + n _v, and ξ ₁, ξ ₂, Λ, ξ _vSeparate, N then ₀Satisfy the smallest sample capacity of many index sampling designs exactly.

Step 4 utilizes collaborative particle swarm optimization that pre existing sampling sampling point scheme is optimized, and obtains the collaborative sampling plan of many indexs, and its step is as follows:

Step (4.1), make up particulate and the regional mapping relations (accompanying drawing 2) of sampling, a scale-of-two particulate is the set of sampling unit, represent a kind of sampling plan, each dimension in the particulate represents a sampling unit, dimension values is that the corresponding sampling unit of 1 expression is chosen as sampling point, and dimension values is that the corresponding sampling unit of 0 expression is not chosen as sampling point; According to mapping relations and pre-sampling sampling point data random initializtion particulate group S, be about to dimension values corresponding with pre-sampling sampling point in the particulate and be set to 1;

Step (4.2), according to branch particulate groups such as sampling index quantity V, when P is divided exactly by V, its neutron particulate group S _vPopulation scale P _v=P/V; When P is not divided exactly by V, lose for fear of particulate group particle information, at first determine the basic particulate number that each subgroup comprises

Before then remaining particulate being distributed to successively

Individual subgroup then from wherein selecting a particulate to copy at random, guarantees each sub-particulate group S for the subgroup of additional allocation particulate not _vPopulation scale be $P_v=\mathrm{int}\left(\frac{p}{v}\right)+1;$

Step (4.3) makes up the ring-type synergetic structure of sub-population, is the head end of ring texture with a sub-population at random, adopts the mode of picked at random to determine the sub-population of its neighborhood, is combined into the ring-type synergetic structure up to all sub-populations by that analogy.

Step (4.4) is a collaborative period T _CoorIn, sub-particulate group S _vIndependently seek the optimal sampling scheme of a sampling index respectively.Setting Flag identifies sub-population and evolves whether finish t _Coor(1≤t _Coor≤ T _Coor) being used for the sign algebraically that in the collaborative cycle evolve in the subgroup, initial value is 1, independent evolutionary step is as follows:

(4.4.1) with golden variance f in the average gram of sampling point ₁With information entropy f ₂As S _vIn each particulate S _Vi(t) fitness weighing criteria calculates the weighted sum value of two criterions as the fitness value of each particulate, and wherein weight is specified in actual implementation process by the user:

${\mathrm{<figure-callout\; id="1"\; label="f"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">f</figure-callout>}}_1=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}(\mathrm{cov}\left(0\right)-W^T\mathrm{cov}\left(x_i{x}_{\mathrm{ij}}\right))$

In the formula, cov (0) is the variance of the pre-sampled data of sampling index, W ^TBe sampling point x _iSampling point x in the adjacent domain _IjWeight matrix, cov (x _ix _Ij) be sampling point x _iSampling point x in the adjacent domain _IjCovariance.According to common gram Li Jinfa, collaborative difference is sampling point x _iTo the interior sampling point x of adjacent domain _IjThe function of distance, so f ₁Value only relevant with the space distribution of sampling point, irrelevant with the concrete value of sampling point.

f ₂＝E[-log{f(x ₁，x ₂，...，x _n)}]

In the formula, f (x ₁, x ₂..., x _n) be its probability density function, x _nThe index space that obtains for step 2 distribute overall in the value at sampling point n place.

(4.4.2) determine particulate S _ViAt individual historical optimum position Sb of the t moment _Vi(t) with particulate group overall situation optimum position Sg _v(t), concrete steps are as follows:

When the fitness of t+1 moment particulate was better than the fitness of its historical optimum, then that particulate is current position was recorded as individual historical optimum position, otherwise remains unchanged; As subgroup S _v(t when t+1 is in a first generation in the new collaborative cycle constantly _Coor=1), then subgroup global optimum position equals subgroup S _V-1Last collaborative end cycle the time position Sg of global optimum that obtains _V-1(t), thereby for the message exchange that guarantees between the subgroup, otherwise, contrast the historical global optimum in optimum individual position and the subgroup position in the current subgroup, will be subgroup S than the superior _vCurrent global optimum position:

