CN106485314A - A kind of optimization method of the flower pollination algorithm based on adaptive Gauss variation - Google Patents

Abstract

The optimization method of algorithm the invention discloses a kind of flower based on adaptive Gauss variation is pollinated, first population is ranked up according to fitness value and is grouped, then update worst individual position in each packet, not only increase the local area deep-searching ability of algorithm and increase population diversity；Secondly, whether local optimum is absorbed in by Billboard dynamic monitoring algorithm, when being absorbed in, Gaussian mutation operation operator will be automatically introduced into, to global optimum's individual execution mutation operation, not only improve the ability that individuality jumps out local optimum, and strengthen population diversity, accelerate convergence rate.The inventive method has more preferable stability and reliability, faster convergence rate and higher low optimization accuracy.

Description

A kind of optimization method of the flower pollination algorithm based on adaptive Gauss variation

Technical field

The optimization method of algorithm the present invention relates to a kind of flower is pollinated, especially relate to a kind of based on adaptive Gauss variation The optimization method of flower pollination algorithm.

Background technology

In optimization problem, most crucial problem is to solve its globally optimal solution or optimal solution set in feasible zone, then from this A little optimal solutions or solution are focused to find out the optimal solution of problem.However as the expansion of problem scale, solve required time exponentially Increase again, or majorized function is required continuously can lead, therefore, the simply efficient optimized algorithm of exploitation is the pass of researchers The focus of note.It is to solve the simple and effective approach of optimization problem based on bionic colony intelligence optimized algorithm, swarm intelligence algorithm is In simulation biosphere, some behavior characteristicss of certain biology are used for solving the problems, such as the actual optimization in reality.

Flower pollination algorithm (Flower Pollination Algorithm, FPA) is a kind of overall situation Stochastic Optimization Algorithms. FPA assumes that every plant only opens a flower, and every flower only produces a pollen gamete, and every flower is the one of solving-optimizing problem Individual solution, controls the conversion between crossing pollination and self-pollination by probability P C.The main thought of this algorithm：Initialization kind first Group, then carries out adaptive value evaluation to population at individual, finds out the optimum individuality of adaptive value as current globally optimal solution, not finally Disconnected iteration execution crossing pollination and two operation operators of self-pollination, till meeting the condition of convergence.This algorithm adopts Lay to tie up (Levy) fly mechanics, preferably achieve freely changing of Local Search and global search by parameter PC, have stronger Global optimizing ability.This algorithm fusion advantage of cuckoo and Vespertilio algorithm (Bat Algorithm, BA), has ginseng simultaneously Number less, realize simple, the advantages of easily adjust, be therefore widely used in multi objective function optimization, production scheduling, text cluster etc. Multi-field.

But this algorithm is similar with other swarm intelligence algorithms (population, Vespertilio algorithm etc.), there is (1) local area deep-searching Ability, low optimization accuracy are low；(2) be easily absorbed in local optimum, late convergence slow the problems such as；(3) this algorithm is inapplicable simultaneously In higher-dimension complexity multi maximum problem.

Content of the invention

For the deficiencies in the prior art, it is an object of the invention to provide a kind of flower pollination based on adaptive Gauss variation The optimization method of algorithm, solution flower pollination algorithm local area deep-searching ability is weak, be easily absorbed in local optimum, late convergence Slow problem.

Technical solution of the present invention is as follows：A kind of optimization method of the flower pollination algorithm based on adaptive Gauss variation, according to Secondary comprise the following steps,

Step one, initialization basic parameter and population position, are NP including setting population scale, and maximum iteration time is iter_max, crossing pollination probability P_C, minimum convergence precision F_minAnd search space D；NP point is generated at random in D dimension space As initial populationWhereinT is current iteration number of times

Step 2, calculating ideal adaptation angle value, determine that current global optimum is individual, and record its positional information；

Step 3, judge whether object function restrains：If then going to step 11, otherwise go to step four；

If step 4 i ＜ NP, go to step five, otherwise t=t+1, go to step six；

Step 5, generate a random number rand [0,1] is upper, if rand is ＜ P_C, then update according to crossing pollination mode Xt i position simultaneously carries out process of crossing the border；Otherwise update X according to self-pollination mode^t _iPosition simultaneously carries out process of crossing the border, i=i+1, turns Step 4；

