CN108256623A - Particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism - Google Patents
Particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism Download PDFInfo
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Abstract
The invention discloses a kind of particle swarm optimizations on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, first, the present invention utilizes the division completed based on the K mean values for improving initial cluster center to population, the determining initial cluster center that will divide population, cluster centre is optimized using the thought of K mean iteratives, obtains stable initial cluster center；Period shared mechanism and knowledge plate are re-introduced into, the period for making the information interval between sub- population certain is updated.Within a search cycle, sub- population collaboratively searching, minor population under the guiding of its adjacent sub- population are independently searched for, and are sequentially completed entire search process.The search condition that the search information of sub- population recorded in knowledge plate simultaneously can assist sub- population to judge particle in search process, adjusts the direction of search, improves the convergence precision of algorithm；Compared with existing Particle Swarm Optimization, the present invention is by considering the stability of population initial division and making full use of the information searched in sub- population search process, the heading of particle is instructed, so as to fulfill the search speed and convergence precision of particle swarm optimization is improved.
Description
Technical field
The invention belongs to the application fields of computer analytical technology that colony intelligence optimization calculates, and in particular to one kind is based on week
The Particle Swarm Optimization on multiple populations of phase shared mechanism and knowledge plate.
Background technology
Colony intelligence optimization algorithm (Swarm Intelligence Algorithm) is looked for food by simulating biology in nature
Process, a kind of Stochastic Optimization Algorithms taken out.Swarm intelligence algorithm has certain memory capability, uses colony intelligence optimization algorithm
During Solve problems, it can quickly find optimal solution than traditional optimization algorithm and gained solution has higher robustness.Due to particle
Group's algorithm is a kind of iteration optimization algorithms based on initial value, in iterative process all particles gradually gather search it is optimal
Near solution, the diversity gathered phenomenon and reduce population of particle.The reduction of population diversity searches for the latter half of algorithm
It slows, search capability dies down.Multifarious missing is stagnated after leading to algorithm search to locally optimal solution, and search is not
To globally optimal solution.In order to improve the ability of searching optimum of particle swarm optimization, enhance the diversity of population, document [7] will be a variety of
The concept of group is introduced into particle swarm optimization, strengthens the ability of searching optimum of algorithm.Particle swarm optimization on multiple populations is by by population
Multiple sub- populations are divided into, solution room is divided into multiple subsolution spaces, and every sub- population optimizes subspace.All
Sub- population was not only independently evolved, but also can be evolved based on the information synergism searched.Particle swarm optimization on multiple populations is by dividing population
The diversity of population is increased, the independent search of sub- population has obvious effects on to improving convergence speed of the algorithm, and sub- population is again
Based on the information synergism search that other sub- populations search, the precision for searching optimal solution is improved.To purposive stroke of sub- population
Divide, sub- population effectively assisted to jump out local optimum etc. in the collaboratively searching method and search process that sub- population is taken after division and be
The further research of particle swarm optimization on multiple populations provides direction.The Cooperative Particle Swarm Optimization on multiple populations of the propositions such as Ben Niu
(MCPSO), be based on master-slave models, be multiple sub- populations by population dividing, including a main population and it is multiple from
Population, the evolutionary process of main population is by the optimal solution searched in main population iterative process and the optimal solution provided from population
Double influence, common evolutionary.The solution Global Optimal Problem that Li et al. proposes competes collaboration Particle Swarm based on information sharing mechanism
Algorithm.
Invention content
To solve the deficiencies in the prior art, it is a kind of based on period shared mechanism and knowledge plate it is an object of the invention to propose
The Particle Swarm Optimization on multiple populations of shared mechanism, this method can enhance the stability for dividing sub- population, improve the receipts of algorithm
Speed is held back, enhances the convergence precision of algorithm.
