CN105260772A - Multi-strategy-based staged population global optimization method - Google Patents

Abstract

The invention relates to a multi-strategy-based staged population global optimization method. The method includes the following steps that: the average distance between individuals in an initial population is calculated, and the whole evolution process of the algorithm is divided into three stages according to the average distance, and a plurality of different mutation strategies are set for each stage; a stage where the algorithm is located is judged in the evolution process according to the crowdedness degree of the individuals of the current population, namely, the average distance between the individuals, and therefore, different mutation strategies are randomly selected out to generate new individuals; and the strategies are adaptively adjusted according to the change rate design parameter of the average distance. The global detection ability and local search ability of the algorithm are balanced through the above design, so that the performance of the algorithm can be improved.

Description

A kind of based on shifty interim colony global optimization method

Technical field

The present invention relates to a kind of intelligent optimization, computer application field, in particular, a kind of based on shifty interim colony global optimization method.

Background technology

Some Global Optimal Problems are often run in the field such as economy, Science and engineering, in global optimization, algorithm needs from numerous locally optimal solutions, find out a globally optimal solution, but, may local optimum be absorbed in exactly for the problem that these global optimization approaches are maximum and cannot globally optimal solution be tried to achieve.Increasingly sophisticated along with engineering optimization, the condition of the objective function of optimization problem also becomes and becomes increasingly complex, normally discontinuous, non-differentiability, nonlinearity, does not have clear and definite analytical expression, and has multiple peak value, multiobject feature.Therefore, traditional optimization method (method as based on gradient) cannot be used for solving challenge.

Evolution algorithm carrys out Solve problems by simulation biological evolution process with machine-processed.Typical evolution algorithm comprises differential evolution algorithm (DE), genetic algorithm (GA), evolution strategy (ES) and evolutional programming (EP) etc., compared with classic method, evolution algorithm is by kind of a group hunting globally optimal solution, and the search behavior adding colony during evolution avoids algorithm to be absorbed in local optimum, thus improve the probability solving globally optimal solution.In addition, evolution algorithm does not need the derivative information of Solve problems, and strong robustness, is therefore widely used in solving of various problem.

The swarm intelligence that DE algorithm is produced by the cooperation and competition in colony between individuality instructs Optimizing Search, have algorithm general, do not rely on problem information, principle is simple, be easy to realize, memory individual optimal solution and population internal information is shared and the feature such as stronger global convergence ability.Therefore, DE algorithm has shown the advantage of its uniqueness in the widespread use in the fields such as electric system, communication, chemical industry, optics and mechanical engineering, but also exposes some weakness in Theory and applications.One of them weakness is exactly, and for a specific problem, how from numerous Mutation Strategies, to choose a most suitable strategy.In DE algorithm, each Mutation Strategy has different characteristics, and such as, some Mutation Strategy overall situation detectivity is comparatively strong, but local search ability is more weak, thus causes algorithm late convergence slower; Some Mutation Strategy overall situation detectivity is more weak, and local search ability is comparatively strong, but easily causes algorithm to be absorbed in local optimum, and occurs Premature Convergence, and therefore, the selection of Mutation Strategy directly affects the performance of algorithm.

Select difficult problem for DE algorithm Mutation Strategy, many scholars propose some strategies in succession.The people such as Xie, based on each Mutation Strategy success ratio in earlier stage, utilize the weight of each Mutation Strategy of the adaptive renewal of neural network; The people such as Zamuda, by arranging a fixing select probability to each Mutation Strategy, then utilize a stray parameter to decide to select which Mutation Strategy; The people such as Qin are provided with multiple Mutation Strategy in DE algorithm, then dynamically update the selected probability of each strategy according to each strategy success ratio in earlier stage.The people such as Wang arrange a group policy pond in the algorithm, then generate new individuality by each strategy competition.These methods achieve certain effect, are so for some extensive problems, and the selection of strategy is still a difficult problem.