Step 6, all ideal adaptation angle value of calculating simultaneously carry out ascending order arrangement, are divided into m mould because of group, and will be currently optimum Individual fitness value and its spatial positional information recorded in Billboard；

Step 7, determine each mould because of optimum individual X in group_bWith worst individuality X_w；And update X_wPosition；When all moulds When all completing to update operation because of group, all individualities of mixing form new population；

Step 8, recalculate new population fitness value and determine current global optimum individuality X '_gIf, f (X '_g) ＜ f (X_g), then update the information in Billboard；

Step 9, judge whether to meet variation condition：If the fitness value f (x in Billboard_i) continuous Q generation do not change or | Variable quantity | ＜ μ, and iterationses ＞ Q-1, then to X_gCarry out Gaussian mutation, wherein Q, μ is predetermined threshold value；IfBetter than former X_g, then useReplace X_g, and update the information in Billboard；Otherwise, abandon the solution after variation；

If step 10 t ＜ iter_maxOr f (x_g) ＞ F_min, go to step three entrance next iterations；Otherwise go to step 11；

Step 11, output optimal value and its corresponding individual positional information.

In described step 2, calculate ideal adaptation angle value, determine that current global optimum individuality is according to the target letter selected Number calculates the adaptive value f (x of currently all population at individuals_i), and choose the minimum individuality of fitness value.

In described step 3, judge object function whether restrain be by the adaptive optimal control angle value of the population at individual calculating with The theoretially optimum value of object function is compared, if it is in range of error, object function is restrained, if not in range of error Interior, then object function is not restrained.

In described step 5, updating Xt i position carrying out process of crossing the border according to crossing pollination mode is to enter as follows OK：

For the position in t iteration for the pollen i, g^*For current global optimum position, γ is scale factor, and L (λ) is clothes From the step-length vector of Levy flight, work as L>When 0,

λ=3/2, Γ (λ) is standard gamma function, and s is moving step length,

It is zero that U obeys average, and standard deviation is δ²Gauss distribution, V obey standard normal distribution；

Update X according to self-pollination mode^t _iPosition carrying out process of crossing the border is to carry out as follows：

ε is that [0,1] is upper obeys equally distributed constant,WithFor the pollen of flowers different in same kind, 1≤j, k≤ NP and j ≠ k ≠ i.

In described step 6, be divided into m mould because group be by sequence after front m individuality be sequentially placed into the 1st, 2 ..., M-th mould because in group, then by m+1～2m individuality be sequentially placed into again the 1st, 2 ..., m-th mould because in group, class successively Push away, until being assigned.

In described step 6, described Billboard arranges t row, global optimum's individuality in the first behavior first time iterative process Fitness value and locus；The individual fitness value of global optimum and locus in second second of behavior iterative process； The individual fitness value of global optimum and locus in the t time iterative process of t behavior.

Described step 7 kind, worst individuality X_wThe more New Policy of position be：

D_j=rand × (X_b-X_w),

X_w'=X_w+D_j,||D_j||≤D_max,

D_jFor the displacement in j dimension, its value does not allow more than maximum moving step length D_max, rand is random on [0,1] Number, X_gIndividual, the X for global optimum_w' for update after individuality, execution update operation after, if fitness value f (X_w')≤f(X_w), Then use X_w' replace X_w；Otherwise use X_gReplace X_b, re-execute more New Policy；If f is (X_w) change not yet, then randomly generate an X_w' Replace X_w.

In described step 9, to X_gCarrying out Gaussian mutation is to carry out as follows

The new explanation producing for Gaussian mutation, α is the variable that successively decreases on [0,1], and N (0,1) obeys μ=0, δ²=1 mark Quasi- Gauss distribution.

The present invention is grouped to population first and is updated poor individual position in each packet, thus strengthening the office of individuality Portion's search capability simultaneously strengthens population diversity；Then whether local optimum is absorbed in by Billboard evaluation algorithm, if then carrying out Gaussian mutation operates, thus effectively improving algorithm to jump out the ability being absorbed in local, strengthening population diversity, accelerating algorithmic statement Speed.