${\mathrm{Sb}}_{\mathrm{vi}}(t+1)=\left\{\begin{array}{cc}{\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)& \mathrm{if}[f_v\left(S_{\mathrm{vi}}(t+1)\right)\&GreaterEqual;f_v\left({\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)\right)]\\ S_{\mathrm{vi}}(t+1)& \mathrm{otherwise}\end{array}\right.$ Formula two;

${\mathrm{Sg}}_v\left(t\right)=\left\{\begin{array}{cc}{\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)& \mathrm{if}[f_v\left({\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)\right)={\min }_{1_S{i}_{S}N}{\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)]\mathrm{and}[t_{\mathrm{coor}}\&NotEqual;1]\\ {\mathrm{Sg}}_{v-1}\left(t\right)& \mathrm{if}[t_{\mathrm{coor}}=1]\end{array}\right.$ Formula three;

(4.4.3) judge whether to satisfy end condition, if satisfy then set Flag=true and skip to (4.5), and the Sg of generation in will (4.4.1) _v(t) export as the optimal sampling plan of subgroup, otherwise will enter (4.4.4).

(4.4.4) judge whether to finish a collaborative cycle (t _Coor=T _Coor), skip to (4.5) if finish then set Flag=false, and with the Sg that generates in (4.4.1) _v(t) export as the optimal sampling plan of subgroup, otherwise enter (4.4.5).

(4.4.5) according to the historical optimum position Sb of the current individuality of particulate _Vi(t) and current global history optimal location Sg _Vj(t) position of renewal particulate, t _CoorAutomatically add 1, and return step (4.4.1), the particulate position is upgraded and is namely determined t+1 subgroup S constantly _vMiddle particulate S _Vi(t) the value x of dimension j _{Vi, j}(t+1):

$\left\{\begin{array}{c}{V}_{\mathrm{vi},j}(t+1)=\mathrm{\&chi;}({\mathrm{wV}}_{\mathrm{vi},j}\left(t\right)+c_1{r}_1({\mathrm{Sb}}_{\mathrm{vi},j}\left(t\right)-S_{\mathrm{vi},j}\left(t\right))+c_2{r}_2({\mathrm{Sg}}_{v,j}\left(t\right)-S_{\mathrm{vi},j}\left(t\right)))\\ x_{\mathrm{vi},j}(t+1)=\left\{\begin{array}{cc}0& \mathrm{if}[r\&GreaterEqual;\mathrm{sig}\left(V_{\mathrm{vi},j}(t+1)\right)]\\ 1& \mathrm{otherwise}\end{array}\right.\end{array}\right.$ Formula four;

Minimum collaborative sample size, sampling accessibility and 3 factors of sampling expense of being subject to are upgraded in the particulate position, and wherein minimum collaborative sample size is calculated by step 3, the number of sampling point in the restriction sampling plan; The restriction of sampling accessibility comprises buildings, waters scope or the zone, abrupt slope in the sampling zone, the locus (accompanying drawing 3) of restriction sampling point; The number of sampling costs constraints sampling point, comprise that total sampling expense is that FT, basic sampling expense are FB and single sampling point sampling expense three parts (accompanying drawing 4), the single sampling point sampling of regulation expense according to " surveying production cost quota " can be divided into I level difficult region (plains region is main), II level difficult region (knob is main) and three kinds of standards of III level difficult region (area, mountain region is main) by the sampling zone, and establishing I level difficult region sampling point sampling expense is FS ₁, sampling point quantity is N ₁, each sampling point sampling expense of II level is FS ₂, sampling point quantity is N ₂, III level zone is FS ₃, sampling point quantity is N ₃, sampling costs constraints condition can be expressed as:

FS ₁* N ₁+ FS ₂* N ₂+ FS ₃* N ₃≤ FT-FB formula five;

Step (4.5) is obtained the current global history optimal location of all subgroups and is formed the Pareto disaggregation as optimum solution, if Flag=true enters (4.6), distributes to adjacent sub-population S otherwise Pareto is separated the optimum solution i that concentrates _I+1As S _I+1(4.4) are also returned in the initial global optimum position in next collaborative cycle, when i=V, then optimum solution i are distributed to sub-population S ₁

Step (4.6) selects an optimum solution as the collaborative sampling plan output of many indexs of physical geography key element from the Pareto solution is concentrated at random.

