CN107292332A - A kind of cuckoo algorithm based on Fuzzy C mean cluster - Google Patents

A kind of cuckoo algorithm based on Fuzzy C mean cluster Download PDF

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CN107292332A
CN107292332A CN201710378473.9A CN201710378473A CN107292332A CN 107292332 A CN107292332 A CN 107292332A CN 201710378473 A CN201710378473 A CN 201710378473A CN 107292332 A CN107292332 A CN 107292332A
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mrow
bird
nest
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于立君
董泽全
王辉
高菁
魏智红
王正安
张雪
丁莹
胡羽坤
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Harbin Engineering University
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Abstract

The invention belongs to function optimization technical field, and in particular to a kind of cuckoo algorithm based on Fuzzy C mean cluster.The present invention concentrates on a class by introducing Fuzzy C mean algorithm in the preference random walk of cuckoo algorithm, by the component with same nature in solution and is updated, and enhances antijamming capability between dimension.The step-length more new range of preference random walk is changed simultaneously, is added the direction of search, is improved the diversity of algorithm.The present invention can effectively improve CS convergences of algorithm speed and improve the quality of solution, especially be embodied in solution high-dimensional function optimization problem.

Description

A kind of cuckoo algorithm based on Fuzzy C-Means Clustering
Technical field
The present invention relates to function optimization field, and in particular to a kind of cuckoo algorithm based on Fuzzy C-Means Clustering.
Background technology
In nature, many biologies show many social actions imagined out of the mankind and height wisdom, such as bird Class migratory behaviour, ant colony foraging behavior.The wisdom behavior of large nature biocenose is referred to as group intelligence, this kind of groups intelligence The independent individual of each intelligent being present in group, does not have Collective stewardship person without common leader yet, and group's behavior is Interactive reaction between perception and individual based on individual to environment.In the research process to nature biotechnology group behavior In, it is proposed that the grain constructed based on the artificial ant algorithm that ant swarm looks for food bionic principle and constructs and based on flock of birds migratory behaviour Subgroup optimized algorithm.What is emphasized in the research of group intelligence is not the labyrinth for probing into composition individual, but swarm intelligence And the ability for adapting to environment that interaction is presented between individual.
Cuckoo algorithm (Cuckoo Search, abbreviation CS) is a kind of emerging Swarm Intelligence Algorithm, and cuckoo algorithm is (Cuckoo search via are proposed by univ cambridge uk scholar Yang Xin-she and Deb Suash in 2009 Levy.2009), their Inspiration Sources are in the brood parasitism behavior to cuckoo and birds or drosophila (L é vy flights) behavior Simulation.CS algorithms have the advantages that simple in construction, parameter is few, are easily achieved, and have been successfully applied to function optimization, neutral net Training, multiple-objection optimization, engineering design optimization, recognition of face scheduling theory and application field.Wherein function optimization problem is in theory There is critically important application with engineering field, many problems can be changed into function optimization problem by certain conversion, it is such as many Parametric function fitting, positron annihilation analysis of spectrum, signal spectral analysis etc..These usual problems be all it is extremely complex, mainly Show as that scale is big, dimension is high, non-linear, non-convex and micro- characteristic such as can not look into.
The superiority of CS algorithms is embodied in the algorithm with two crucial components:L é vy flights random walks and partially Good random walk, the combination of two components can balance global search and the Local Search of the algorithm.In view of CS algorithms is simple Efficiently, lot of domestic and foreign scholar is improved CS algorithms, relate generally to step-length improve, it is adaptive and melt with other algorithms In terms of conjunction.As British scholar S.Walton et al. is improved CS algorithms (Modified cuckoo search:A new gradient free optimization algorithm.2011);Hu Xinxin proposes a kind of cloth of adaptation mechanism The improved method of paddy bird algorithm, improves convergence rate and refinement ability (the improvement cuckoo of solved function optimization problem of function Bird searching algorithm .2013);A kind of clear et al. the cuckoo algorithms for proposing adaptive step of Zheng Hong, solve Levy flight The problem of step-length lacks adaptivity is produced, according to the search result of different phase, the size of adaptive dynamic adjusting step, place The relation (a kind of adaptive step cuckoo searching algorithm .2013) in the middle of global optimizing ability and optimizing intensive reading is managed.