The advantage of technical scheme provided by the present invention is：

1st, improve the local search ability of algorithm；

2nd, it is prevented effectively to a certain extent and be absorbed in local optimum；

3rd, strengthen population diversity, accelerate algorithm the convergence speed.

Brief description

Fig. 1 is the inventive method schematic flow sheet.

Fig. 2 is f₁Convergence curve (D=30).

Fig. 3 is f₂Convergence curve (D=50).

Fig. 4 is f₃Convergence curve (D=30).

Fig. 5 is f₄Convergence curve (D=50).

Fig. 6 is f₅Convergence curve (D=2).

Fig. 7 is f₆Convergence curve (D=50).

Fig. 8 is f₁Convergence curve on high-dimension function.

Fig. 9 is f₂Convergence curve on high-dimension function.

Figure 10 is f₃Convergence curve on high-dimension function.

Figure 11 is convergence curve on high-dimension function for the f4.

Specific embodiment

With reference to embodiment, the invention will be further described, but not as a limitation of the invention.

Incorporated by reference to Fig. 1, being embodied as of the optimization method of the flower pollination algorithm based on adaptive Gauss variation is so 's：

Step one, initialization basic parameter and population position, it is NP that initialization basic parameter includes arranging population scale, Big iterationses are itermax, crossing pollination probability P_C, minimum convergence precision F_minAnd search space D etc., initialize population Position：In feasible zone, (in D dimension space) generates NP point at random as initial populationWhereinT is current iteration number of times, and D is search space；

The object function that step 2, basis are selected calculates the adaptive value f (x of currently all population at individuals_i) (to be minimised as Example), and choose the minimum individuality of fitness value as current global optimum individuality, and record its corresponding spatial positional information；

Step 3, judge whether object function restrains, by the adaptive optimal control angle value of the population at individual calculating and target letter Number theoretially optimum value be compared, if its in range of error then it is assumed that object function convergence,

|f_min-F_min| ＜ Δ

Wherein, f_minFor obtained optimal value in experiment, F_minFor object function theoretially optimum value, Δ is range of error, if It is to go to step 11, otherwise go to step four；

If step 4 i ＜ NP, go to step five, otherwise t=t+1, go to step six；

Step 5, generate a random number rand [0,1] is upper, if rand is ＜ P_C, then update according to crossing pollination modePosition simultaneously carries out process of crossing the border,

For the position in t iteration for the pollen i, g^*For current global optimum position, γ is scale factor, for controlling Moving step length, L (λ) is the step-length vector obeying Levy flight, works as L>When 0, Lay dimension distribution computing formula is as follows：

λ=3/2, Γ (λ) is standard gamma function, and s is moving step length, and its value directly affects convergence, because This FPA adopts Man Teniya algorithm to produce most effective step-length s,

It is zero that U obeys average, and standard deviation is δ²Gauss distribution, V obey standard normal distribution；

Otherwise update according to self-pollination modePosition simultaneously carries out process of crossing the border,

ε is that [0,1] is upper obeys equally distributed constant,WithFor the pollen of flowers different in same kind, 1≤j, k≤ NP and j ≠ k ≠ i,

I=i+1, goes to step four；

Step 6, all ideal adaptation angle value of calculating simultaneously carry out ascending order arrangement, and the population after sequence is divided as follows It is fitted on m mould because in group, each mould is individual and meet relation NP=m × n because comprising n in group,

Wherein M^kRepresent k-th mould because of group, the front m individuality after will sorting be sequentially placed into the 1st, 2 ..., m-th Mould because in group, then by m+1～2m individuality be sequentially placed into again the 1st, 2 ..., m-th mould because in group, the like, directly To being assigned；

Determine current optimum individual and its fitness value, and its spatial positional information be recorded in Billboard.Billboard Introduce in order to evaluation algorithm whether is absorbed in local optimum, be mainly used in recording the fitness value of optimum individual and position letter Breath, it is as shown in the table for its structure：

Wherein, the individual fitness value of global optimum and locus in the first behavior first time iterative process；Second row For the individual fitness value of global optimum in second iterative process and locus；The overall situation in the t time iterative process of t behavior The fitness value of optimum individual and locus；Will record in each iterative process the individual fitness value of global optimum and Its corresponding positional information；