Below be the experiment of adopting the said method flow process that the Hengshan County, Shaanxi Province is carried out:

Select the Hengshan County, Shaanxi Province as test site (accompanying drawing 5), write computer program according to the present invention, soil organic matter content (SOM), soil moisture content (WATER) and three indexs of quick-acting potassium content (AK) of test site are worked in coordination with space sampling plan design.

(1) experimental data and pre-service (accompanying drawing 6).Experimental data comprises present status of land utilization data, 1: 5 ten thousand digital elevation model, and (Digital Elevation Model, DEM) land quality of data and 2004 is monitored pre-sampled data.Wherein, the constraint condition that present status of land utilization data and dem data are laid as sampling point, pre-sampled data is used for estimation to parameter such as population mean, variance and each variable space variation structure as the priori of test block.

Pre-sampled data comprises 251 sampling points altogether, and the statistical nature of the content of organic matter (SOM), soil moisture content (WATER), available potassium (AK) is as shown in table 1:

The statistical nature of table 1 soil index

Experimental data has been carried out following processing: be the sampling base map with the administrative area, adopt the 750m*750m graticule mesh to divide base map and generate sampling unit that dividing back sampling frame total size is 7864;

(2) simulate the actual overall of each index.The variable of disobeying the distribution of normal distribution or similar normal state in the pre-sampled data is carried out normal transformation (Log/Normal score conversion); Adopt common gram Li Jinfa respectively the semivariable function of above-mentioned three soil indexs to be carried out match, it is as shown in the table to obtain fitting result:

The match semivariable function parameter of table 2 SOM, WATER and AK

Variable	Fitting function	The piece gold number	The base station value	Degree of variation
					SOM	Gaussian	0.029	0.104	0.283
WATER	Spherical	11.235	85.213	0.132
					AK	Gaussian	1882.2	1920.5	0.980

Be constraint with pre-sampled data, adopt sequential Gaussian plan method respectively to total n-body simulation n of above-mentioned variable 100 times on the semivariable function basis of match, get its average result conduct actual overall of index separately, be used for the repeated sampling of achievement data and the comparative analysis of the sampling results that distinct methods obtains.

(3) calculate minimum collaborative sample size.1., according to population variance and the total size of soil organic matter content (SOM), soil moisture content (WATER) and quick-acting potassium content (AK), calculated that confidence level is 95%, the expectation precision is the smallest sample amount of 90% o'clock each index and adopts random sampling pattern to determine its sampling point layout (table 3) respectively not considering to use under the situation of conspiracy relation between the spatial correlation and index between the sampling point following formula; 2., the smallest sample amount of each index was respectively 90,198 and 79 when the flow process of using the 4.4.4.1 joint was determined collaborative sampling successively, then the smallest sample amount of final many indexs of determining under collaborative is 367:

${\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">n</figure-callout>}}_1=\frac{{{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}^2{{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="111229120543.png,111229120604.png"\; state="\{\{state\}\}">s</figure-callout>}}_1}^2}{{(\stackrel{\&OverBar;}{x_{1n}}-{\mathrm{\&mu;}}_1)}^2}$ Formula six

The accuracy requirement p of index 1 in the formula ₁, population mean μ ₁, index 1 sampling mean

And standard deviation s ₁

Smallest sample amount under index more than the table 3 is collaborative

(4) parameter is set, according to the pre-service result minimum collaborative sample size being set is 367; The gradient condition of setting in the sampling accessibility according to slope map and regional actual conditions is smaller or equal to 60 °.Because the sampling expense is closely related with the fiscal capacity of sampling exploiting entity with the difficulty of sampling on the spot, therefore difficult definite definite single cost of sample usefulness is not considered the constraint of sampling expense in the experiment.Collaborative particle swarm optimization parameter is as shown in table 4:

The collaborative particle swarm optimization parameter of table 4 scale-of-two is set

Wherein inertia weight factor w is regarded as the linear decrease function of particulate group iterations, and its scope is set is 0.98 to 0.48, then its computing formula is as follows:

$w\left(t\right)=0.98-\frac{t}{T_{\mathrm{Max}}}\&times;0.5$ Formula seven;

T wherein _MaxBe maximum iteration time.