But whether CS algorithms or CS innovatory algorithm, component L é vy flights random walks and preference are swum at random The new explanation of movable property life is all that after whole updating, these solutions could be evaluated, i.e., change its institute simultaneously to each new explanation Just solution is evaluated after important value.For Multidimensional object, due to the presence of static couple so that whole updating The quality of convergence rate reconciliation will be reduced.
The content of the invention
It is an object of the invention to provide a kind of cuckoo algorithm (abbreviation FCMCS) based on Fuzzy C-Means Clustering.
The object of the present invention is achieved like this:
For a kind of cuckoo algorithm based on Fuzzy C-Means Clustering, its specific design procedure is as follows:
The position of n Bird's Nest of step 1. random initializtion, evaluates the quality of bird egg in Bird's Nest;
Step 2. sets the error threshold of optimization aim, and circulation performs following step always if being unsatisfactory for condition:
Step 2.1. is in original cuckoo algorithm, and i-th cuckoo is moved to the step-length s of next nestiIt is defined as
Wherein, α is constant, and u and v obey variance for σ respectivelyuAnd σvNormal distribution N (0, σ2), wherein, σv=1, σuIt is fixed Justice is
Wherein, Γ () represents gamma function, σuValue adjusted with β, xiLocation updating formula can be described as
xi(k+1)←xi(k)+ri·si(k) (3)
Wherein, ri, it is (0,1) interval uniform random number;
It can be obtained for the stepsize formula for producing new nest by following formula:
R '=rand (xi∈[1,n]-xj∈[1,n]) (4)
Wherein, xi∈[1,n]And xj∈[1,n]It is randomly selected two solutions from whole population, in order to increase the direction of search Diversity above formula can be changed to
R '=r (xi∈[1,n]-xj∈[1,n]) (5)
Wherein, r is the random number between [1, -1], and the location updating formula of new nest can be described as
Wherein, probability of detection paIt is the random number between [0,1];
The route direction and its length of n cuckoo next time are calculated using formula (1), new n Bird's Nests position can be obtained, Evaluate the quality of Bird's Nest and compared with a upper Bird's Nest quality, if degradation, keep a Bird's Nest constant, if matter Quantitative change is good, then abandons original Bird's Nest into new Bird's Nest;
Step 2.2. is for n Bird's Nest, if the host bird in Bird's Nest is found according to probability of detection after the bird egg of cuckoo, New Bird's Nest position is produced according to formula (6), and it is poly- according to Fuzzy C-Means Clustering Algorithm to component in n Bird's Nest position vector Class, is evaluated by being substituted into a corresponding upper Bird's Nest position vector for class, will be upper if the quality after replacing improves The corresponding position in one Bird's Nest position is replaced, if be deteriorated, keeps constant;
Step 2.3. is finally evaluated all Bird's Nest positions, keeps top-quality position, and perform step successively Rapid 2.1 and 2.2.
The quality of evaluation bird egg described in step 1 refers to we assume that 1 cuckoo only produces a bird egg for 1 time, and with Machine selects 1 Bird's Nest to place, and every cuckoo bird egg represents new explanation, if new explanation is more excellent than old solution fitness, i.e. bird egg matter Amount is more preferable, then only remains new explanation, and final high-quality bird egg will be retained to the next generation.
The value of error threshold described in step 2 depends on test function in itself.
Described new explanation is after preference random walk plays a role, and the component with same nature is concentrated into one in new explanation Other components of each class and present age solution are reassembled into an interim solution respectively afterwards, interim solution are evaluated by class.
Described uses greedy strategy method to solving the evaluation method evaluated temporarily, i.e., can only improve current solution New explanation can just be carried over into the next generation.
The beneficial effects of the present invention are:
Component with same nature in new explanation is concentrated on a class by the present invention after preference random walk plays a role, More capable evaluation is carried out by class, so as to reduce static couple, save function evaluation number of times;Afterwards respectively by each class and the present age Other components solved reassemble into one and solve temporarily and interim solution is evaluated, and greediness is used more to interim result appraisal strategy New strategy, it is ensured that the degeneration of other dimensions does not interfere with the reservation for dimension of evolving, and strengthens the local search ability of this algorithm, so that Faster convergence rate and higher-quality solution are obtained, and as this advantage of the increase of dimension can become apparent from;By more Change the step-length more new formula of preference random walk, add the direction of search, improve the diversity of algorithm;Fitness function is direct Object function is used, and fitness function need not be rebuild.
