CN110442143B - Unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization - Google Patents
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Abstract
The invention discloses an unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization, which comprises the following steps: loading a data set; calculating a difference matrix and an adjacency matrix of the data set; solving a minimum spanning tree by utilizing a primm algorithm; dividing the edge set in the minimum spanning tree into a strong connection edge set and a weak connection edge set; decoding the strong connection edge set, and performing pre-calculation of clustering; generating an initial pigeon group, decoding to obtain a clustering result, and evaluating the pigeon group at the initial moment by adopting compactness and continuity; carrying out non-dominated sorting on the initial pigeon group, and determining the global historical optimal position and the central position of the pigeon group at the current moment; and updating the position and the speed of the pigeon group, decoding the position of the pigeon group to obtain a clustering result, updating the global historical optimal position and the central position of the pigeon group, and continuing the process until a termination condition is met. The method is simple to implement, reduces the calculation load and the dimensionality of a decision space, is easier to search an optimal solution, and has the capability of better adapting to different clustering requirements.
Description
Technical Field
The invention relates to an unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization, and belongs to the technical field of data mining.
Background
The unmanned aerial vehicle has the advantages of low manufacturing cost, good economy, long idle time, capability of executing tasks in severe environment, capability of avoiding casualties and the like, and is widely applied to civil fields such as power grid inspection, search and rescue, aerial photography and the like and military fields such as target reconnaissance, tracking, striking and the like. The single unmanned aerial vehicle is limited by factors such as sensing range, weapon load and computing power, and is difficult to complete complex tasks. Many unmanned aerial vehicles pass through the interactive sharing of information to tasks such as search, reconnaissance and strike are executed in coordination to the form of function distribution, can effectively improve system survival rate and whole efficiency of execution. In the process of cooperatively executing tasks by multiple unmanned aerial vehicles, situation awareness is the basis of unmanned aerial vehicle behavior decision, each unmanned aerial vehicle in an unmanned aerial vehicle cluster needs to perform data mining according to comprehensive information such as perception information of the surrounding environment and received information of nearby friends and airplanes, and performs knowledge mining and mode classification on the information, so that valuable knowledge and important information are extracted. However, due to the coexistence of a plurality of unmanned aerial vehicles and the transient change of environmental information, the amount of information to be processed is increased dramatically, and the information processing capacity and the calculation capacity of the unmanned aerial vehicle are limited. Therefore, it is important to design a reasonable and efficient data mining method. The invention aims to improve the capability of processing large-scale data mining by the unmanned aerial vehicle and reduce the calculation load by designing a data clustering analysis method based on combined multi-target pigeon swarm optimization, so that valuable knowledge and important information can be extracted from massive data, and the situation assessment and behavior decision of the unmanned aerial vehicle are facilitated.
Data clustering is a common method in data mining, and belongs to unsupervised learning. Common data clustering methods mainly include partition-based clustering (K-means and K-center algorithms), hierarchy-based clustering (Chameleon algorithm), density-based clustering (DBSCAN algorithm), and the like. The proposed methods effectively solve the problem of data clustering, but as the dimensionality of the data increases, its performance decreases accordingly. In addition, since data clustering belongs to unsupervised learning, data is unlabeled, and different evaluation indexes may cause different clustering results under the condition of lacking prior knowledge. The current clustering method mostly adopts a single evaluation index to guide the clustering process, such as: compactness or separability, a single evaluation index often cannot be effective for most data sets given different information sets. Therefore, aiming at the problems existing in the conventional clustering method, the data clustering problem is converted into an optimization problem, a plurality of suitable clustering evaluation indexes which possibly have mutual constraint relation are simultaneously selected according to requirements, then a data clustering analysis method which can be used for large-scale data is designed based on a combined multi-target pigeon group optimization method, and different characteristics of a data set are obtained by simultaneously optimizing the plurality of evaluation indexes, so that favorable support is provided for the unmanned aerial vehicle to obtain more valuable information from complex and massive situation information.
Disclosure of Invention
The invention provides an unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization, which aims to convert a data clustering problem into an optimization problem and design a combined multi-target pigeon swarm optimization algorithm to solve the problem so as to realize cluster analysis of data.
The invention provides an unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization aiming at the problem of data clustering, the implementation block diagram of the method is shown in figure 1, and the main implementation steps are as follows:
the method comprises the following steps: loading an unmanned aerial vehicle situation dataset
Loading a data set to be processed and calculating the number N of data in the data setdataAnd dimension M of the datadataBy using
To represent the ith data node in the data set.