In order to realize above-mentioned target, the present invention adopts the following technical scheme that：
Particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, includes the following steps：
Step 1 initializes the particle in population, includes number, the dimension of search space of particle in initialization population
The parameters such as number, inertia weight, cognition coefficient, coefficient of association, coefficient of concordance, maximum speed, to participating in the particle of search in population
Speed, position random initializtion, and flying speed and position are provided boundary limitation, find out the individual under particle original state
History optimal value and group's optimal value；
Step 2 determines the initial cluster center of population by optimum binary tree thought, according to the K- mean values of cluster centre
Method completes the division to population；
Step 3 in the sub- population search process after division, introduces period shared mechanism, makes between the information between sub- population
It is updated every certain period；Detailed process includes the following steps：
Step a, if t is less than collaborative lifecycle, each sub- population is independently searched for and each sub- population is according to formula (1) and formula (2)
Update speed and the position of itself；
vi(t+1)=w*vi(t)+c2*r2*(pg(t)-xi(t)) (1)
xi(t+1)=xi(t)+vi(t+1)
(2)
Wherein v represents the flying speed of particle, and t represents the iterations of particle, and c1 represents the autognosis coefficient of particle,
C2 represents the coefficient of association of particle.
Step b, if t is more than collaborative lifecycle and is less than maximum iteration, sub- population k is in previous sub- population adjacent thereto
(k-1) collaboratively searching under guiding is independently searched according to formula (3) and formula (4) update position and speed, minor population
Rope, according to formula (1) and formula (2) renewal speed and position；
Wherein v represents the flying speed of particle, and t represents the iterations of particle, and c1 represents the autognosis coefficient of particle,
C2 represents the coefficient of association of particle.
Step c, judges whether each sub- population completes collaboration, the return to step b if collaboration is not completed, until all sons kind
Group completes collaboratively searching；
Step 4, if collaboration subgroup be absorbed in local optimum, judge whether to meet required precision, if meet if output as a result,
Return to step three if being unsatisfactory for；
If collaboration subgroup is not absorbed in local optimum, knowledge plate is introduced into sub- population search process, is remembered in knowledge plate
The information of record is timely fed back to the sub- population, and sub- population adjusts the direction of search, jump out part most in time according to feedack
It is excellent, it is searched for towards the direction of global optimum；Detailed process includes the following steps:
Step a, parameter initialization：Set particle number N, the dimension D of search space, inertia weight ω, cognition coefficient c1,
Coefficient of association c2, coefficient of concordance c3, maximum speed VmaxEtc. parameters；
Step b, the speed of the particle to participating in search in population, position random initializtion, and to flying speed and position
Boundary limitation is provided, that is, meets xi∈[xmin,xmax]D, vi∈[vmin,vmax]D, find out the individual history under particle original state
Optimal value pbest and group optimal value gbest；
All particles in Particle Swarm are regarded as the root node of one tree by step c, and the generation according to optimum binary tree is former
Then, by this generation one tree, according to the cluster number K of setting, backward finds suitable leaf node, you can finds K and initially gathers
Class center；Then can be K son by entire population dividing when cluster centre no longer changes by the iteration of K mean cluster algorithm
Population；
Entire iterations are divided into multiple small periods by step d, and in a cycle, all sub- populations are independent
Search according to formula (1) and formula (2), carries out the update of speed and position；
vi(t+1)=w*vi(t)+c2*r2*(pg(t)-xi(t)) (1)
xi(t+1)=xi(t)+vi(t+1) (2)
And the globally optimal solution PG=(pg that will be searched1, pg2, pg3…pgK) be saved in knowledge plate；K-th of period
Interior, sub- population k participates in collaboratively searching, if it is stronger to learn that sub- population k has in solution space according to the information on knowledge plate
Search capability, then sub- population k is according to the optimal location collaboratively searching searched of sub- population k-1；If it is determined that sub- population k is being solved
The search capability in space is weaker, then the information synergism search on sub- population knowledge based plate, using formula (5) and formula (6) more
New position and speed, independently search updates position and speed to minor population using formula (1) and formula (2)；
Wherein
Step e, if not up to maximum iteration or being unsatisfactory for required precision (not searching globally optimal solution 0),
Return to step three；Otherwise it continues search for, cycle is jumped out until meeting convergence precision.