Brief description of the drawings
Fig. 1 is flow (false code) figure of FCMCS algorithms.
Fig. 2 is FCMCS algorithms and CS Algorithm for Solving f1Convergence curve figure during function.
Fig. 3 is FCMCS algorithms and CS Algorithm for Solving f2Convergence curve figure during function.
Fig. 4 is FCMCS algorithms and CS Algorithm for Solving f3Convergence curve figure during function.
Fig. 5 is FCMCS algorithms and CS Algorithm for Solving f4Convergence curve figure during function.
Fig. 6 is FCMCS algorithms and CS Algorithm for Solving f5Convergence curve figure during function.
Fig. 7 is FCMCS algorithms and CS Algorithm for Solving f6Convergence curve figure during function.
Fig. 8 is FCMCS algorithms and CS Algorithm for Solving f7Convergence curve figure during function.
Embodiment
Illustrate below in conjunction with the accompanying drawings and the present invention is described in more detail:
The present invention relates to function optimization technical field, the quality and convergence rate of original cuckoo algorithm solution are improved, is proposed A kind of cuckoo searching algorithm based on Fuzzy C-Means Clustering, solves cuckoo searching algorithm and uses whole updating to solution Strategy, the problem of causing to there is static couple when solving high-dimension function.Using Fuzzy C-Means Clustering Algorithm by phase in individual A class is polymerized to like component, evaluation renewal is carried out by class, and receive to improve the new explanation currently solved using greedy strategy.More simultaneously Change the step-length more new formula of preference random walk, increase the direction of search, improve the diversity of algorithm.Simulation result illustrates, improves Cuckoo algorithm can effectively improve the quality and convergence rate of cuckoo algorithm solution, and as the increase of dimension is this excellent Gesture is also gradually becoming obvious.
It is an object of the invention to for current cuckoo searching algorithm and its innovatory algorithm when solving high-dimension function pair Solution uses whole updating strategy, but due to there is static couple, causes the shortcoming that the quality and convergence rate of solution decline to be changed Enter, devise the cuckoo algorithm based on Fuzzy C-Means Clustering and similar component in individual is polymerized to a class, evaluated by class Update, and receive that using greedy strategy the new explanation that currently solves can be improved, can so effectively improve CS algorithm solutions quality and Convergence rate, and as this advantage of the increase of dimension is also gradually becoming obvious.
The innovatory algorithm of the present invention is based on cuckoo algorithm, supplemented by FCM Algorithms, by cuckoo algorithm Preference random walk in be introduced into phase in the new explanation that Fuzzy C-Means Clustering Algorithm will be produced by L é vy flights random walks Connatural component concentrates on a class and is updated, and can strengthen antijamming capability between dimension.Change preference random walk simultaneously Step-length more new formula, increases the direction of search, improves the diversity of algorithm.It should be strongly noted that the fitness in the present invention Function directly uses object function, and need not rebuild fitness function.
The present invention after preference random walk plays a role to solution institute it is important cluster, with same nature dividing Gather for a class, other the such correspondence position components of removing solved respectively by each class component and before playing a role reassemble into one and faced Shi Xie, is evaluated interim solution.Both antijamming capability between dimension is enhanced, evaluation number of times is saved again;To interim result appraisal Using greedy Evaluation Strategy, i.e., can only improve the new explanation currently solved can just be carried over into the next generation, accelerate convergence speed Degree;The step-length more new formula of preference random walk is changed, increases the direction of search, the diversity of algorithm is improved.
A kind of cuckoo searching algorithm based on Fuzzy C-Means Clustering proposed by the present invention specifically includes following step Suddenly:
Step one:Cuckoo algorithm principle is described.