Therefore, the existing global optimization method based on colony's algorithm also exists defect in Mutation Strategy selection, needs to improve.

Summary of the invention

In order to overcome the existing deficiency of global optimization method in Mutation Strategy selection based on colony's algorithm, whole evolutionary process is divided into three phases according to the mean distance change between individuality each in population by the present invention, multiple Mutation Strategy is arranged to each stage, thus propose a kind of effective avoidance strategy select improper and affect algorithm performance, promote Optimal performance based on shifty interim colony global optimization method.

The technical solution adopted for the present invention to solve the technical problems is:

A kind of based on shifty interim colony global optimization method, described optimization method comprises the following steps:

1) initialization: population scale N is set _p, initial crossover probability C _r, initial gain constant F;

2) stochastic generation initial population P={x ^{1, g}, x ^{2, g}..., x ^{np, g}, and calculate the target function value of each individuality, wherein, g is evolutionary generation, x ^i,g, i=1,2 ..., Np represents that g is for the individuality of i-th in population, if g=0, then represents initial population;

3) the mean distance d in initial population between each individuality is calculated according to formula (1) _initial;

$d_{initial}=\left(\underset{i=1}{\overset{N_p}{\Σ}}\underset{k=i+1}{\overset{N_P}{\Σ}}\sqrt{\underset{j=1}{\overset{N}{\Σ}}{\left(x_j^{i,g}-x_j^{k,g}\right)}^2}\right)/\left(N_p\right(N_p-1)/2)---\left(1\right)$

Wherein, represent that g is in population iindividual x ^i,gjth dimension element, represent that g is in population kindividual x ^k,gjth dimension element, N is problem dimension, N _pfor population scale;

4) current g is calculated for the mean distance between individuality each in population according to formula (1)

5) judge the stage residing for evolutionary process, each individual Stochastic choice Mutation Strategy in population made a variation:

5.1) if then algorithm is in the first stage, makes a variation according to formula (2):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{a,g}+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{b,g}-x_j^{c,g})+F_i^g\·(x_j^{d,g}-x_j^{e,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{a,g}-x_j^{i,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& otherwise\end{array}\right.---\left(2\right)$

5.2) if then algorithm is in subordinate phase, makes a variation according to formula (3):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{pbest,g}+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{pbest,g}-x_j^{a,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{pbest,g}-x_j^{i,g})+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& otherwise\end{array}\right.---\left(3\right)$

5.3) except 5.1) and 5.2) except situation, then algorithm is in the phase III, then make a variation according to formula (4):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{best,g}+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{best,g}-x_j^{a,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{best,g}-x_j^{i,g})+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& otherwise\end{array}\right.---\left(4\right)$

In situation 5.1) ~ 5.3) in, j=1,2 ..., N, N are problem dimension, and g is evolutionary generation, and randn (1,3) represents stochastic generation integer between interval [1,3], a, b, c, d, e ∈ 1,2 ..., N _p, a ≠ b ≠ c ≠ d ≠ e ≠ i, i is the index of current goal individuality, be the jth dimension element of g for the variation individuality of i-th target individual in population, be respectively the jth dimension element of g for a, b, c, d, e individuality in population, for the jth dimension element of the optimum individual in 0.5NP*randb (0, the 1) individuality of random selecting, randb (0,1) represents the random decimal produced between 0 to 1, for current g is for the jth dimension element of the optimum individual in population, F _i ^grepresent i-th individual gain constant in g generation, represent that average is standard deviation is the normal distribution random number of 0.1, wherein calculate according to formula (5):

${\mathrm{\μ}}_F^g={\mathrm{\μ}}_F^{g-1}\·c+(1-c)\·S_F^{g-1},g>1---\left(5\right)$

Wherein, during g=0, represent all in g-1 generation and successfully can enter individual F of future generation _i ^g-1mean value, represent the normal distribution average in g-1 generation, c is the rate of change of distance, calculates according to formula (6):