The aforementioned particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism passes through in step 2
Optimum binary tree thought determines that the initial cluster center of population specifically comprises the following steps：
Step a, Particle Swarm can be described as the search space of a D dimension, there is N number of particle X=(X1,X2,…XN), i-th
The position of son is Xi=(xi1,xi2,…xiD), i=1,2 ... N.N number of particle is regarded as to the root node of one tree, each particle pair
The position answered is considered as the weights of corresponding root node；
Step b chooses two root nodes that path minimum is generated in X, merges the two root nodes, generates a new section
Point (leaf node) generates the weights pass criteria function ω of leaf node, k=(ωi+ωj)/2 generate；
Step c deletes X=(X1,X2,…XN) in work i-th, j root node, while the leaf node k of generation, add in
Into set X；
Step d repeats step b, step c, until, only comprising a leaf node, generating an optimum binary tree in X；
Step e according to the optimum binary tree of cluster number k trimming generations, obtains k initial cluster center.
The aforementioned particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, it is optimal in step 2
The forming process of binary tree includes the following steps：
The division of population is specifically comprised the following steps according to the completion of the K- averaging methods of cluster centre：
All particles are regarded as the root node of one tree by step a, random initializtion population, selected distance principle of optimality, according to
The leaf node of secondary spanning tree to the last only remains a node, generates a tree, is chosen from top to bottom properly using backward principle
Node as divide initial center pointUpper footnote is iterations；
Sample is assigned to closest cluster by step b according to minimal distance principle, if having progressed to nth iteration, if
For all i (i ≠ j), a certain sample x hasThen Be withClass for cluster centre；
With such method until whole samples are assigned in k class；
Step c recalculates the new cluster centre of each cluster
WhereinForIn number of samples.Because step requirement calculates the sample average of k cluster centre, therefore is known as
K- averaging methods；
Step d, ifJ=1,2 ... k, then return to step 2, untilOr E converges to minimum
Value reaches preset cycle-index；
The aforementioned particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, in step 4
Required precision includes：Search solution on benchmark test function reaches the search on the best values of test function or benchmark test function
Solution reaches maximum iteration.
The aforementioned particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, in Sphere (f1)The best values that the precision of solution is searched on benchmark test function are 5.7986e-052, average value 4.6789e-
036, worst-case value 3.2986e-035.
The aforementioned particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, in Ackley (f2)The best values that the precision of solution is searched on benchmark test function are 7.1681e-008, are put down
Mean value is 2.8983e-001, worst-case value 3.2985e+001.
The aforementioned particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, in Griewangk
(f3)The best values that the precision of solution is searched on benchmark test function are 0,
Average value is 3.5628e-010, worst-case value 6.7895e-010.
The aforementioned particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, in Rosenbrock
(f4)The best values that the precision of solution is searched on benchmark test function are 0, are put down
Mean value is 3.9867e+000, worst-case value 9.6234.
The aforementioned particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, in Rastrigin
(f5)The best values that the precision of solution is searched on benchmark test function are 0, average
It is worth for 2.8969e-020, worst-case value 4.6859e-015.
The invention has the beneficial effects that：The present invention passes through son by the way that concept on multiple populations is introduced into particle swarm optimization
The collaboratively searching of population can accelerate convergence speed of the algorithm and improve the convergence precision of algorithm.Introducing period shared mechanism makes to search
Rope to information transmitted in time between sub- population, sub- population be based on the information search, the information that particle is made full use of to search,
Improve convergence energy.Improved K- means clustering algorithms are introduced into particle swarm optimization on multiple populations, population is had into mesh
Be divided into multiple sub- populations；The search process of sub- population is carried out based on the ring topology for introducing period shared mechanism
's.Knowledge plate is introduced into improved particle swarm optimization on multiple populations, the search information of sub- population is recorded by knowledge plate, is judged
The search capability of sub- population, if the search capability of fruit population reduces, then the information in knowledge based plate adjusts searching for sub- population
Suo Fangxiang improves the ability of searching optimum of algorithm.