Step two: computing a difference matrix and an adjacency matrix for a dataset
The purpose of data clustering is to divide data with high similarity into the same cluster and divide data with low similarity into different clusters according to a certain standard or the intrinsic property and rule of the data. By using Euclidean distance between nodes
The difference between a node i and a node j in the data set is represented, and the smaller the Euclidean distance is, the smaller the difference between the two nodes in the data set is, and the higher the possibility that the two nodes are divided into the same cluster is. Calculating Euclidean distance d between all nodes in data setijAnd normalizing it
Then the difference matrix D of the available nodesdataComprises the following steps:
sorting the difference matrix shown in the formula (1) in ascending order to obtain an adjacent matrix shown in the formula (2):
wherein,
and the serial numbers of the adjacent nodes are obtained by sequencing from small to large according to the differences between all the nodes and the node j in the data set.
Step three: solving a minimum spanning tree
And (3) solving the minimum spanning tree by adopting a primm algorithm according to the adjacency matrix shown in the formula (2). Randomly selecting a node i as a starting point, selecting a node j with the minimum difference, and adding the node to a vertex set S ═ i]In (e), then S ═ U [ i ] U]＝[i,j]. In addition, the generated edge j → i is added to the edge set V, [ j → i ═ V]. In j → i, the starting point j of the edge is stored in the starting point set SspIn the middle, the terminal i is stored in the terminal set SepIn, Sep(j) I denotes that node j is connected to node i, i being the end set SepAnd j is called element i in the end point set SepIndex number of (1). Repeating the step, sequentially selecting the nodes which are not in the vertex set and have the minimum difference with any node in the vertex set, generating a new edge, updating the vertex set, the edge set, the starting point set and the end point set, and terminating the step when all the nodes in the data set are added into the vertex set. Sequentially collecting the terminal points SepAnd their element index labels, can generate a minimum spanning tree for the data set.
Step four: partitioning edge sets in a minimum spanning tree into strongly connected edge sets and weakly connected edge sets
Adjacency matrix N according to equation (3) and data setnearestAnd a difference matrix DdataCalculating the weight value W of each edge j → iji：
Where nn (i, j) is used to compute that node j is the next nearest neighbor to node i. According to the adjacency matrix NnearestIt can be obtained if nn (i, j) ═ nikThen it means that node j is the kth nearest neighbor of node i. Weighted value WjiThe larger the difference between the representation node j and the representation node i, the smaller the possibility that it is divided into the same cluster.
Calculating the weighted values W of all edges of the minimum spanning tree of the data set according to the formula (3), sorting the weighted values corresponding to the edges in a descending order, and sorting the weighted values with larger weighted value of lambdax (N)data-1), λ is more than or equal to 0 and less than or equal to 1 edge, and a weak connection edge set E is added into the edgesThe remaining (1-lambda) × (N)data-1) adding strong connecting edge set E to edgesw. Simultaneous starting set SspIs also divided into weakly connected start point sets S accordinglyspwAnd strong connection starting point set Ssps。
The data are solved by adopting a pigeon group optimization algorithm in the following stepsIn the process of clustering optimization problem, the connection relation of all strong connection edges is not changed, the weak connection edge set is abandoned, and the weak connection starting point set S is givenspsAll the nodes j in the cluster redistribute the connection terminal points k (k is the adjacent nodes in the m fields of the nodes j), thereby forming a new connection relation j → k to replace the original weak connection edge j → i, and all the weak connection terminal points k form the position of the ith pigeon
Wherein N iswsIs SspsThe number of intermediate nodes.
Step five: decoding the strong connection edge set to obtain a pre-polymerization result
Because the strong connection edge set is not changed in the subsequent clustering optimization solution, the strong connection edge set can be decoded to obtain a data pre-clustering result. Set of strong connection starting points SspsRandomly selecting a node as a starting point, dividing all the nodes connected together into the same class, and introducing a classification mark vector
Reference numerals indicating classes to which respective nodes in the data set are assigned, e.g. a (2) ═ 3 indicates that node 2 is classified into class 3, for weakly connected start set SspwThe classification flags of the nodes are initialized to A (i) -1, i belongs to SspwRepeating the steps until all strong connection starting point sets SspsThe nodes in (1) are all allocated.
Step six: generation of an initial Pigeon group
Random generation of psizeIndividual pigeons, each pigeon containing a spatial position
And velocity
Wherein i is the number of the pigeon and the spatial position of the pigeon
Indicating the connection end k of all new weakly connected edges. Different weak connection edge sets can be obtained by updating the spatial position of the pigeons. And setting the current simulation time as t to be 0. R is map and compass operator, beta1And beta2For randomly generated random numbers following a Gaussian distribution, σ is the transfer factor, TmaxIn order to be the maximum number of iterations,
is 1 XNswA row vector of dimensions.