Step 7, determine each mould because optimum in group, worst individuality X_bAnd X_w；And update X_wPosition, when all moulds are because of group When all completing to update operation, all individual formation new populations of mixing, specifically include following steps：

Step 701, taking minimize as a example, each mould is optimum individual (i.e. first because of the minimum individuality of fitness value in group Individuality) use X_bRepresent, the maximum individuality of fitness value is that worst individual (being that last is individual) uses X_wRepresent；

To each mould because of individuality X worst in group in step 702, each iterative process_wPosition be updated, its more New Policy For：

D_j=rand × (X_b-X_w)

X_w'=X_w+D_j,||D_j||≤D_max

Wherein, D_jFor the displacement in j dimension, its value does not allow more than maximum moving step length D_max, rand is on [0,1] Random number, X_bAnd X_wIt is respectively mould because of individuality optimum and worst in group, X_gIndividual, the X for global optimum_w' it is individual after updating Body.

After step 703, execution update operation, if fitness value f (X_w')≤f(X_w), then use X_w' replace X_w；Otherwise use X_gGeneration For X_b, re-execute more New Policy；If f is (X_w) do not change yet or vary less, then randomly generate an X_w' replace X_w；When all When mould all completes to organize inner iteration successively because organizing, all individual formation new populations of mixing；

Step 8, recalculate the fitness value of new population according to object function, determine current global optimum individuality X '_g； The individual fitness value of current global optimum is compared with the optimal value of Billboard, if f is (X '_g) ＜ f (X_g), then update public Show the information in board；

Step 9, judge whether to meet variation condition：If the fitness value f (x in Billboard_i) continuous Q generation do not change or Vary less (| variable quantity | ＜ μ), and iterationses ＞ Q-1, then to X_gCarry out Gaussian mutation.IfBetter than former X_g, then useReplace X_g, and update the information in Billboard；Otherwise, abandon the solution after variation.Specifically：

Step 901, in the algorithm two threshold values Q of setting and μ, did not change when the continuous Q of the fitness value in Billboard generation Or during | variable quantity | ＜ μ, then it is absorbed in local optimum depending on this algorithm.Now, algorithm will be automatically introduced into Gaussian mutation strategy, that is, utilize Below equation is to current globally optimal solution X_gCarry out Gaussian mutation, make population at individual jump out local optimum, strengthen population various Property.

Wherein,The new explanation producing for Gaussian mutation, α is the variable that successively decreases on [0,1], and N (0,1) obeys μ=0, δ²= 1 standard gaussian distribution.

If the individuality after step 902 renewalBetter than former X_g, then useReplace X_g, all individual existLead Under towards optimal solution direction move.Otherwise, abandon the solution after variation.

If step 10 t ＜ iter_max||f(x_g) ＞ F_min, go to step three entrance next iterations；Otherwise go to step 11.

Step 11, output optimal value and its corresponding individual positional information.

Employ test function the effectiveness using Matlab R2012b verification algorithm of six standards, and with BA, mixed Leapfrog algorithm, FPA of conjunction is compared.Wherein f₁For unimodal, f₂～f₆For Solving Multimodal Function, test function is as follows：

Function is in x_iGlobal optimum min (f is obtained at=0₁(x))=0, wherein i=1,2 ..., n.

2)

Function is in x_iGlobal optimum min (f is obtained at=0₂(x))=0, wherein i=1,2 ..., n.

3)

Function is in x_iGlobal optimum min (f is obtained at=0₃(x))=0, wherein i=1,2 ..., n.

4)

Function is in x_iGlobal optimum min (f is obtained at=0₄(x))=0, wherein i=1,2 ..., n.

5)

Function is in x_iGlobal optimum min (f is obtained at=0₅(x))=- 1, wherein i=1,2.

6)

Function is in x_iGlobal optimum min (f is obtained at=0₆(x))=0, wherein i=1,2 ..., n.

Understand in conjunction with Fig. 2 to Fig. 7, for function f₁～f₆, the inventive method (IFPA) received at first with convergence rate the fastest Hold back theoretially optimum value, shuffled frog leaping algorithm (Shuffled Frog Leaping Algorithm, SFLA) takes second place, BA and FPA Convergence rate is the slowest even cannot to find theoretially optimum value.