Description of the drawings
Fig. 1 is that IKMPSO in the present invention (particle swarm optimization on multiple populations based on K- mean clusters and period shared mechanism) is calculated
The structure diagram of method；
Fig. 2 is the structural frames of KBMPSO in the present invention (particle swarm optimization on multiple populations of knowledge based plate shared mechanism) algorithm
Figure
Fig. 3 is that IKMPSO in the present invention (particle swarm optimization on multiple populations based on K- mean clusters and period shared mechanism) is calculated
Convergence curve figure of the method on benchmark test function；
Fig. 4 is that (particle swarm optimization on multiple populations of the knowledge based plate shared mechanism) algorithms of KBMPSO in the present invention are surveyed in benchmark
Convergence curve figure on trial function.
Specific embodiment
Make specific introduce to the present invention below in conjunction with the drawings and specific embodiments.
A kind of particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, includes the following steps：
Step 1 initializes the particle in population, includes number, the dimension of search space of particle in initialization population
The parameters such as number, inertia weight, cognition coefficient, coefficient of association, coefficient of concordance, maximum speed, to participating in the particle of search in population
Speed, position random initializtion, and flying speed and position are provided boundary limitation, find out the individual under particle original state
History optimal value and group's optimal value；
Step 2 determines the initial cluster center of population by optimum binary tree thought, according to the K- mean values of cluster centre
Method completes the division to population；
The initial cluster center for determining population by optimum binary tree thought specifically comprises the following steps：
Step a, Particle Swarm can be described as the search space of a D dimension, there is N number of particle X=(X1,X2,…XN), i-th
The position of son is Xi=(xi1,xi2,…xiD), i=1,2 ... N.N number of particle is regarded as to the root node of one tree, each particle pair
The position answered is considered as the weights of corresponding root node；
Step b chooses two root nodes that path minimum is generated in X, merges the two root nodes, generates a new section
Point (leaf node) generates the weights pass criteria function ω of leaf node, k=(ωi+ωj)/2 generate；
Step c deletes X=(X1,X2,…XN) in work i-th, j root node, while the leaf node k of generation, add in
Into set X；
Step d repeats step b, step c, until, only comprising a leaf node, generating an optimum binary tree in X；
Step e according to the optimum binary tree of cluster number k trimming generations, obtains k initial cluster center.
The forming process of optimum binary tree includes the following steps：
The division of population is specifically comprised the following steps according to the completion of the K- averaging methods of cluster centre：
All particles are regarded as the root node of one tree by step a, random initializtion population, selected distance principle of optimality, according to
The leaf node of secondary spanning tree to the last only remains a node, generates a tree, is chosen from top to bottom properly using backward principle
Node as divide initial center pointUpper footnote is iterations；
Sample is assigned to closest cluster by step b according to minimal distance principle, if having progressed to nth iteration, if
For all i (i ≠ j), a certain sample x hasThen Be withClass for cluster centre；
With such method until whole samples are assigned in k class；
Step c recalculates the new cluster centre of each cluster
WhereinForIn number of samples.Because step requirement calculates the sample average of k cluster centre, therefore is known as
K- averaging methods；
Step d, ifJ=1,2 ... k, then return to step 2, untilOr E converges to minimum
Value reaches preset cycle-index；
Step 3 in the sub- population search process after division, introduces period shared mechanism, makes between the information between sub- population
It is updated every certain period；Detailed process includes the following steps：
Step a, if t is less than collaborative lifecycle, each sub- population is independently searched for and each sub- population is according to formula (1) and formula (2)
Update speed and the position of itself；
vi(t+1)=w*vi(t)+c2*r2*(pg(t)-xi(t)) (1)
xi(t+1)=xi(t)+vi(t+1) (2)
Wherein v represents the flying speed of particle, and t represents the iterations of particle, and c1 represents the autognosis coefficient of particle,
C2 represents the social recognition coefficient of particle.