WA method and simulated annealing parameter: to soil quality classification ability height, the weight of SOM, WATER and AK is made as 0.408,0.316 and 0.276 (concrete computation process is referring to 4.5.3.1) respectively in the method for weighted mean (WA) according to variable; In addition, the initial temperature T of space simulated annealing among the WA ₀Be made as 1, isothermal coefficient L is 300 times, cooling coefficient ρ=0.25, and energy function adopts golden variance criterion in the minimum gram.

(5) many soil index sampling plan design.At SOM, WATER and three indexs of AK, adopt collaborative particulate group method and weighted sum and simulated annealing combined techniques to carry out the collaborative sampling plan design of many indexs, obtain the optimization result shown in the accompanying drawing 7.Above-mentioned optimization result is carried out statistical study, obtain statisticses such as the optimization target values of different samples and sample size.As can be seen from Table 5: the cooperative ability of (1) collaborative particle swarm optimization is better than the WA method on the whole, the sample MKV value average increment of its corresponding three variablees is less than WA, especially it has promoted the precision of the more AK variable of spatial variability sample, and has kept the lower amount of increase of sample size as far as possible.But for indivedual indexs (SOM) wherein, the WA method can be partial to the index of weight maximum in the sampling plan design process, thereby preferentially satisfy its sampling precision requirement, so the range of decrease of SOM sample sampling precision is little than this index sampling precision in the collaborative particle swarm optimization in the WA method.

The sampling precision contrast of the collaborative sample plan of index more than the table 5

From efficiency of algorithm, collaborative particle swarm optimization also is better than the simulated annealing (SSA) (table 6, accompanying drawing 8) in the weighted sum method in addition.On the one hand, collaborative particulate group method convergence effect is better relatively, and wherein golden variance desired value all is less than the convergence result of SSA in the gram of WATER and two sampling plans of AK; On the other hand, collaborative particle swarm optimization speed of convergence is very fast, show that the time that its convergence consumes only is 76% of simulated annealing, and convergence curve is relatively stable, and golden variance desired value is stable downtrending in the gram of three indexs.

The convergence result of the collaborative particle swarm optimization of table 6

(6) minimum collaborative sample size c in the sampling plan ₁(S) and the collaborative period T of collaborative particle swarm optimization _CoorImpact analysis.

1. the influence of minimum collaborative sample size.Point centered by the collaborative sample size of the minimum of calculating amplifies sample size respectively and dwindles 20% and analyze it to influence (accompanying drawing 9 and Figure 10) of sampling sample relative accuracy (being normalized into aurin degree in the average gram in [0,100] scope) and particulate group efficient.As seen, increase along with the smallest sample amount, the sample sampling precision improves gradually, this is consistent with the conclusion of traditional sampling theory, and the conspicuousness of ascendant trend is the boundary line with the collaborative sample size of optimum, when sample size was worth less than this, sampling precision rose very fast, and then the sampling precision lifting is no longer remarkable when being worth greater than this; In addition along with sample size increases, particulate group convergence time constantly increases, this mainly is that this quantity is along with the increase of smallest sample amount is the geometric trend growth because the search volume scale of particle swarm optimization algorithm and sample size, all possible number of combinations of sampling point layout are proportional.But because minimum collaborative sample size only is an elastic restraint condition in the algorithm optimization process, so its influence to sampling precision and efficiency of algorithm is not the above-mentioned trend of complete match.