Cuckoo hatches the bird egg of cuckoo using host bird by the way of being laid eggs in host's bird Bird's Nest.If posted Main bird finds there are exotic bird eggs in Bird's Nest, then external bird egg can be abandoned or be abandoned the nest of oneself, and build elsewhere Found new nest.In CS algorithms, each bird egg represents a solution in a nest, wherein every cuckoo bird egg all represents newly Solution.If new explanation is more excellent than old solution fitness, new explanation will be remained, and old solution will be replaced.For mathematical computations can be carried out, Assuming that L é vy flights rules are obeyed in an only bird egg in each nest, the generation of new explanation.Yang and Deb has found to pass through L é vy Flights performs random walk and is more prone to search for optimal solution than simple random walk.To put it more simply, CS is based on three ideals Rule:
Rule 1:1 cuckoo, 1 only one bird egg of production, and randomly choose 1 Bird's Nest placement.
Rule 2:Best nest and high-quality bird egg will be retained to the next generation.
Rule 3:Can be fixed with the sum of nest, and host bird finds that the probability of exotic bird eggs is pa∈[0,1]。
The new position x produced according to foregoing description, bird egg by L é vy flightsi
Wherein,It is dot-product (entry-wise multiplications).α > 0 are related to target problem step-length Parameter.L é vy flights arbitrary width obeys L é vy distributions.
In original CS algorithms, i-th cuckoo is moved to the step-length s of next nestiIt is defined as:
Wherein, α is constant, and u and v obey variance for σ respectivelyuAnd σvNormal distribution N (0, σ2).And σv=1, σuDefinition For:
Wherein, Γ () represents gamma function.σuValue adjusted with β.xiLocation updating formula can be described as:
xi(k+1)←xi(k)+ri·si(k)
Wherein, riIt is (0,1) interval uniform random number.
It can be obtained for the stepsize formula for producing new nest by following formula:
R '=rand (xi∈[1,n]-xj∈[1,n])
Wherein, xi∈[1,n]And xj∈[1,n]It is randomly selected two solutions from whole population.In order to increase the direction of search Diversity above formula can be changed to:
R '=r (xi∈[1,n]-xj∈[1,n])
Wherein, r is the random number between [1, -1].The location updating formula of new nest can be described as:
Wherein, probability of detection paIt is the random number between [0,1].
Step 2:Fuzzy C-Means Clustering Algorithm principle is described.
The basic thought of FCM algorithms is n vector xi(i=1,2 ... n) are divided into c Fuzzy Cluster, and try to achieve each cluster Cluster centre, target function value is reached minimum, FCM object function is defined as:
Wherein,uik∈ (0,1),Relative to hard clustering algorithm, FCM algorithms Fuzzy weighted values exponent m is added in object function, in order that object function reaches minimum value, cluster centre can be released and be subordinate to The more new formula of degree:
FCM algorithms, which have, to be calculated simple, computing soon and is widely used and work with more clear and definite geometric meaning In journey practice.
Step 3:Cuckoo algorithm principle based on Fuzzy C-Means Clustering is described.
For multidimensional objective function, because CS algorithms use whole updating Evaluation Strategy, by influence algorithmic statement speed Spend the quality conciliate.Assuming that object function isAnd i-th of solution X in g generationsg,i=(1,1,1,1), now mesh Offer of tender numerical value is f (Xg,i)=4.First, it is assumed that updating X using formula (6)g,iObtain i-th of solution X in g+1 generationsg+1,i=(0, 0,2, -2), now target function value is changed into f (Xg+1,i)=8.Due to f (Xg+1,i) > f (Xg,i) show not improve current solution, So original solution will be kept constant.But contrast globally optimal solution Xopt=(0,0,0,0) understands that the value of the first peacekeeping second dimension is by 1 It is changed into 0, the value of the third dimension and fourth dimension is changed into 2 and -2 respectively from 1, because the influence of the third dimension and fourth dimension causes the first peacekeeping Second dimension has reached that the component of global optimum is rejected originally, causes to evaluate number of times increase, convergence rate reduction.