Step b, if t is more than collaborative lifecycle and is less than maximum iteration, sub- population k is in previous sub- population adjacent thereto
(k-1) collaboratively searching under guiding is independently searched according to formula (3) and formula (4) update position and speed, minor population
Rope, according to formula (1) and formula (2) renewal speed and position；
Wherein vi kThe flying speed of particle i in k-th of sub- population is represented, t represents the iteration cycle of particle, and c1 represents particle
Autognosis coefficient, c2 represents the social recognition coefficient of particle.
Step c, judges whether each sub- population completes collaboration, the return to step b if collaboration is not completed, until all sons kind
Group completes collaboratively searching；
Step 4, if collaboration subgroup be absorbed in local optimum, judge whether to meet required precision, if meet if output as a result,
Return to step three if being unsatisfactory for；Required precision includes：Search solution on benchmark test function reaches the best values of test function
Or the search solution on benchmark test function reaches maximum iteration.
If collaboration subgroup is not absorbed in local optimum, knowledge plate is introduced into sub- population search process, is remembered in knowledge plate
The information of record is timely fed back to the sub- population, and sub- population adjusts the direction of search, jump out part most in time according to feedack
It is excellent, it is searched for towards the direction of global optimum；Detailed process includes the following steps:
Step a, parameter initialization：Set particle number N, the dimension D of search space, inertia weight ω, cognition coefficient c1,
Coefficient of association c2, coefficient of concordance c3, maximum speed VmaxEtc. parameters；
Step b, the speed of the particle to participating in search in population, position random initializtion, and to flying speed and position
Boundary limitation is provided, that is, meets xi∈[xmin,xmax]D, vi∈[vmin,vmax]D, find out the individual history under particle original state
Optimal value pbest and group optimal value gbest；
All particles in Particle Swarm are regarded as the root node of one tree by step c, and the generation according to optimum binary tree is former
Then, by this generation one tree, according to the cluster number K of setting, backward finds suitable leaf node, you can finds K and initially gathers
Class center；Then can be K son by entire population dividing when cluster centre no longer changes by the iteration of K mean cluster algorithm
Population；
Entire iterations are divided into multiple small periods by step d, and in a cycle, all sub- populations are independent
Search according to formula (1) and formula (2), carries out the update of speed and position；
vi(t+1)=w*vi(t)+c2*r2*(pg(t)-xi(t)) (1)
xi(t+1)=xi(t)+vi(t+1) (2)
And the globally optimal solution PG=(pg that will be searched1, pg2, pg3…pgK) be saved in knowledge plate；K-th of period
Interior, sub- population k participates in collaboratively searching, if it is stronger to learn that sub- population k has in solution space according to the information on knowledge plate
Search capability, then sub- population k is according to the optimal location collaboratively searching searched of sub- population k-1；If it is determined that sub- population k is being solved
The search capability in space is weaker, then the information synergism search on sub- population knowledge based plate, using formula (5) and formula (6) more
New position and speed, independently search updates position and speed to minor population using formula (1) and formula (2)；
Wherein
Step e, if not up to maximum iteration or being unsatisfactory for required precision, return to step three；Otherwise continue to search
Rope jumps out cycle until meeting convergence precision.
Present invention proposition considers the period shared mechanism of information and the information sharing mechanism of knowledge plate between sub- population,
To strengthen the interaction of the information between sub- population, so as to improve the precision for the speed reconciliation for searching optimal solution.
The benchmark test function used in the implementation procedure of the present invention is as shown in table 1.
Table 1 is used to test five groups of benchmark test functions of the present invention
Table 2 gives the present invention and the precision of solution is searched on five groups of benchmark test functions, by can with other algorithm comparisons
Know, the present invention can preferably improve the precision of search solution.