Step seven: evaluating the target function of the pigeon group at the moment t-0
According to the spatial position of pigeons
And end point set SepReconstructing the full coding length of the spatial position of the pigeon, decoding the reconstructed pigeon to obtain the connection relation between the nodes, and then identifying all the classification identifications as A (i) ═ 1 according to the connection relation between the nodes, wherein i belongs to SspwThe nodes are distributed to the corresponding classes until the classification identifiers A (i) ≠ -1 of all the nodes, i belongs to Sspw. Obtaining a clustering result C of all data in the data set according to the classification mark vector Ai＝[c1,c2,…,cγ]Where γ is the number of classes formed, cττ is 1,2, …, and γ is τ -th group.
Selecting two cluster evaluation indexes (target functions) of compactness and continuity to evaluate the quality of a cluster result, and representing the continuity of the cluster by using a cluster clustering distance (target function f)1)：
Representing cluster compactness by intra-class clustering distance (objective function f)2). The average distance from each node in each class to the cluster center is first calculated according to equation (5).
Wherein cdτDenotes the average distance of each node in the τ -th class to the cluster center, cτIs a node set of the τ -th class, | cτ| is the number of nodes contained in the τ -th class,
is the cluster center of the τ -th class. Repeating the steps until the objective function values corresponding to all pigeons in the pigeon group are calculated, wherein the pigeon i represents the ith clustering result C ═ C1,c2,…,cγ]The corresponding objective function value is Fi(t)＝[fi1(t),fi2(t)]。
Step eight: performing non-dominant sorting on the initial pigeon group, and determining the global historical optimal position and the central position of the pigeon group at the current moment
And comparing the dominance relation between the pigeon i and the pigeon j based on the objective function values, and layering the whole pigeon group by a Pareto (Pareto) non-dominance sorting algorithm. If all objective function values F of pigeon ii(t)＝[fi1(t),fi2(t)]Objective function values F all superior to pigeon jj(t)＝[fj1(t),fj2(t)]I.e. fi1(t)≤fj1(t) and fi2(t)≤fj2(t), the pigeon i is said to dominate the pigeon j, and if the pigeon i is not dominated by another pigeon, the pigeon is said to be a non-dominated pigeon, and the pigeon is divided into first-stage non-dominated layers.
All non-dominated pigeons positioned at the first-level non-dominated layer are stored in an external archive set AS, one pigeons is randomly selected from the external archive set AS and is used AS the global optimal position p at the time tbest(t) taking the average position of all pigeons in the first level non-dominant layer in the external archive set AS AS pcenter(t)。
Step nine: updating the position and velocity of pigeons
Introducing an auxiliary vector ζi＝[ζi1,ζi2,…,ζiNws]，ζij∈[-1,0,1]The optimization algorithm of the continuous pigeon flock is converted into a combined optimization algorithm, so that the combined optimization algorithm can be used for solving a clustering optimization problem:
wherein p iscenterj(t) center position p of pigeon group at time tcenterThe j-th element of (t), pgbestj(t) History optimal position p of pigeon flock at time tgbestThe jth element of (t). The velocity update formula of the pigeon obtained according to the formula (7) is as follows:
wherein, beta1And beta2For randomly generated random numbers following a gaussian distribution,
is 1 XNswA row vector of dimensions.
Then according to the speed v of the pigeon at the moment t +1i(t +1) calculation of ζi(t+1)：
Wherein the updated ζ is a predetermined constanti(t +1) updating the position of the pigeon at time t + 1, instead of equation (10):
wherein λ is randomly selected pij(t) nearest neighbors. This step is repeated until the position and velocity updates for all pigeons are completed.
Step ten: evaluating fitness function of pigeon group at t +1 moment
Decoding the pigeons according to the sixth step to form clusters, and calculating the fitness function F of the pigeon group at the moment of t +1i(t+1)＝[fi1(t+1),fi2(t+1)]. Comparing pigeons p based on objective function valuesi(t +1) with pigeon pjAnd (t +1) storing all non-dominated pigeons positioned at the first-level non-dominated layer into an external archive set AS.
Step eleven: sorting the external archive set AS in a non-dominated way, and selecting pigeons needing to be discarded in the AS according to the congestion distance
And (3) sorting all pigeons stored in the external archive set AS at the time of t +1 in a non-dominated way, discarding the pigeons which are not in the first-level non-dominated layer and calculating the crowding distance of the pigeons which are not in the first-level non-dominated layer, and discarding the pigeons with large crowding distance.