2. collaborative cycle influence.Collaborative cycle of collaborative particle swarm optimization is adjusted to 10 from 1, analyze it to the influence of particle swarm optimization convergence time, the result as shown in Figure 11.The result shows that the collaborative cycle is more little, and sub-particulate group trends towards independent evolution more, information interchange increased frequency between the subgroup, and the algorithm convergence time is elongated; Along with collaborative cycle increases, algorithm convergence presents linear decrease earlier, and after reaching some cycles (T _Coor=5), the algorithm convergence time remains unchanged substantially.But can predict, it is slow that the excessive collaborative cycle will cause sharing between the sub-particulate group information updating speed limit, coevolution ability degeneration between the sub-particulate group, thus make particulate group convergence capabilities descend.

Specific embodiment described herein only is that the present invention's spirit is illustrated.Those skilled in the art can make various modifications or replenish or adopt similar mode to substitute described specific embodiment, but can't depart from spirit of the present invention or surmount the defined scope of appended claims.

Claims (7)

1. the collaborative sampling plan method for designing of the multiple goal of a stochastic distribution type geographic element is characterized in that, may further comprise the steps:

Step 1, select a plurality of geographic elements with random distribution characteristic as the sampling index, obtain the pre-sampling sampling point data of index, the zone of will sampling is carried out graticule mesh and is divided, the grid cell that forms is as sampling unit, and the sampling unit set in the sampling zone is as the sampling frame;

Step 2, utilize common gram Li Jinfa to explore the spatial variability structure of pre-sampled data, match generates the theoretical semivariable function of each index, according to the pre-sampling sampling point data in theoretical semivariable function and the step 1, it is overall to adopt the sequential Method of Stochastic of Gauss to obtain the space distribution of each index;

Step 3 is calculated minimum collaborative sample size according to accuracy requirement and the prior variance of index, and collaborative particle swarm optimization parameter is set, and the step of wherein calculating minimum collaborative sample size is as follows:

Definition sampling sample space A, the sampling unit number is N, and sampling index quantity is V, establishes the sampling design that there is an optimum in index i, and its accuracy requirement is p _i, the corresponding sample capacity is n _i

Step 3.1, the accuracy requirement p of setting index 1 ₁, population mean μ ₁, index 1 sampling mean And standard deviation s ₁, adopt the smallest sample amount computing formula in traditional arbitrary sampling method to determine that the smallest sample capacity of index 1 is n ₁, the sampling sample of formation is ξ ₁

Wherein, $n_1=\frac{{p_1}^2{s_1}^2}{{(\stackrel{-}{x_{1n}}-{\mathrm{\&mu;}}_1)}^2}$ Formula one;

Step 3.2 is according to the sampling precision requirement test samples ξ of index 2 ₁, rejecting does not form one group of new sample ξ ' after meeting the sampling point of index 2 sampling designing requirements ₁;

Step 3.3 according to the accuracy requirement of index 2, is extrapolated sample ξ ' ₁The maximum subsample space A that can represent ₂And residue sample space A ' ₂, A ' ₂=A/A ₂

Step 3.4, A in the residue sample space ₂, adopt arbitrary sampling method to determine that capacity is n according to the sampling designing requirement of index 2 ₂A sample ξ ₂, then capacity is n ₁+ n ₂Sample ξ ₁∪ ξ ₂It is the one group of smallest sample that satisfies index 1 and index 2 sampling designs simultaneously;

Step 3.5, repeated execution of steps 3.1 are to step 3.4, and repeating number of times is V-1 time, wherein, and N ₀=n ₁+ n ₂+ ...+n _V, and ξ ₁, ξ ₂, ∧, ξ _VSeparate, N then ₀Satisfy the smallest sample capacity of the collaborative sampling design of many indexs exactly;

Step 4 utilizes collaborative particle swarm optimization that pre existing sampling sampling point scheme is optimized, and obtains the collaborative sampling plan of many indexs, and described pre existing sampling sampling point scheme is the described pre-sampling sampling point data of obtaining index of step 1.