$c=\frac{\left|d_{ave}^g-d_{ave}^{g-1}\right|}{d_{ave}^{g-1}},g>1---\left(6\right)$

Wherein, during g=0, c=0.1, represent that g-1 is for the mean distance between individuality each in population;

6) according to formula (7), intersection is carried out to each variation individuality and generate new individual trial ^i,g:

${\mathrm{trial}}_j^{i,g}=\left\{\begin{array}{cc}{v}_j^{i,g}& \begin{array}{ccc}if\left(randb\right(0,1)\≤C_{Ri}^g& or& j=rnbr\left(j\right)\end{array}\\ x_j^{i,g}& otherwise\end{array}\right.---\left(7\right)$

Wherein, j=1,2 ..., N, represent that g is for new individual trial corresponding to i-th target individual in population ^i,gjth dimension element, randb (0,1) is expressed as the random decimal produced between 0 to 1, and rnbr (j) represents the random integer produced between 1 to N, represent i-th individual crossover probability in g generation, represent with for average, the normal distribution random number being error with 0.1, wherein calculate according to formula (8):

${\mathrm{\μ}}_{C_R}^g={\mathrm{\μ}}_{C_R}^{g-1}\·c+(1-c)\·S_{C_R}^{g-1}---\left(8\right)$

Wherein, during g=0, represent in g-1 generation all can successfully enter of future generation individual mean value, distance standardized rate c calculates according to formula (6), represent g-1 generation normal distribution average;

7) according to formula (9), population recruitment is carried out to each new individuality:

$x^{i,g+1}=\left\{\begin{array}{cc}{\mathrm{trial}}^{i,g},& iff\left({\mathrm{trial}}^{i,g}\right)\≤f\left(x^{i,g}\right)\\ x^{i,g},& otherwise\end{array}\right.---\left(9\right)$

Wherein, ${\mathrm{trial}}^{i,g}=({\mathrm{trial}}_1^{i,g},{\mathrm{trial}}_2^{i,g},...,{\mathrm{trial}}_N^{i,g}),x^{i,g+1}=(x_1^{i,g+1},x_2^{i,g+1},...,x_N^{i,g+1}),x^{i,g}=$ $(x_1^{i,g},x_2^{i,g},...,x_N^{i,g}),$ Formula (9) shows, if new individuality is better than target individual, then and new individual replacement target individual, otherwise keep target individual constant;

8) judge whether to meet end condition, if met, then saving result exiting, otherwise return step 4).

Further, described step 8) in, end condition is function evaluates number of times.Certainly, also can be other end conditions.

Technical conceive of the present invention is: first, calculates the mean distance between each individuality in initial population, and according to initial mean distance, the whole evolutionary process of algorithm is divided into three phases, and arranges multiple different Mutation Strategy to each stage; Then, during evolution according to the degree of crowding of current population at individual, the stage residing for mean distance evaluation algorithm namely between each individuality, thus the different Mutation Strategy of random selecting produces new individuality; Secondly, according to the rate of change design parameter adaptive re-configuration police of mean distance; By overall detectivity and the local search ability of above design balance algorithm, to improve the performance of algorithm.

Beneficial effect of the present invention shows: carry out the stage residing for evaluation algorithm according to the mean distance of individuality, and multiple suitable Mutation Strategy is set in each stage, thus the Mutation Strategy that Stochastic choice is different in each iteration in each stage produces new individuality, avoidance strategy is selected improper and affects the performance of algorithm, effectively achieves algorithm from the overall situation simultaneously and detects seamlessly transitting of Local Search; In addition, according to mean distance rate of change design parameter adaptation mechanism, improve the performance of algorithm further.

Accompanying drawing explanation

Fig. 1 is the basic flow sheet based on shifty interim colony global optimization method.