Step twelve: updating global optimum position and central position of pigeons, and updating pigeon group number
Randomly selecting a pigeon from an external archive set AS, and taking the position of the pigeon AS a global optimal position p at the moment t +1best(t +1) the central position of the non-dominant pigeon in the first-stage non-dominant layer is defined as the central position p of the pigeon flockcenter(t + 1). The number of pigeons will gradually decrease during each iteration.
Psize(t+1)＝Psize(t)-Pdec(11)
Wherein, PdecThe number of pigeons discarded.
Step thirteen: determining whether to stop iteration
The simulation iteration time t is t + 1. If T is larger than the maximum simulation iteration number TmaxIf yes, ending the simulation and entering a step fourteen; otherwise, returning to the step eight.
Fourteen steps: outputting data clustering results
And outputting a clustering result and drawing a Pareto leading edge curve.
The invention provides an unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization. The clustering method provided by the invention has the advantages that: firstly, a pigeon position (clustering result) coding mechanism effectively reduces the calculation load of large-scale data and the dimensionality of a decision space, so that an optimal solution (an optimal clustering result) is easier to search by a combined multi-target pigeon group optimization algorithm; secondly, the designed auxiliary vector effectively converts the continuous pigeon group optimization algorithm into a combined optimization algorithm, so that the original pigeon group optimization algorithm has the capability of solving the discrete optimization problem, and the application field of the pigeon group optimization algorithm is widened; finally, in the optimization process, the two clustering evaluation indexes of compactness and continuity are considered at the same time, so that the capability of better adapting to different clustering requirements can be obtained, different characteristics of a data set are obtained, and favorable support is provided for the unmanned aerial vehicle to obtain more valuable information from complex and massive situation information.
Drawings
FIG. 1 is a flow chart of data clustering analysis based on combination multi-objective pigeon swarm optimization
2a, b, c, d cluster pigeon position code map, wherein FIG. 2a is the minimum spanning tree of the data set and its representation; FIG. 2b is a diagram illustrating the ordering of the edges of the minimum spanning tree according to the weight of the connection; FIG. 2c is a diagram showing the generation of a pre-polymerization result from the strong connection edge set after the weak connection edge set is removed; fig. 2d shows the creation of a new connection (pigeon position storage connection termination) instead of a weak connection edge.
FIG. 3 clustered pigeon position decoding diagram
FIG. 4a-e clustering result plot and Pareto front curve for dataset 1
FIGS. 5a-f clustering result plot and Pareto front curve for dataset 2
FIGS. 6a-f clustering result plot and Pareto front curve for dataset 3
The reference numbers and symbols in the figures are as follows:
t-number of simulated iterations
psize-total number of pigeons in a group of pigeons
i-number of pigeons
TmaxMaximum number of simulation iterations
U-end point corresponding to start point of weak connection edge to be determined
f1-an objective function representing continuity of cluster evaluation index
f2-objective function representing cluster evaluation index compactness
X-abscissa of two-dimensional data set
Y-ordinate of a two-dimensional data set
A-different clustering index values (f)1，f2) Corresponding clustering result
B-different clustering index values (f)1，f2) Corresponding clustering result
C-different clustering index values (f)1，f2) Corresponding clustering result
D-different clustering index values (f)1，f2) Corresponding clustering result
Detailed Description
The effectiveness of the method provided by the invention is verified by a specific data clustering example. The method comprises the following specific steps:
the method comprises the following steps: loading an unmanned aerial vehicle situation dataset
And loading the data set to be processed, and carrying out cluster analysis on three different types of data sets in total, wherein the first data set is used for explanation. The data set contains N data12 data, respectively: x is the number of1＝[1,1]、 x2＝[1,1.2]、x3＝[1.2,1]、x4＝[1.2,1.2]、x5＝[2,2]、x6＝[2.2,2]、x7＝[2,2.2]、 x8＝[2.2,2.2]、x9＝[3,1]、x10＝[3.2,1]、x11＝[3,1.2]、x12＝[3.2,1.2]Dimension M of datadata＝2。
Step two: computing a difference matrix and an adjacency matrix for a dataset
Calculating Euclidean distance d between all nodes in data setij＝||xi-xjAnd normalizing the same
Then a node difference matrix D is obtaineddataComprises the following steps:
for difference matrix DdataSorting the rows in ascending order to obtain an adjacent matrix NnearestComprises the following steps:
each row of the data set represents that differences between all nodes in the data set and the first node in the row are sorted from small to large.