Based on problems, clustered set forth herein important to the institute of solution after preference random walk plays a role, Component with similitude gathers for a class.Other components of each class and present age solution are reassembled into an interim solution respectively afterwards, Interim result appraisal is used based on greedy Evaluation Strategy, i.e., can only improve the new explanation currently solved can just be carried over into down A generation.For example, after FCM algorithm performs are finished, Xg+1,iIt is divided into 3 classes, respectively X1=(0,0), X2=(2), X3=(- 2), New explanation after restructuring is respectively Xg+1,i,1=(0,0,1,1), Xg+1,i,2=(1,1,2,1), Xg+1,i,3=(1,1,1, -2).New explanation Target function value relation with old solution is respectively Xg+1,i,1=2 < Xg,i=4, Xg+1,i,2=7 > Xg,i=4, Xg+1,i,3=7 > Xg,i =4, evaluation result is that the first kind is received, and Equations of The Second Kind and the 3rd class are abandoned, and obtain last solution Xg+1,i=(0,0,1,1).Base It ensure that the degeneration of other dimensions does not interfere with the reservation for dimension of evolving in greedy more new strategy, strengthen the Local Search of algorithm, So as to obtain faster convergence rate and higher-quality solution.
Step 4:Cuckoo algorithm flow based on Fuzzy C-Means Clustering.
First, the position (bird egg or solution) of n Bird's Nest of random initializtion, evaluates the quality of bird egg.
Secondly, the error threshold of optimization aim is set, and circulation performs following step always if being unsatisfactory for condition:
1. calculating the route direction and its length of n cuckoo next time, new n Bird's Nests position can be obtained.Evaluate Bird's Nest Quality and compared with a upper Bird's Nest quality, if degradation, keep a Bird's Nest constant;And if quality becomes It is good, then original Bird's Nest is abandoned into new Bird's Nest.
2. for n Bird's Nest, if the host bird in Bird's Nest is found according to probability of detection after the bird egg of cuckoo, calculate new The position of Bird's Nest, and component in n Bird's Nest position vector is clustered according to Fuzzy C-Means Clustering Algorithm.By being substituted into pair for class Evaluated in the upper Bird's Nest position vector answered, if the quality after replacing improves, by upper Bird's Nest position correspondence Position replace;If be deteriorated, keep constant.
3. last, all Bird's Nest positions are evaluated, top-quality position is kept, and order perform step 1 with 2。
Cuckoo searching algorithm flow (false code) based on FCM is as shown in Figure 1.
Step 5:Emulation in all directions is carried out to the cuckoo algorithm based on Fuzzy C-Means Clustering.
In order to analyze the shadow for the quality that innovatory algorithm is conciliate when solving multidimensional function optimization problem to convergence rate comprehensively Ring, emulation experiment have selected 7 test functions in table 1,7 test functions are the function that expression formula is fixed.
The test function of table 1
Table 2 gives CS algorithms and FCMCS algorithms from low-dimensional gradually to the average function value error on higher dimensional space.Wherein Population scale NP=D, probability of detection pa=0.25, cluster numbers c=10, each algorithm independent operating 50 times.
The CS of table 2 and FCMCS average function value error (D=25)
As can be seen from Table 2 for unimodal function, CS algorithms and FCMCS algorithms in the case where identical evaluates number of times and dimension Compare, FCMCS algorithms can increase substantially the quality of solution.For Solving Multimodal Function, innovatory algorithm is in function f2、f4、f6、 f7On equally significantly improve the quality of understanding.As function f3、f5In low-dimensional, FCMCS algorithms are not to what the quality of solution improved It is obvious that still all the more being protruded as the increase FCMCS algorithms of dimension improve ability compared to CS algorithms to the quality of solution.
Analysis of convergence speed:Table 3 gives required iterations and number of success when algorithm reaches specification error threshold value
The mean error that the CS of table 3 and FCMCS converges on specification error threshold value evaluates number of times (D=25)
Table 3 gives algorithmic statement in evaluation number of times and number of success required for specification error threshold value, and "/" represents algorithm Specification error threshold value can not be converged to.CS algorithms and FCMCS algorithms are in unimodal function f as can be seen from Table 31With Solving Multimodal Function f3 Converge in specification error threshold value, but FCMCS algorithms significantly improve convergence rate.And to Solving Multimodal Function f2、f4、f6、f7 For, CS algorithms can not be converged in specification error threshold value when function increases to certain dimension, and FCMCS is for any dimension All converge on specification error threshold value and improve convergence rate.For function f5Although saying that two kinds of algorithms are all not converged to specified Error threshold in, but according to the data of table 2 understand FCMCS convergences of algorithm speed faster.