2. the multiple goal of a kind of stochastic distribution type geographic element according to claim 1 is worked in coordination with the sampling plan method for designing, it is characterized in that described step 4 concrete operations step is as follows:

Step 4.1 makes up particulate and the regional mapping relations of sampling, according to mapping relations initialization particulate group S;

Step 4.2, according to branch particulate groups such as index quantity V, when population scale P is divided exactly by V, sub-particulate group S then _vPopulation scale P _v=P/V; When population scale P is not divided exactly by V, lose for fear of particulate group particle information, at first determine the basic particulate number that each subgroup comprises

Before then remaining particulate being distributed to successively

Individual subgroup then from wherein selecting a particulate to copy at random, guarantees each sub-particulate group S for the subgroup of additional allocation particulate not _vPopulation scale be $P_v=\mathrm{int}\left(\frac{P}{V}\right)+1,$ Wherein

Be bracket function;

Step 4.3 makes up the ring-type synergetic structure of sub-population, is the head end of ring texture with a sub-population at random, adopts the mode of picked at random to determine the sub-population of its neighborhood, repeats this step and is combined into the ring-type synergetic structure up to all sub-populations;

Step 4.4 is a collaborative period T _CoorIn, setting Flag identifies sub-population and independently evolves whether finish t _CoorThe sign algebraically that in the collaborative cycle evolve in the subgroup, initial value is 1, sub-particulate group S _vIndependently seek the optimal sampling scheme of a soil attribute respectively, wherein, (1≤t _Coor≤ T _Coor);

Step 4.5 is obtained the current global history optimal location of all subgroups and is formed the Pareto disaggregation as optimum solution, if Flag=true enters step 4.6, distributes to adjacent sub-population S otherwise Pareto is separated the optimum solution i that concentrates _I+1As S _I+1Step 4.4 is also returned in the initial global optimum position in next collaborative cycle, when i=V, then optimum solution is distributed to sub-population S ₁;

Step 4.6 selects an optimum solution as the collaborative sampling plan output of the multiple goal of stochastic distribution type geographic element from the Pareto solution is concentrated at random.

3. the multiple goal of a kind of stochastic distribution type geographic element according to claim 2 is worked in coordination with the sampling plan method for designing, it is characterized in that in the described step 4.4, independent evolutionary step is as follows:

Step 4.4.1 calculates S _vIn each particulate S _Vi(t) fitness;

Step 4.4.2 determines the individual historical optimum position of particulate and global history optimal location;

Step 4.4.3 judges whether to satisfy end condition, if satisfy then set Flag=true and execution in step 4.5, simultaneously with the Sg that generates among the step 4.4.1 _v(t) export as the optimal sampling plan of subgroup, otherwise will enter step 4.4.4;

Step 4.4.4 judges whether to finish a collaborative cycle t _Coor=T _CoorIf, finish then set Flag=false skipping to step 4.5, and with the Sg that generates among the step 4.4.1 _v(t) export as the optimal sampling plan of subgroup, otherwise enter step 4.4.5;

Step 4.4.5 is according to the position of the historical optimum position of the current individuality of particulate and current global history optimal location renewal particulate, t _CoorAutomatically add 1, and return step 4.4.1.

4. the multiple goal of a kind of stochastic distribution type geographic element according to claim 1 is worked in coordination with the sampling plan method for designing, it is characterized in that, in the described step 3, the parameter of particulate clustering class algorithm comprises population scale p, maximum iteration time, inertia weight w, stray parameter r ₁And r ₂, individual information aceleration pulse c ₁, the aceleration pulse c of social information ₂, the collaborative period T of converging factor χ and sub-population _Coor, adopt maximum iteration time as the algorithm end condition.

5. the multiple goal of a kind of stochastic distribution type geographic element according to claim 2 is worked in coordination with the sampling plan method for designing, it is characterized in that, in the mapping relations that described step 4.1 makes up, a scale-of-two particulate is the set of sampling unit, represent a kind of sampling plan, each dimension in the particulate represents a sampling unit, and dimension values is that the corresponding sampling unit of 1 expression is chosen as sampling point, and dimension values is that the corresponding sampling unit of 0 expression is not chosen as sampling point.