Step three: solving a minimum spanning tree
According to the adjacency matrix NnearestAnd solving the minimum spanning tree by adopting a prim algorithm. Randomly selecting a node 5 as a starting point, and selecting a node 6 with the minimum difference to be added into a vertex set S-5]In (1), then S ═ U [6 ]]＝[5,6]. Edge set V ═ 6 → 5]. Set of starting points Ssp＝[5,6]Middle and end point set SepS ofep(6) 5. Repeating the step, sequentially selecting nodes which are not in the vertex set and have the minimum difference with any node in the vertex set, generating a new edge, updating the vertex set, the edge set, the starting point set and the end point set, terminating the step when all nodes in the data set are added into the vertex set, wherein the starting point set is Ssp＝[5,6,7,8,4,2,3,1,11,9,12,10]The end point set is Sep＝[2,4,4,5,5,5,5,6,11,12,6,11]. According to SepAnd the element index labels (i.e. the starting node of each edge) can be connected in the following relationship: node 1 → node 2, node 2 → node 4, node 3 → node 4, node 4 → node 5, node 5 → node 5, node 6 → node 5, node 7 → node 5, node 8 → node 6, node 9 → node 11, node 10 → node 12, node 11 → node 6, node 12 → node 11, which are the same or different, and which are the same or different from each otherThe generated minimum spanning tree is shown in fig. 2 a.
Step four: calculating the weight value of each edge in the minimum spanning tree, and dividing the edge set in the minimum spanning tree into a strong connection edge set and a weak connection edge set according to the weight values
According to equation (3) and adjacency matrix NnearestAnd a difference matrix DdataCalculating the weight value W of each edge j → iji. As shown in FIG. 2a, each edge of the minimum spanning tree (from set of starting points S)sp＝[5,6,7,8,4,2,3,1,11,9,12,10]End point set Sep＝[2,4,4,5,5,5,5,6,11,12,6,11]And an end-set element index Sep_index＝[1,2,3,4,5,6,7,8,9,10,11,12]Is expressed) corresponds to a weight value of W ═ 2.1, 0, 2.1,2.1, 5.5,2.1,3.1,2.1]. By applying all weight values WjiAfter descending order selection, if λ is 0.4, the edges of the minimum spanning tree can be divided into a strong connection edge set and a weak connection edge set as shown in fig. 2 b. Wherein the weak connection starting point set is Sspw＝[3,4,11,12]The weak connecting edge set is E s1, {3 → 4,4 → 5,11 → 6, 12 → 11}, and the set of strong connecting start points is Ssps＝[1,2,6,7,8,9,10]The strongly connected edge set is E w1 → 2,2 → 4,6 → 5,7 → 5,8 → 6,9 → 11,10 → 12 }. After deleting the weak connection edge, the terminal set is changed into Sep＝[2,4,U,U,5,5,5,6,11,12,U,U]Wherein U represents a weak connection starting point set S to be confirmedspw＝[3,4,11,12]E.g., fig. 2 d.
Step five: decoding the strong connection edge set to obtain a pre-polymerization result
Set of strong connection starting points Ssps＝[1,2,6,7,8,9,10]Randomly selecting a node as a starting point, dividing all the nodes connected together into the same class, and introducing a classification mark vector
Reference numerals indicating classes to which respective nodes in the data set are assigned, e.g. a (2) ═ 3 indicates that node 2 is divided into class 3, for the weakly connected set of starting points SspwThe classification flags of the nodes are initialized to A (i) -1, i belongs to SspwRepeating theStep until all strong connection starting point sets SspsThe nodes in (1) are all allocated. The result of pre-clustering is shown in FIG. 2 c.
Step six: generation of an initial Pigeon group
Random generation of psizeEach pigeon comprises a spatial position
And speed
Wherein N iswsNumber of nodes is concentrated for weak connection edge starting point, and NwsI is the number of the pigeon 4. Setting the current simulation time as T as 0 and the maximum iteration number as TmaxThe map and compass operator is R0.3, the transfer factor is σ 0.45, and the threshold is 3.6.
Step seven: evaluating the target function of the pigeon group at the moment t-0
P is to bei＝[pi1,pi2,pi3,pi4]And end point set Sep＝[2,4,U,U,5,5,5,6,11,12,U,U]S can be obtained by reconstructing the full code length of the spatial position of the pigeonep＝[2,4,pi1,pi2,5,5,5,6,11,12,pi3,pi4]Decoding the node connection relation to obtain the node connection relation shown in fig. 3, and then identifying all classes as a (i) -1, i e S according to the connection relation between the nodesspwThe node (S) of (a) is allocated to the corresponding class until the class identifiers A (i) ≠ 1 of all nodes, i ∈ Sspw. Obtaining a clustering result C of all data in the data set according to the classification mark vector Ai＝[c1,c2,…,cγ]Where γ is the number of classes formed, cττ is 1,2, …, and γ is τ -th group.