Table 2：Operation result (D=10) of the present invention on five kinds of benchmark test functions
By each algorithm of the data record in analytical table 2, the function of independent operating 20 times is fitted on 10 dimension test functions
The best values that should be worth, worst-case value, average value.By the data analysis in table 2 it is found that KBMPSO algorithms can be with preferable more
Sample increases the search capability of algorithm.The shared mechanism of knowledge based plate can perceive the search condition of sub- population, while root
It is reported that the shared information known on plate adjusts the direction of search of sub- population, enhance the search capability of algorithm.Therefore, KBMPSO algorithms with
Other algorithms are compared, and have higher convergence precision and convergence rate.
Fig. 4 (a~e) presents the convergent characteristic of six kinds of algorithm search optimal adaptation values；By being restrained in Fig. 4 (a~e)
The curve of characteristic can show that algorithm can be easier to search globally optimal solution when solving unimodal function.The storage of knowledge plate
Information is mainly used for improving the problem of algorithm is absorbed in local optimum in solving complexity Solving Multimodal Function.Therefore, KBMPSO algorithms exist
Stronger advantage is shown during solving complexity function, because other algorithms are in solving complexity function, due to being absorbed in local optimum
It can not jump out, and search for less than globally optimal solution.
The present invention can be accelerated by the way that concept on multiple populations is introduced into particle swarm optimization by the collaboratively searching of sub- population
Convergence speed of the algorithm and the convergence precision for improving algorithm.Introducing period shared mechanism makes the information searched between sub- population
It transmits in time, sub- population is based on the information search, and the information that particle is made full use of to search improves convergence energy.It will
Improved K- means clustering algorithms are introduced into particle swarm optimization on multiple populations, are divided into multiple sub- populations by population is purposive；
The search process of sub- population is carried out based on the ring topology for introducing period shared mechanism.Knowledge plate is introduced into improvement
Particle swarm optimization on multiple populations in, the search information of sub- population is recorded by knowledge plate, judges the search capability of sub- population, if
The search capability of sub- population reduces, then the information in knowledge based plate adjusts the direction of search of sub- population, improves the overall situation of algorithm
Search capability.
The basic principles, main features and advantages of the invention have been shown and described above.The technical staff of the industry should
Understand, the invention is not limited in any way above-described embodiment, all to be obtained by the way of equivalent substitution or equivalent transformation
Technical solution is all fallen in protection scope of the present invention.
Claims (9)
1. the particle swarm optimization on multiple populations based on period interaction mechanism and knowledge plate synergistic mechanism, it is characterised in that make full use of and search
The information that particle searches during rope improves the search precision and search speed of population, mainly includes the following steps：
Step 1 initializes the particle in population, including initializing the dimension of the number of particle in population, search space, being used to
Property weight, cognition coefficient, coefficient of association, coefficient of concordance, the parameters such as maximum speed, the speed of the particle to participating in search in population
Degree, position random initializtion, and boundary limitation is provided to flying speed and position, find out the individual history under particle original state
Optimal value and group's optimal value；
Step 2 is determined the initial cluster center of population using improved K mean cluster algorithm, realizes the division to population；
Step 3 in the sub- population search process after division, introduces period shared mechanism, makes the information interval one between sub- population
The fixed period is updated；Detailed process includes the following steps：
Step a, if t is less than collaborative lifecycle, each sub- population is independently searched for and each sub- population is according to formula (1) and formula (2) update
The speed of itself and position；
vi(t+1)=w*vi(t)+c2*r2*(pg(t)-xi(t)) (1)
xi(t+1)=xi(t)+vi(t+1) (2)
Wherein v represents the flying speed of particle, and t represents the newer algebraically of particle, c2Represent the social recognition coefficient of particle.
Step b, if t is more than collaborative lifecycle and less than maximum iteration, sub- population k is in previous sub- population adjacent thereto
(k-1) collaboratively searching under guiding is independently searched according to formula (3) and formula (4) update position and speed, minor population
Rope, according to formula (1) and formula (2) renewal speed and position；
Wherein v represents the flying speed of particle, and t represents the newer algebraically of particle, c1Represent the autognosis coefficient of particle, c2Generation
The social recognition coefficient of table particle.