Fig. 2 is that how tactful interim colony global optimization method is to convergence in mean curve map during 30 dimension Rosenbrock Optimization Solution.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

See figures.1.and.2, a kind of based on shifty interim colony global optimization method, comprise the following steps:

1) initialization: population scale N is set _p, initial crossover probability C _r, initial gain constant F;

2) stochastic generation initial population P={x ^{1, g}, x ^{2, g}..., x ^{np, g}, and calculate the target function value of each individuality, wherein, g is evolutionary generation, x ^i,g, i=1,2 ..., Np represents that g is for the individuality of i-th in population, if g=0, then represents initial population;

3) the mean distance d in initial population between each individuality is calculated according to formula (1) _initial;

$d_{initial}=\left(\underset{i=1}{\overset{N_p}{\Σ}}\underset{k=i+1}{\overset{N_P}{\Σ}}\sqrt{\underset{j=1}{\overset{N}{\Σ}}{\left(x_j^{i,g}-x_j^{k,g}\right)}^2}\right)/\left(N_p\right(N_p-1)/2)---\left(1\right)$

Wherein, represent that g is in population iindividual x ^i,gjth dimension element, represent that g is in population kindividual x ^k,gjth dimension element, N is problem dimension, N _pfor population scale;

4) current g is calculated for the mean distance between individuality each in population according to formula (1)

5) judge the stage residing for evolutionary process, each individual Stochastic choice Mutation Strategy in population made a variation:

5.1) if then algorithm is in the first stage, makes a variation according to formula (2):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{a,g}+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{b,g}-x_j^{c,g})+F_i^g\·(x_j^{d,g}-x_j^{e,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{a,g}-x_j^{i,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& otherwise\end{array}\right.---\left(2\right)$

5.2) if then algorithm is in subordinate phase, makes a variation according to formula (3):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{pbest,g}+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{pbest,g}-x_j^{a,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{pbest,g}-x_j^{i,g})+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& otherwise\end{array}\right.---\left(3\right)$

5.3) except 5.1) and 5.2) except situation, then algorithm is in the phase III, then carry out according to formula (4)

Variation:

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{best,g}+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{best,g}-x_j^{a,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{best,g}-x_j^{i,g})+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& otherwise\end{array}\right.---\left(4\right)$

In situation 5.1) ~ 5.3) in, j=1,2 ..., N, N are problem dimension, and g is evolutionary generation, and randn (1,3) represents stochastic generation integer between interval [1,3], a, b, c, d, e ∈ 1,2 ..., N _p, a ≠ b ≠ c ≠ d ≠ e ≠ i, i is the index of current goal individuality, be the jth dimension element of g for the variation individuality of i-th target individual in population, be respectively the jth dimension element of g for a, b, c, d, e individuality in population, for the jth dimension element of the optimum individual in 0.5NP*randb (0, the 1) individuality of random selecting, randb (0,1) represents the random decimal produced between 0 to 1, for current g is for the jth dimension element of the optimum individual in population, F _i ^grepresent i-th individual gain constant in g generation, represent that average is standard deviation is the normal distribution random number of 0.1, wherein calculate according to formula (5):

${\mathrm{\μ}}_F^g={\mathrm{\μ}}_F^{g-1}\·c+(1-c)\·S_F^{g-1},g>1---\left(5\right)$

Wherein, during g=0, represent all in g-1 generation and successfully can enter individual F of future generation _i ^g-1mean value, represent the normal distribution average in g-1 generation, c is the rate of change of distance, calculates according to formula (6):

$c=\frac{\left|d_{ave}^g-d_{ave}^{g-1}\right|}{d_{ave}^{g-1}},g>1---\left(6\right)$

Wherein, during g=0, c=0.1, represent that g-1 is for the mean distance between individuality each in population;

6) according to formula (7), intersection is carried out to each variation individuality and generate new individual trial ^i,g:

${\mathrm{trial}}_j^{i,g}=\left\{\begin{array}{cc}{v}_j^{i,g}& \begin{array}{ccc}if\left(randb\right(0,1)\≤C_{Ri}^g& or& j=rnbr\left(j\right)\end{array}\\ x_j^{i,g}& otherwise\end{array}\right.---\left(7\right)$

Wherein, j=1,2 ..., N, represent that g is for new individual trial corresponding to i-th target individual in population ^i,gjth dimension element, randb (0,1) is expressed as the random decimal produced between 0 to 1, and rnbr (j) represents the random integer produced between 1 to N, represent i-th individual crossover probability in g generation, represent with for average, the normal distribution random number being error with 0.1, wherein calculate according to formula (8):

${\mathrm{\μ}}_{C_R}^g={\mathrm{\μ}}_{C_R}^{g-1}\·c+(1-c)\·S_{C_R}^{g-1}---\left(8\right)$

Wherein, during g=0, represent in g-1 generation all can successfully enter of future generation individual mean value, distance standardized rate c can calculate according to formula (6), represent g-1 generation normal distribution average;

7) according to formula (9), population recruitment is carried out to each new individuality:

$x^{i,g+1}=\left\{\begin{array}{cc}{\mathrm{trial}}^{i,g},& iff\left({\mathrm{trial}}^{i,g}\right)\≤f\left(x^{i,g}\right)\\ x^{i,g},& otherwise\end{array}\right.---\left(9\right)$

Wherein, ${\mathrm{trial}}^{i,g}=({\mathrm{trial}}_1^{i,g},{\mathrm{trial}}_2^{i,g},...,{\mathrm{trial}}_N^{i,g}),x^{i,g+1}=(x_1^{i,g+1},x_2^{i,g+1},...,x_N^{i,g+1}),x^{i,g}=$ $(x_1^{i,g},x_2^{i,g},...,x_N^{i,g}),$ Formula (9) shows, if new individuality is better than target individual, then and new individual replacement target individual, otherwise keep target individual constant;

8) judge whether to meet end condition, if met, then saving result exiting, otherwise return step 4).

Further, described step 8) in, end condition is function evaluates number of times.Certainly, also can be other end conditions.

The present embodiment is with 30 of classics dimension Rosenbrock functions for embodiment, and one, based on shifty interim colony global optimization method, wherein comprises following steps:

1) initialization: population scale N is set _p=100, initial crossover probability C _r=0.5, initial gain constant F=0.5;

2) stochastic generation initial population P={x ^{1, g}, x ^{2, g}..., x ^{np, g}, and calculate the target function value of each individuality, wherein, g is evolutionary generation, x ^i,g, i=1,2 ..., Np represents that g is for the individuality of i-th in population, if g=0, then represents initial population;

3) the mean distance d in initial population between each individuality is calculated according to formula (1) _initial;

$d_{initial}=\left(\underset{i=1}{\overset{N_p}{\Σ}}\underset{k=i+1}{\overset{N_P}{\Σ}}\sqrt{\underset{j=1}{\overset{N}{\Σ}}{\left(x_j^{i,g}-x_j^{k,g}\right)}^2}\right)/\left(N_p\right(N_p-1)/2)---\left(1\right)$

Wherein, represent that g is in population iindividual x ^i,gjth dimension element, represent that g is in population kindividual x ^k,gjth dimension element, N is problem dimension, N _pfor population scale;

4) current g is calculated for the mean distance between individuality each in population according to formula (1)

5) judge the stage residing for evolutionary process, each individual Stochastic choice Mutation Strategy in population made a variation:

5.1) if then algorithm is in the first stage, makes a variation according to formula (2):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{a,g}+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{b,g}-x_j^{c,g})+F_i^g\·(x_j^{d,g}-x_j^{e,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{a,g}-x_j^{i,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& otherwise\end{array}\right.---\left(2\right)$