6. the multiple goal of a kind of stochastic distribution type geographic element according to claim 3 is worked in coordination with the sampling plan method for designing, it is characterized in that, among the described step 4.4.1, golden variance and sampling point information entropy were weighed in the fitness of particulate adopted and on average restrains, and determined particulate S _ViAt individual historical optimum position Sb of the t moment _Vi(t) with particulate group overall situation optimum position Sg _v(t) step is as follows:

When the fitness of t+1 moment particulate was better than the fitness of its historical optimum, then that particulate is current position was recorded as individual historical optimum position, otherwise remains unchanged;

As subgroup S _vWhen t+1 is in a first generation in the new collaborative cycle constantly, t wherein _Coor=1, then subgroup global optimum position equals subgroup S _V-1Last collaborative end cycle the time position Sg of global optimum that obtains _V-1(t), thereby for the message exchange that guarantees between the subgroup, otherwise, contrast the historical global optimum in optimum individual position and the subgroup position in the current subgroup, will be subgroup S than the superior _vCurrent global optimum position:

${\mathrm{Sb}}_{\mathrm{vi}}(t+1)=\left\{\begin{array}{cc}{\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)& \mathrm{if}[f_v\left(S_{\mathrm{vi}}(t+1)\right)\&GreaterEqual;f_v\left({\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)\right)]\\ S_{\mathrm{vi}}(t+1)& \mathrm{otherwise}\end{array}\right.$ Formula two;

${\mathrm{Sg}}_v\left(t\right)=\left\{\begin{array}{cc}{\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)& \mathrm{if}[f_v\left({\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)\right)={\min }_{1\&le;i\&le;N}{\mathrm{Sb}}_{\mathrm{vi}}\left(t\right)]\mathrm{and}[t_{\mathrm{coor}}\&NotEqual;1]\\ {\mathrm{Sg}}_{v-1}\left(t\right)& \mathrm{if}[t_{\mathrm{coor}}=1]\end{array}\right.$ Formula three.

7. the collaborative sampling plan method for designing of the multiple goal of a kind of stochastic distribution type geographic element according to claim 3 is characterized in that among the described step 4.4.5, the particulate position is upgraded namely according to subgroup S _vMiddle particulate S _Vi(t) the historical optimum position Sb of current individuality _Vi(t) and current global history optimal location Sg _v(t) determine its t+1 value x of dimension j constantly _{Vi, j}(t+1):

$\left\{\begin{array}{c}{V}_{\mathrm{vi},j}(t+1)=\mathrm{\&chi;}(w{V}_{\mathrm{vi},j}\left(t\right)+c_1{r}_1({\mathrm{Sb}}_{\mathrm{vi},j}\left(t\right)-S_{\mathrm{vi},j}\left(t\right))+c_2{r}_2({\mathrm{Sg}}_{v,j}\left(t\right)-S_{\mathrm{vi},j}\left(t\right)))\\ x_{\mathrm{vi},j}(t+1)=\left\{\begin{array}{cc}0& \mathrm{if}[r\&GreaterEqual;\mathrm{sig}\left(V_{\mathrm{vi},j}(t+1)\right)\\ 1& \mathrm{otherwise}\end{array}\right.\end{array}\right.$ Formula four;

Its Position Updating is subject to minimum collaborative sample size, sampling accessibility and 3 factors of sampling expense, and wherein minimum collaborative sample size is calculated by step 3, the number of sampling point in the restriction sampling plan; The restriction of sampling accessibility comprises buildings, waters scope or the zone, abrupt slope in the sampling zone, the locus of restriction sampling point; The number of sampling costs constraints sampling point, comprise that total sampling expense is that FT, basic sampling expense are FB and single sampling point sampling expense three parts, single sampling point sampling expense is divided into I level difficult region, II level difficult region and III level difficult region by the sampling zone, and establishing I level difficult region sampling point sampling expense is FS ₁, sampling point quantity is N ₁, each sampling point sampling expense of II level is FS ₂, sampling point quantity is N ₂, III level zone is FS ₃, sampling point quantity is N ₃, sampling costs constraints condition can be expressed as:

FS ₁* N ₁+ FS ₂* N ₂+ FS ₃* N ₃≤ FT one FB formula five.

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