According to the clustering result CiAnd equations (4) to (6) calculate the objective function fi1(Cluster continuity indicator, objective function f corresponding to ith pigeon1) And an objective function fi2(Cluster tightness index, target function f corresponding to ith pigeon2) Repeating the steps until the meter is obtainedCalculating objective function values F corresponding to all pigeons in the pigeon groupi(t)＝[fi1(t),fi2(t)]。
Step eight: non-dominant ranking of initial pigeon lots
Comparing pigeons p based on objective function valuesi(t) with pigeon pj(t) the dominant relationship, layering the entire pigeon population by Pareto non-dominant ranking algorithm. All non-dominated pigeons positioned at the first-level non-dominated layer are stored in an external archive set AS, one pigeons is randomly selected from the external archive set AS and is used AS the global optimal position p at the time tbest(t) taking the average position of the non-dominant pigeons of the first-level non-dominant layer in the external archive set AS AS the central position p of the pigeon flock at the time tcenter(t)。
Step nine: updating the position and velocity of pigeons
P is to bebest(t)、pcenter(t) and the positions of all pigeons at the time t are substituted into formula (7) to be calculated to obtain the pigeon position pi(t) corresponding auxiliary vector ζi(t) and then the position p of the t +1 velocity pigeon can be calculated according to the velocity updating formula (8), the position auxiliary vector updating formula (9) and the position updating formula (10) of the pigeoni(t +1) and velocity vi(t + 1). This step is repeated until the positions and velocities of all pigeons are updated.
Step ten: evaluating objective function values of a pigeon flock at time t + 1
Decoding the pigeons according to the sixth step to form clusters, and calculating the fitness function F of the pigeon group at the moment of t +1i(t+1)＝[fi1(t+1),fi2(t+1)]. Comparing pigeons p based on objective function valuesi(t +1) with pigeon pjAnd (t +1) storing all non-dominated pigeons positioned at the first-level non-dominated layer into an external archive set AS.
Step eleven: sorting the external archive set AS in a non-dominated way, and selecting pigeons needing to be discarded in the AS according to the congestion distance
And (3) sorting all pigeons stored in the external archive set AS at the time of t +1 in a non-dominated way, discarding the pigeons which are not in the first-level non-dominated layer and calculating the crowding distance of the pigeons which are not in the first-level non-dominated layer, and discarding the pigeons with large crowding distance.
Step twelve: updating global optimum position and central position of pigeons, and updating pigeon group number
Randomly selecting a pigeon from an external archive set AS, and taking the position of the pigeon AS a global optimal position p at the moment t +1best(t +1) the central position of the non-dominant pigeon in the first-stage non-dominant layer is defined as the central position p of the pigeon flockcenter(t + 1). Updating the number P of pigeons according to equation (11)size(t+1)。
Step thirteen: determining whether to stop iteration
The simulation iteration time t is t + 1. If T is larger than the maximum simulation iteration number TmaxIf the result is 50, the simulation is ended; and if not, returning to the step eight.
Fourteen steps: outputting data clustering results
And outputting a clustering result, and drawing a Pareto frontier curve, wherein the clustering results of three different data sets are respectively shown in fig. 4 to 6. Fig. 4a is a given clustering result of the data set 1, and fig. 4e is a clustering Pareto front curve of the data set 1 obtained by adopting a combined multi-target pigeon group optimization algorithm, which represents a set of the best solution of a clustering objective function, and different optimal data clustering results can be obtained according to the requirements of clustering indexes. Fig. 4B is a data clustering result corresponding to a point a on the Pareto curve in fig. 4e, fig. 4C is a data clustering result corresponding to a point B on the Pareto curve in fig. 4e, and fig. 4d is a data clustering result corresponding to a point C on the Pareto curve in fig. 4 e. Fig. 5a is a given clustering result of the data set 2, and fig. 5f is a clustering Pareto front curve of the data set 2 obtained by adopting a combined multi-objective pigeon group optimization algorithm. Fig. 5B, fig. 5C, fig. 5D and fig. 5e are data clustering results corresponding to four points, namely point a, point B, point C and point D, on the Pareto curve in fig. 5f, respectively. Fig. 6a is a given clustering result of the data set 3, and fig. 6f is a clustering Pareto front curve of the data set 3 obtained by adopting a combined multi-objective pigeon group optimization algorithm. Fig. 6B, fig. 6C, fig. 6D and fig. 6e are data clustering results corresponding to four points, namely point a, point B, point C and point D, on the Pareto curve in fig. 6 f.