In order to more intuitively illustrate that FCMCS convergences of algorithm speed is better than CS algorithms, Fig. 2 to Fig. 8 illustrates two kinds of algorithms The convergence process converged to when several functions 500 are tieed up in specification error threshold value.The wherein deeper curve of color represents CS algorithms, The shallower curve of color represents FCMCS algorithms, and as can be seen from the figure FCMCS algorithms substantially have more preferable convergence curve, and It is faster than CS algorithm and have in the later stage and solve quality well in the convergence rate of early stage.
Table 4 gives a kind of innovatory algorithm of CS algorithms, and the population of cuckoo (DDICS) algorithm and standard is improved by dimension (PSO) result that algorithm is tested from 10 dimensions to 500 dimensions 7 test functions.Wherein, population scale NP=D, each algorithm Independent operating 50 times.Wherein " ↑ " represents algorithm because operation time is long and can not the average calculation error.
The comparative result (D=25) of the FCMCS algorithms of table 4 and other algorithms
Different algorithms has different manifestations, function f to different functions as seen from the table1、f4The FCMCS algorithms in low-dimensional Performance is weaker than DDICS algorithms, but FCMCS gradually occupies advantage after 50 dimensions.Although FCMCS algorithms are in function f2Middle performance is weak In DDICS algorithms, but small in not cripetura with the increase gap of dimension, during 500 dimension FCMCS algorithms with DDICS algorithm bases This maintains an equal level, and has certain advantage in high-dimensional function optimization this demonstrate FCMCS algorithms.For function f3For FCMCS calculate Method is dominant comprehensively.For function f6、f7For DDICS algorithms be better than FCMCS algorithms, it is but better than PSO algorithm performance.In reality Emulation in find DDICS algorithms run time significantly extend with the increase of dimension, this aspect is due to FCMCS Algorithm uses FCM algorithms, so the increase of Riming time of algorithm is not apparent.
Because there is static couple in the whole updating strategy of CS algorithms, waste a certain degree of function evaluate number of times and then Cause the decline of convergence rate, and FCMCS algorithms employ FCM algorithms, and similar component is gathered and evaluated for a class, strengthen Local refinement ability, improves the quality and convergence rate understood.From simulation result, FCMCS algorithms are with the increase of dimension Simultaneously advantage is increasing for the improvement CS algorithms that can stablize.Compared with related CS algorithms and other evolution algorithmics, experiment knot Fruit shows that innovatory algorithm has greater advantage on multidimensional function problem is solved.

Claims (5)

1. a kind of cuckoo algorithm based on Fuzzy C-Means Clustering, it is characterised in that concrete implementation step is as follows:
The position of n Bird's Nest of step 1. random initializtion, evaluates the quality of bird egg in Bird's Nest;
Step 2. sets the error threshold of optimization aim, and circulation performs following step always if being unsatisfactory for condition:
Step 2.1. is in original cuckoo algorithm, and i-th cuckoo is moved to the step-length s of next nestiIt is defined as
Wherein, α is constant, and u and v obey variance for σ respectivelyuAnd σvNormal distribution N (0, σ2), wherein, σv=1, σuIt is defined as
<mrow> <mi>&amp;sigma;</mi> <mo>=</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mfrac> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&amp;pi;</mi> <mi>&amp;beta;</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>+</mo> <mi>&amp;beta;</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mn>2</mn> <mrow> <mo>(</mo> <mi>&amp;beta;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mi>&amp;beta;</mi> <mi>&amp;Gamma;</mi> <mrow> <mo>(</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mi>&amp;beta;</mi> </mrow> <mn>2</mn> </mfrac> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mi>&amp;beta;</mi> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein, Γ () represents gamma function, σuValue adjusted with β, xiLocation updating formula can be described as
xi(k+1)←xi(k)+ri·si(k) (3)
Wherein, riIt is (0,1) interval uniform random number;
Different from formula (1), it can be obtained for the stepsize formula for producing new nest by following formula
R '=rand (xI ∈ [1, n]-xJ ∈ [1, n]) (4)