Four kinds of algorithms optimizing Performance comparision under fixed number of iterations

As shown in Table 1：The optimal value of IFPA, meansigma methodss, worst-case value are respectively less than other three kinds of algorithms；Standard deviation is minimum, calculates Method performance is the most stable；Optimizing success rate highest.For function f₂～f₄, BA, FPA cannot find object function optimal solution, and IFPA Theoretially optimum value can be rapidly converged to.SFLA optimizing success rate is higher relative to BA, FPA, but is still below IFPA, and standard deviation is relatively Larger, be not as stable as IFPA.Under fixed number of iterations, compared to other three kinds of algorithms, improved IFPA has and receives faster Hold back speed and higher low optimization accuracy, and algorithm stability, robustness are preferable.

In order to verify the convergence of IFPA, first fixed function convergence precision, then respectively 50 times are carried out to four kinds of algorithms Independent experiment, experimental result is as shown in table 2.

The comparison of optimizing performance under fixed precision for the 2 four kinds of algorithms of table

As shown in Table 2, IFPA reaches the fixed precision set by each function with minimum convergence number of times；Convergence in mean number of times It is significantly less than other three kinds of algorithms, and restrain success rate highest.For function f₁, IFPA converges power ratio FPA height 73%；For function f₅, IFPA converges to optimal value in the 1st iteration；For function f₂～f₄, IFPA is respectively average 18.21st, converge to theoretially optimum value, for f 109.18,157.26 times₁And f₆, though BA and SFLA is restrained with 100% success rate To fixed precision, but it is minimum, convergence in mean algebraically is all higher than IFPA.As can be seen here, under fixing convergence precision, IFPA restrains Property is substantially better than other three kinds of algorithms, and convergence rate is improved significantly.

Table 3IFPA and the comparison of FPA Riming time of algorithm

As shown in Table 3：IFPA carries out to population being grouped, merges, is grouped, for f again₁～f₆, it is minimum, when averagely running Between more slightly longer than FPA but be more or less the same.

In order to verify effectiveness on high-dimensional nonlinear system for the IFPA, respectively in different dimensions, to f₁～f₄Surveyed Examination, result is as shown in Figs. 8 to 11, and when solving high-dimensional nonlinear system, convergence rate will not increase with dimension and fall into IFPA Enter " dimension disaster ".The low optimization accuracy in higher-dimension for the IFPA, is more or less the same with convergence rate compared with low-dimensional, by less shadow Ring.

Taking following object function (Solving Multimodal Function) as a example：

Wherein function is in x_iGlobal optimum min (f (x))=0, wherein i=1,2 ..., n is obtained at=0.

Initialization basic parameter：Feasibility for more comprehensive checking innovatory algorithm and effectiveness, will be with BA, SFLA, FPA Three kinds of algorithms are compared.In experiment, each parameter setting is as follows：The population scale NP=20 of all algorithms, maximum iteration time iter_max=2000；IFPA：P_C=0.8, F_min=min (f (x))=0, D=n, Δ=10^-3, Q=3, μ=10^-4, m=4, n =5；FPA:P_C=0.8；BA：A=0.25, r=0.5, α=0.95, γ=0.05；SFLA:M=4, n=5.

Initialization population position：Tie up in n and generate 20 points in search space at random as the position of initial population, 20 flowers The position of powder is as shown in the table, and makes t=0, i=1, and wherein t is current iteration number of times, and i is that i-th pollen is carrying out updating Operation.

According to stating the corresponding fitness value of object function f (x) 20 pollen of calculating, it is as shown in the table：

WillIt is ranked up, choose fitness value minimumPosition as global optimum position, and make

Whether evaluation algorithm restrains, when meeting formula below then it is assumed that function convergence is to optimal value.

Wherein,For global optimum during current t iteration, F_min=min (f (x))=0 is that object function is theoretical Optimal value, Δ=10^-3For range of error.

If i ＜ 20, when that is, epicycle iteration does not also complete, go to step five, proceed epicycle iteration；Otherwise, when i >=20 When, that is, 20 pollen all complete once to update operation, t=t+1, go to step six, enter next iteration.