The clustering results of three different types of data sets verify that the unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization can effectively realize data clustering analysis.
Claims (8)
1. An unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization is characterized in that: the method comprises the following steps:
the method comprises the following steps: loading an unmanned aerial vehicle situation data set;
loading a data set to be processed and calculating the number N of data in the data setdataAnd dimension M of the datadataBy using
To represent the ith data node in the data set;
step two: calculating a difference matrix and an adjacency matrix of the data set;
step three: solving a minimum spanning tree;
solving a minimum spanning tree by adopting a primm algorithm according to the adjacency matrix;
step four: dividing the edge set in the minimum spanning tree into a strong connection edge set and a weak connection edge set;
step five: decoding the strong connection edge set to obtain a pre-polymerization result;
step six: generating an initial pigeon population;
random generation of psizeEach pigeon comprises a spatial position and a speed;
step seven: evaluating the target function of the pigeon group at the moment t-0;
step eight: carrying out non-dominated sorting on the initial pigeon group, and determining the global historical optimal position and the central position of the pigeon group at the current moment;
step nine: updating the position and the speed of the pigeons;
step ten: evaluating a fitness function of the pigeon group at the t +1 moment;
according to the sixth step, the pigeons are decoded to form clusters, and calculation is carried outA fitness function of the pigeon group at the moment t + 1; comparing pigeons p based on objective function valuesi(t +1) with pigeon pj(t +1) storing all non-dominated pigeons located at the first-level non-dominated layer into an external archive set AS;
step eleven: sorting the external archive sets AS in a non-dominated way, and selecting pigeons needing to be discarded in the AS according to the crowding distance;
step twelve: updating the global optimal position and the central position of the pigeons, and updating the number of the pigeon groups;
step thirteen: judging whether to stop iteration;
the simulation iteration time t is t + 1; if T is larger than the maximum simulation iteration number TmaxIf yes, ending the simulation and entering a step fourteen; otherwise, returning to the step eight;
fourteen steps: outputting a data clustering result;
outputting a clustering result and drawing a Pareto leading edge curve;
the specific process of the step four is as follows: adjacency matrix N according to equation (3) and data setnearestAnd a difference matrix DdataCalculating the weight value W of each edge j → iji：
Wherein nn (i, j) is used to calculate that node j is the nearest neighbor of node i; according to the adjacency matrix NnearestIt can be obtained if nn (i, j) ═ nikThen, it means that node j is the kth nearest neighbor of node i; nn (j, i) is used to compute that node i is the next nearest neighbor to node j;
the normalized Euclidean distance between a node j and a node i in the data set is obtained;
calculating the weighted values W of all edges of the minimum spanning tree of the data set, sorting the weighted values corresponding to the edges in a descending order, and sorting the weighted values with larger weighted value of lambdx (N)data-1), λ is more than or equal to 0 and less than or equal to 1 edge, and weak connection edge set E is added into the edgesThe remaining (1-lambda) × (N)data-1) adding strong connecting edge set E to edgesw(ii) a Simultaneous starting set SspIs also divided into weakly connected start point sets S accordinglyspwAnd strong connection starting point set Ssps(ii) a λ is the selected code length coefficient.
2. The unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization according to claim 1, characterized in that: the specific process of the second step is as follows: by using Euclidean distance between nodes
To represent the difference between the node i and the node j in the data set; calculating Euclidean distance d between all nodes in data setijAnd normalizing it
Then the difference matrix D of the available nodesdataComprises the following steps:
wherein d isminIs the minimum of the Euclidean distances between all nodes, dmaxThe maximum value of the Euclidean distances among all the nodes is obtained;
sorting the difference matrix shown in the formula (1) in ascending order to obtain an adjacent matrix shown in the formula (2):
wherein,
and the serial numbers of the adjacent nodes are obtained by sequencing from small to large according to the differences between all the nodes and the node j in the data set.
3. The unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization according to claim 1, characterized in that: the specific process of the third step is as follows:
randomly selecting a node i as a starting point, selecting a node j with the minimum difference from the starting point, and adding the node into a vertex set S ═ i]In (e), then S ═ U [ i ] U]＝[i,j](ii) a In addition, the generated edge j → i is added to the edge set V, [ j → i ═ V](ii) a In j → i, the starting point j of the edge is stored in the starting point set SspIn the middle, the terminal i is stored in the terminal set SepIn, Sep(j) I denotes that node j is connected to node i, i being the end set SepAnd j is called element i in the end point set SepThe element index number in (1); repeating the step, sequentially selecting nodes which are not in the vertex set and have the minimum difference with any node in the vertex set, generating a new edge, updating the vertex set, the edge set, the starting point set and the end point set, and terminating the step when all nodes in the data set are added into the vertex set; sequentially collecting the terminal points SepAnd their element index labels, can generate a minimum spanning tree for the data set.