5.2) if then algorithm is in subordinate phase, makes a variation according to formula (3):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{pbest,g}+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{pbest,g}-x_j^{a,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{pbest,g}-x_j^{i,g})+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& otherwise\end{array}\right.---\left(3\right)$

5.3) except 5.1) and 5.2) except situation, then algorithm is in the phase III, then make a variation according to formula (4):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{best,g}+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{best,g}-x_j^{a,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{best,g}-x_j^{i,g})+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& otherwise\end{array}\right.---\left(4\right)$

In situation 5.1) ~ 5.3) in, j=1,2 ..., N, N are problem dimension, and g is evolutionary generation, and randn (1,3) represents stochastic generation integer between interval [1,3], a, b, c, d, e ∈ 1,2 ..., N _p, a ≠ b ≠ c ≠ d ≠ e ≠ i, i is the index of current goal individuality, be the jth dimension element of g for the variation individuality of i-th target individual in population, be respectively the jth dimension element of g for a, b, c, d, e individuality in population, for the jth dimension element of the optimum individual in 0.5NP*randb (0, the 1) individuality of random selecting, randb (0,1) represents the random decimal produced between 0 to 1, for current g is for the jth dimension element of the optimum individual in population, F _i ^grepresent i-th individual gain constant in g generation, represent that average is standard deviation is the normal distribution random number of 0.1, wherein calculate according to formula (5):

${\mathrm{\μ}}_F^g={\mathrm{\μ}}_F^{g-1}\·c+(1-c)\·S_F^{g-1},g>1---\left(5\right)$

Wherein, during g=0, represent all in g-1 generation and successfully can enter individual F of future generation _i ^g-1mean value, represent the normal distribution average in g-1 generation, c is the rate of change of distance, calculates according to formula (6):

$c=\frac{\left|d_{ave}^g-d_{ave}^{g-1}\right|}{d_{ave}^{g-1}},g>1---\left(6\right)$

Wherein, during g=0, c=0.1, represent that g-1 is for the mean distance between individuality each in population;

6) according to formula (7), intersection is carried out to each variation individuality and generate new individual trial ^i,g:

${\mathrm{trial}}_j^{i,g}=\left\{\begin{array}{cc}{v}_j^{i,g}& \begin{array}{ccc}if\left(randb\right(0,1)\≤C_{Ri}^g& or& j=rnbr\left(j\right)\end{array}\\ x_j^{i,g}& otherwise\end{array}\right.---\left(7\right)$

Wherein, j=1,2 ..., N, represent that g is for new individual trial corresponding to i-th target individual in population ^i,gjth dimension element, randb (0,1) is expressed as the random decimal produced between 0 to 1, and rnbr (j) represents the random integer produced between 1 to N, represent i-th individual crossover probability in g generation, represent with for average, the normal distribution random number being error with 0.1, wherein can calculate according to formula (8):

${\mathrm{\μ}}_{C_R}^g={\mathrm{\μ}}_{C_R}^{g-1}\·c+(1-c)\·S_{C_R}^{g-1}---\left(8\right)$

Wherein, during g=0, represent in g-1 generation all can successfully enter of future generation individual mean value, distance standardized rate c can calculate according to formula (6), represent g-1 generation normal distribution average;

7) according to formula (9), population recruitment is carried out to each new individuality:

$x^{i,g+1}=\left\{\begin{array}{cc}{\mathrm{trial}}^{i,g},& iff\left({\mathrm{trial}}^{i,g}\right)\≤f\left(x^{i,g}\right)\\ x^{i,g},& otherwise\end{array}\right.---\left(9\right)$

Wherein, ${\mathrm{trial}}^{i,g}=({\mathrm{trial}}_1^{i,g},{\mathrm{trial}}_2^{i,g},...,{\mathrm{trial}}_N^{i,g}),x^{i,g+1}=(x_1^{i,g+1},x_2^{i,g+1},...,x_N^{i,g+1}),x^{i,g}=$ $(x_1^{i,g},x_2^{i,g},...,x_N^{i,g}),$ Formula (9) shows, if new individuality is better than target individual, then and new individual replacement target individual, otherwise keep target individual constant;

8) judge that objective function is evaluated number of times and whether reached 150000, if reached, then saving result exiting, otherwise return step 4).