In one random number rand of [0,1] upper generation, if rand ＜ 0.8, carry out crossing pollination, update by formula (2) Position simultaneously carries out process of crossing the border；If rand >=0.8, carry out self-pollination, update by formula (5)Position simultaneously carries out process of crossing the border.

According to stating the corresponding fitness value of object function f (x) 20 pollen of calculating, it is as shown in the table：

WillIt is ranked up by ascending order, after sorting, population assigns to m mould because of the front m in group, after will sorting by (6) Individuality be sequentially placed into the 1st, 2 ..., m-th mould because in group, then by m+1～2m individuality be sequentially placed into again the 1st, 2 Individual ..., m-th mould because in group, the like, until being assigned.After the completion of packet, each mould is respectively because of the individuality in group： 1、5、9、13、17；2、6、10、14、18；3、7、11、15、19；4、8、12、16、20.

Then the relevant information of first flower (global optimum's individuality) after sequence is stored in Billboard.

Determine each mould because of optimum in group, worst individuality X_bAnd X_w, that is, each mould because optimum in group, worst individual be respectively 1, 17；2、18；3、19；4、20；Then update each mould because of individuality X worst in group_wPosition, that is, respectively update the 17th, 18,19,20 The position of individual pollen.When all moulds all complete once to organize inner iteration because of group, all individual formation new populations of mixing.

Recalculate the fitness value of new population (20 individualities) according to object function f (x), and determine current global optimum Individual

The individual fitness value of current global optimum is compared with the optimal value of Billboard, ifThen more Information in new Billboard.

Do not change or | variable quantity | ＜ 10 when continuous 3 generations of the fitness value in Billboard^-4When, then it is absorbed in office depending on this algorithm Portion is optimum.Now, algorithm will be automatically introduced into Gaussian mutation strategy, that is, utilize formula (8) to current globally optimal solution X_gCarry out height This variation is so that population at individual has the ability jumping out local optimum, and strengthens population diversity.

If the individuality after updatingBetter than former X_g, then useReplace X_g, all individual existLeading under towards The direction of excellent solution is moved.Otherwise, abandon the solution after variation.

When iterationses t is less than set maximum iteration time 2000 in experiment, or in experiment object function is The figure of merit is more than set minimum convergence precision (f (x_g) ＞ 0) when, then carry out next iteration, re-start iterative.

Output optimal valueAndCorresponding positional information

Claims (8)

1. a kind of optimization method of the flower pollination algorithm based on adaptive Gauss variation is it is characterised in that include following successively Step,

Step one, initialization basic parameter and population position, are NP including setting population scale, and maximum iteration time is iter_max, crossing pollination probability P_C, minimum convergence precision F_minAnd search space D；NP point is generated at random in D dimension space As initial population P (t)={ X^t _i, whereinT is current iteration time Number

Step 2, calculating ideal adaptation angle value, determine that current global optimum is individual, and record its positional information；

Step 3, judge whether object function restrains：If then going to step 11, otherwise go to step four；

If step 4 i ＜ NP, go to step five, otherwise t=t+1, go to step six；

Step 5, generate a random number rand [0,1] is upper, if rand is ＜ P_C, then update Xti position according to crossing pollination mode Put and carry out process of crossing the border；Otherwise update X according to self-pollination mode^t _iPosition simultaneously carries out process of crossing the border, i=i+1, goes to step Four；

Step 6, calculate all ideal adaptation angle value and simultaneously carry out ascending order arrangement, be divided into m mould because of group, and by current optimum individual Fitness value and its spatial positional information recorded in Billboard；

Step 7, determine each mould because of optimum individual X in group_bWith worst individuality X_w；And update X_wPosition；When all moulds are because of group When all completing to update operation, all individual formation new populations of mixing；

Step 8, recalculate new population fitness value and determine current global optimum individuality X '_gIf, f (X '_g) ＜ f (X_g), then Update the information in Billboard；

Step 9, judge whether to meet variation condition：If the fitness value f (x in Billboard_i) continuous Q generation do not change or | change Amount | ＜ μ, and iterationses ＞ Q-1, then to X_gCarry out Gaussian mutation, wherein Q, μ is predetermined threshold value；IfBetter than former X_g, then WithReplace X_g, and update the information in Billboard；Otherwise, abandon the solution after variation；

If step 10 t ＜ iter_maxOr f (x_g) ＞ F_min, go to step three entrance next iterations；Otherwise go to step 11；

Step 11, output optimal value and its corresponding individual positional information.