Wherein, xI ∈ [1, n]And xJ ∈ [1, n]It is randomly selected two solutions from whole population, in order to increase the various of the direction of search Property above formula can be changed to
R '=r (xI ∈ [1, n]-xJ ∈ [1, n]) (5)
Wherein, r is the random number between [1, -1], and the location updating formula of new nest can be described as
<mrow> <msup> <mi>x</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <msup> <mi>r</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> </mrow> </mtd> <mtd> <mrow> <msub> <mi>P</mi> <mi>a</mi> </msub> <mo>&gt;</mo> <msub> <mi>p</mi> <mi>a</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mi>i</mi> </msub> </mtd> <mtd> <mrow> <mi>e</mi> <mi>l</mi> <mi>s</mi> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
Wherein, probability of detection paIt is the random number between [0,1];
The route direction and its length of n cuckoo next time are calculated using formula (1), new n Bird's Nests position can be obtained, evaluated The quality of Bird's Nest is simultaneously compared with a upper Bird's Nest quality, if degradation, keeps a Bird's Nest constant, if quality becomes It is good, then original Bird's Nest is abandoned into new Bird's Nest;
Step 2.2. is for n Bird's Nest, if the host bird in Bird's Nest is found according to probability of detection after the bird egg of cuckoo, according to Formula (6) produces new Bird's Nest position, and component in n Bird's Nest position vector is clustered according to Fuzzy C-Means Clustering Algorithm, Evaluated by being substituted into a corresponding upper Bird's Nest position vector for class, if the quality after replacing improves, by upper one The corresponding position in individual Bird's Nest position is replaced, if be deteriorated, keeps constant;
Step 2.3. is finally evaluated all Bird's Nest positions, keeps top-quality position, and performs step 2.1 successively With step 2.2.
2. a kind of cuckoo algorithm based on Fuzzy C-Means Clustering according to claim 1, it is characterised in that:Step 1 Described in the quality of evaluation bird egg refer to we assume that 1 cuckoo only produces a bird egg 1 time, and randomly chooses 1 Bird's Nest Place, every cuckoo bird egg represents new explanation, if new explanation is more excellent than old solution fitness, i.e. bird egg better quality then only will New explanation is remained, and final high-quality bird egg will be retained to the next generation.
3. a kind of cuckoo algorithm based on Fuzzy C-Means Clustering according to claim 1, it is characterised in that:Step 2 Described in error threshold value depend on test function in itself.
4. a kind of cuckoo algorithm based on Fuzzy C-Means Clustering according to claim 2, it is characterised in that:Described New explanation is after preference random walk plays a role, and the component with same nature is concentrated into a class in new explanation, respectively will afterwards Other components of each class and present age solution reassemble into an interim solution, and interim solution is evaluated.
5. a kind of cuckoo algorithm based on Fuzzy C-Means Clustering according to claim 4, it is characterised in that:Described The evaluation method evaluated solving temporarily uses greedy strategy method, i.e., can only improve the new explanation currently solved could be protected It is left to the next generation.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108901074A (en) * 2018-07-23 2018-11-27 华东交通大学 A kind of mobile subscriber's frequency spectrum distributing method based on cuckoo searching algorithm
CN109471363A (en) * 2018-12-28 2019-03-15 浙江大学 Industrial melt index soft measurement method based on aftereffect function and cuckoo search
CN109813264A (en) * 2019-02-21 2019-05-28 重庆潍柴发动机有限公司 The method and device of measuring result error assessment

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108901074A (en) * 2018-07-23 2018-11-27 华东交通大学 A kind of mobile subscriber's frequency spectrum distributing method based on cuckoo searching algorithm
CN108901074B (en) * 2018-07-23 2023-03-24 华东交通大学 Mobile user frequency spectrum allocation method based on cuckoo search algorithm
CN109471363A (en) * 2018-12-28 2019-03-15 浙江大学 Industrial melt index soft measurement method based on aftereffect function and cuckoo search
CN109471363B (en) * 2018-12-28 2020-08-04 浙江大学 Industrial melt index soft measurement method based on post-effect function and rhododendron search
CN109813264A (en) * 2019-02-21 2019-05-28 重庆潍柴发动机有限公司 The method and device of measuring result error assessment

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