Step c, judges whether each sub- population completes collaboration, the return to step b if collaboration is not completed, until all sub- populations are equal
Complete collaboratively searching；
Step 4 if collaboration subgroup is absorbed in local optimum, judges whether to meet required precision, if output is not as a result, if meeting
Meet then return to step three；
If subgroup is cooperateed with to be absorbed in local optimum in search process, period shared mechanism can only accelerate population to be absorbed in local optimum at this time
Solution, can not jump out, therefore knowledge plate is introduced into sub- population search process, and the information recorded in knowledge plate is timely fed back to the son
Population, sub- population adjust the direction of search, jump out local optimum, searched towards the direction of global optimum in time according to feedack
Rope；Detailed process includes the following steps:
Step a, parameter initialization：Set particle number N, the dimension D of search space, inertia weight ω, cognition coefficient c1, society
Coefficient c2, coefficient of concordance c3, maximum speed VmaxEtc. parameters；
Step b, the speed of the particle to participating in search in population, position random initializtion, and flying speed and position are provided
Boundary limits, that is, meets xi∈[xmin,xmax]D, vi ∈ [vmin,vmax]D, the individual history found out under particle original state is optimal
Value pbest and group optimal value gbest；
All particles in Particle Swarm are regarded as the root node of one tree by step c, will according to the generation principle of optimum binary tree
This generation one tree, according to the cluster number K of setting, backward finds suitable leaf node, you can finds in K initial clustering
The heart；Then can be K son kind by entire population dividing when cluster centre no longer changes by the iteration of K mean cluster algorithm
Group；
Entire iterations are divided into multiple small periods by step d, in a cycle, the independent search of all sub- populations,
According to formula (1) and formula (2), the update of speed and position is carried out；
vi(t+1)=w*vi(t)+c2*r2*(pg(t)-xi(t)) (1)
xi(t+1)=xi(t)+vi(t+1) (2)
And the globally optimal solution PG=(pg that will be searched1, p, g2, pg3…pgK) be saved in knowledge plate；In k-th of period, son
Population k participates in collaboratively searching, if learning that sub- population k has stronger search energy in solution space according to the information on knowledge plate
Power, then sub- population k is according to the optimal location collaboratively searching searched of sub- population k-1；If it is determined that sub- population k is in solution space
Search capability is weaker, then the information synergism search on sub- population knowledge based plate, updates position using formula (5) and formula (6)
And speed, independently search updates position and speed to minor population using formula (1) and formula (2)；
Wherein
Step e, if not up to maximum iteration or being unsatisfactory for required precision, return to step three；Otherwise it continues search for, directly
Cycle is jumped out to convergence precision is met.
2. according to claim 1 calculated based on the Particle Swarm on multiple populations of period interaction mechanism and knowledge plate synergistic mechanism
Method, which is characterized in that determine that the initial cluster center of population specifically includes following step by optimum binary tree thought in step 2
Suddenly：
Step a, Particle Swarm can be described as the search space of a D dimension, there is N number of particle X=(X1,X2,…XN), i-th particle
Position is Xi=(xi1,xi2,…xiD), i=1,2 ... N.N number of particle is regarded as to the root node of one tree, each particle is corresponding
Position is considered as the weights of corresponding root node；
Step b chooses two root nodes that path minimum is generated in X, merges the two root nodes, generates a new node
(leaf node) generates the weights pass criteria function ω ' of leaf nodek=(ωi+ωj)/2 generate；
Step c deletes X=(X1,X2,…XN) in work i-th, j root node, while the leaf node k of generation, be added to collection
It closes in X；
Step d repeats step b, step c, until, only comprising a leaf node, generating an optimum binary tree in X；
Step e according to the optimum binary tree of cluster number k trimming generations, obtains k initial cluster center.