2. the optimization method of the flower pollination algorithm based on adaptive Gauss variation according to claim 1, its feature exists In, in described step 2, calculating ideal adaptation angle value, determine that current global optimum individuality is to calculate according to the object function selected The currently adaptive value f (x of all population at individuals_i), and choose the minimum individuality of fitness value.

3. the optimization method of the flower pollination algorithm based on adaptive Gauss variation according to claim 1, its feature exists In, in described step 3, judging whether object function restrains is by the adaptive optimal control angle value of the population at individual calculating and target The theoretially optimum value of function is compared, if it is in range of error, object function is restrained, if not in range of error, Object function is not restrained.

4. the optimization method of the flower pollination algorithm based on adaptive Gauss variation according to claim 1, its feature exists In, in described step 5, updating Xt i position carrying out process of crossing the border according to crossing pollination mode is to carry out as follows：

$x_i^{t+1}=x_i^t+\mathrm{\γ}L\left(\mathrm{\λ}\right)(g^{*}-x_i^t),$

For the position in t iteration for the pollen i, g^*For current global optimum position, γ is scale factor, and L (λ) is to obey The step-length vector of Levy flight, works as L>When 0,

$L~\frac{\mathrm{\λ}\mathrm{\Γ}\left(\mathrm{\λ}\right)\sin (\mathrm{\π}\mathrm{\λ}/2)}{\mathrm{\π}}\frac{1}{s^{1+\mathrm{\λ}}},(s>>s_0>0)$

λ=3/2, Γ (λ) is standard gamma function, and s is moving step length,

$s=\frac{U}{|V{|}^{1/\mathrm{\λ}}},U~N(0,{\mathrm{\σ}}^2),V~N(0,1),$

It is zero that U obeys average, and standard deviation is δ²Gauss distribution, V obey standard normal distribution；

Update X according to self-pollination mode^t _iPosition carrying out process of crossing the border is to carry out as follows：

$x_i^{t+1}=x_i^t+\mathrm{\ϵ}(x_j^t-x_k^t),$

ε is that [0,1] is upper obeys equally distributed constant,WithFor the pollen of flowers different in same kind, 1≤j, k≤NP and j≠k≠i.

5. the optimization method of the flower pollination algorithm based on adaptive Gauss variation according to claim 1, its feature exists In, in described step 6, be divided into m mould because group be by sequence after front m individuality be sequentially placed into the 1st, 2 ..., m-th Mould because in group, then by m+1～2m individuality be sequentially placed into again the 1st, 2 ..., m-th mould because in group, the like, directly To being assigned.

6. the optimization method of the flower pollination algorithm based on adaptive Gauss variation according to claim 1, its feature exists In in described step 6, described Billboard arranges t row, the individual adaptation of global optimum in the first behavior first time iterative process Angle value and locus；The individual fitness value of global optimum and locus in second second of behavior iterative process；T row For the individual fitness value of global optimum in the t time iterative process and locus.

7. the optimization method of the flower pollination algorithm based on adaptive Gauss variation according to claim 1, its feature exists In, described step 7 kind, worst individuality X_wThe more New Policy of position be：

D_j=rand × (X_b-X_w),

X_w'=X_w+D_j,||D_j||≤D_max,

D_jFor the displacement in j dimension, its value does not allow more than maximum moving step length D_max, rand is the random number on [0,1], X_g Individual, the X for global optimum_w' for update after individuality, execution update operation after, if fitness value f (X_w')≤f(X_w), then use X_w' replace X_w；Otherwise use X_gReplace X_b, re-execute more New Policy；If f is (X_w) change not yet, then randomly generate an X_w' replace X_w.

8. the optimization method of the flower pollination algorithm based on adaptive Gauss variation according to claim 1, its feature exists In in described step 9, to X_gCarrying out Gaussian mutation is to carry out as follows

$X_g^{new}=X_g+\mathrm{\α}\×X_g\×N(0,1),$

The new explanation producing for Gaussian mutation, α is the variable that successively decreases on [0,1], and N (0,1) obeys μ=0, δ²=1 standard is high This distribution.