4. The unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization according to claim 1, characterized in that: further, a strong connection starting point set SspsAll nodes j in the cluster are redistributed with connection end points k, k are adjacent nodes in m fields of the nodes j, so that a new connection relation j → k is formed to replace the original weak connection edge j → i, and all the weak connection end points k form the position of the ith pigeon
Wherein N iswsIs SspsThe number of intermediate nodes.
5. The unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization according to claim 1, characterized in that: the concrete process of the step five is as follows: from strong connectionSet of points SspsRandomly selecting a node as a starting point, dividing all the nodes connected together into the same class, and introducing a classification mark vector
Reference numbers indicating classes to which respective nodes in the data set are assigned, for the weakly connected set of starting points SspwThe classification flags of the nodes are initialized to A (i) -1, i belongs to SspwRepeating the steps until all strong connection starting point sets SspsThe nodes in (1) are all allocated.
6. The unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization according to claim 1, characterized in that: the concrete process of the step six is as follows:
according to the spatial position of pigeons
And end point set SepReconstructing the full coding length of the spatial position of the pigeon, decoding the reconstructed pigeon to obtain the connection relation between the nodes, and then identifying all the classification identifications as A (i) ═ 1 according to the connection relation between the nodes, wherein i belongs to SspwUntil all the classification identifiers A (i) ≠ -1, i belongs to Sspw(ii) a Obtaining a clustering result C of all data in the data set according to the classification mark vector Ai＝[c1,c2,…,cγ]Where γ is the number of classes formed, cττ is 1,2, …, γ is τ -th group;
is composed of NwsPosition of i-th pigeon composed of elements, NwsSet of starting points S for weak connectionspsThe number of intermediate nodes;
selecting two cluster evaluation indexes of compactness and continuity to evaluate the quality of a cluster result, and representing the continuity of the cluster by using a cluster clustering distance:
wherein cdiRepresenting the average distance from each node in the ith class to the cluster center;
representing the cluster compactness by using the cluster clustering distance; firstly, calculating the average distance from each node in each class to a cluster center according to a formula (5);
wherein cdτDenotes the average distance of each node in the τ -th class to the cluster center, cτIs a node set of the τ -th class, | cτ| is the number of nodes contained in the τ -th class,
cluster center for the τ -th class; repeating the steps until the objective function values corresponding to all pigeons in the pigeon group are calculated, wherein the pigeon i represents the ith clustering result C ═ C1,c2,…,cγ]The corresponding objective function value is Fi(t)＝[fi1(t),fi2(t)]；xτRepresents any node in the τ -th class; i | for calculating xτAnd cenτThe distance of (c).
7. The unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization according to claim 1, characterized in that: the concrete process of the step eight is as follows:
comparing the domination relationship between the pigeon i and the pigeon j based on the objective function values, and layering the whole pigeon group through a Pareto non-domination sorting algorithm; saving all non-dominated pigeons at the first level non-dominated layer to an external archive set AS, fromRandomly selecting a pigeon from an external archive set AS AS a global optimal position p at the moment tbest(t) taking the average position of all pigeons in the first level non-dominant layer in the external archive set AS AS pcenter(t)。
8. The unmanned aerial vehicle situation data clustering method based on combined multi-target pigeon swarm optimization according to claim 1, characterized in that: the concrete process of the ninth step is as follows: introducing auxiliary vectors
ζij∈[-1,0,1]The optimization algorithm of the continuous pigeon flock is converted into a combined optimization algorithm, so that the combined optimization algorithm can be used for solving a clustering optimization problem:
wherein p iscenterj(t) center position p of pigeon group at time tcenterThe j-th element of (t), pgbestj(t) History optimal position p of pigeon flock at time tgbestThe jth element of (t); the velocity update formula of the pigeon obtained according to the formula (7) is as follows:
wherein, beta1And beta2For randomly generated random numbers following a gaussian distribution,
is 1 XNswA row vector of dimensions; r is a map and compass operator, and sigma is a transfer factor; p is a radical ofi(t) is the position of the ith pigeon at time t;
then according to the speed v of the pigeon at the moment t +1i(t +1) calculation of ζiValue at time t + 1:
wherein, is a predetermined constant, ζij(t +1) is ζiThe jth element of (1); will update ζi(t +1) updating the position of the pigeon at time t +1, instead of equation (10):
wherein λ is randomly selected pij(t) nearest neighbors; this step is repeated until the position and velocity update of all pigeons is completed.
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