3. according to claim 1 calculated based on the Particle Swarm on multiple populations of period interaction mechanism and knowledge plate synergistic mechanism
Method, which is characterized in that the forming process of optimum binary tree includes the following steps in step 2：
The division of population is specifically comprised the following steps according to the completion of the K- averaging methods of cluster centre：
All particles are regarded as the root node of one tree by step a, random initializtion population, and selected distance principle of optimality is given birth to successively
The leaf node of Cheng Shu to the last only remains a node, generates a tree, suitable section is chosen from top to bottom using backward principle
Point is as the initial center point dividedUpper footnote is iterations；
Sample is assigned to closest cluster by step b according to minimal distance principle, if having progressed to nth iteration, if for
All i (i ≠ j), a certain sample x haveThen Be withClass for cluster centre；With
Such method is until whole samples are assigned in k class；
Step c recalculates the new cluster centre of each cluster
WhereinForIn number of samples.Because step requirement calculates the sample average of k cluster centre, therefore referred to as K- is equal
Value method；
Step d, ifJ=1,2 ... k, then return to step 2, untilEither E converge to minimum value or
Reach preset cycle-index；
4. according to claim 1 calculated based on the Particle Swarm on multiple populations of period interaction mechanism and knowledge plate synergistic mechanism
Method, which is characterized in that the required precision in step 4 includes：Search solution on benchmark test function reaches the best of test function
Search solution in value or benchmark test function reaches maximum iteration.
5. according to claim 1 calculated based on the Particle Swarm on multiple populations of period interaction mechanism and knowledge plate synergistic mechanism
Method, which is characterized in that at Sphere (f1)The best values that the precision of solution is searched on benchmark test function are
5.7986e-052 average value 4.6789e-036, worst-case value 3.2986e-035.
6. the particle swarm optimization on multiple populations according to claim 1 based on period interaction mechanism and knowledge plate synergistic mechanism,
It is characterized in that, at Ackley (f2)The precision of solution is searched on benchmark test function
Best values be 7.1681e-008, average value 2.8953e-001, worst-case value 3.2985e+001.
7. the particle swarm optimization on multiple populations according to claim 1 based on period interaction mechanism and knowledge plate synergistic mechanism,
It is characterized in that, at Griewangk (f3)It is searched on benchmark test function
The best values for the precision sought the meaning are 0, average value 3.5628e-010, worst-case value 6.7895e-010.
8. the particle swarm optimization on multiple populations according to claim 1 based on period interaction mechanism and knowledge plate synergistic mechanism,
It is characterized in that, at Rosenbrock (f4)It is searched on benchmark test function
The best values of the precision of solution are 0, average value 3.9867, worst-case value 9.6234.
9. the particle swarm optimization on multiple populations according to claim 1 based on period interaction mechanism and knowledge plate synergistic mechanism,
It is characterized in that, at Rastrigin (f5)Search solution on benchmark test function
The best values of precision are 0, average value 2.8969e-020, worst-case value 4.6859e-015.
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|---|---|---|---|---|
| CN111144541A (en) * | 2019-12-12 | 2020-05-12 | 中国地质大学（武汉） | Microwave filter debugging method based on multi-population particle swarm optimization method |
| CN112258587A (en) * | 2020-10-27 | 2021-01-22 | 上海电力大学 | Camera calibration method based on wolf-wolf particle swarm hybrid algorithm |
| CN113887692A (en) * | 2021-09-15 | 2022-01-04 | 中南大学 | Research method of controlled particle group based on group activity sensing |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111144541A (en) * | 2019-12-12 | 2020-05-12 | 中国地质大学（武汉） | Microwave filter debugging method based on multi-population particle swarm optimization method |
| CN112258587A (en) * | 2020-10-27 | 2021-01-22 | 上海电力大学 | Camera calibration method based on wolf-wolf particle swarm hybrid algorithm |
| CN112258587B (en) * | 2020-10-27 | 2023-07-07 | 上海电力大学 | Camera calibration method based on gray wolf particle swarm mixing algorithm |
| CN113887692A (en) * | 2021-09-15 | 2022-01-04 | 中南大学 | Research method of controlled particle group based on group activity sensing |
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