With 30 dimension Rosenbrock functions for embodiment, the average success rate of 30 independent operatings is 100% (being successfully solve when the degree of accuracy of the optimum solution that regulation algorithm finds in 150000 objective function evaluation number of times is 0.00001), the mean value of the solution of trying to achieve in 300000 function evaluates number of times is 2.97E-12, and standard deviation is 6.96E-12.

What more than set forth is the excellent effect of optimization that an embodiment that the present invention provides shows, obvious the present invention is not only applicable to above-described embodiment, and the every field that can be applied in Practical Project is (as protein structure prediction, electric system, the optimization problems such as path planning), simultaneously do not depart from essence spirit of the present invention and do not exceed content involved by flesh and blood of the present invention prerequisite under can do many variations to it and implemented.

Claims (2)

1., based on a shifty interim colony global optimization method, it is characterized in that: described optimization method comprises the following steps:

1) initialization: population scale N is set _p, initial crossover probability C _r, initial gain constant F;

2) stochastic generation initial population P={x ^{1, g}, x ^{2, g}..., x ^{np, g}, and calculate the target function value of each individuality, wherein, g is evolutionary generation, x ^i,g, i=1,2 ..., Np represents that g is for the individuality of i-th in population, if g=0, then represents initial population;

3) the mean distance d in initial population between each individuality is calculated according to formula (1) _initial;

$d_{initial}=\left(\underset{i=1}{\overset{N_p}{\Σ}}\underset{k=i+1}{\overset{N_P}{\Σ}}\sqrt{\underset{j=1}{\overset{N}{\Σ}}{(x_j^{i,g}-x_j^{k,g})}^2}\right)/\left(N_p\right(N_p-1)/2)---\left(1\right)$

Wherein, represent that g is in population iindividual x ^i,gjth dimension element, represent that g is in population kindividual x ^{k, g}jth dimension element, N is problem dimension, N _pfor population scale;

4) current g is calculated for the mean distance between individuality each in population according to formula (1)

5) judge the stage residing for evolutionary process, each individual Stochastic choice Mutation Strategy in population made a variation:

5.1) if then algorithm is in the first stage, makes a variation according to formula (2):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{a,g}+F_i^g\·\left(x_j^{b,g}-x_j^{c,g}\right),& ifrandn\left(1,3\right)=1\\ x_j^{a,g}+F_i^g\·\left(x_j^{b,g}-x_j^{c,g}\right)+F_i^g\·\left(x_j^{d,g}-x_j^{e,g}\right),& ifrandn\left(1,3\right)=2\\ x_j^{i,g}+F_i^g\·\left(x_j^{a,g}-x_j^{i,g}\right)+F_i^g\·\left(x_j^{b,g}-x_j^{c,g}\right),& otherwise\end{array}\right.---\left(2\right)$

5.2) if then algorithm is in subordinate phase, makes a variation according to formula (3):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{pbest,g}+F_i^g\·\left(x_j^{a,g}-x_j^{b,g}\right),& ifrandn\left(1,3\right)=1\\ x_j^{a,g}+F_i^g\·\left(x_j^{pbest,g}-x_j^{a,g}\right)+F_i^g\·\left(x_j^{b,g}-x_j^{c,g}\right),& ifrandn\left(1,3\right)=2\\ x_j^{i,g}+F_i^g\·\left(x_j^{pbest,g}-x_j^{i,g}\right)+F_i^g\·\left(x_j^{a,g}-x_j^{b,g}\right),& otherwise\end{array}\right.---\left(3\right)$

5.3) except 5.1) and 5.2) except situation, then algorithm is in the phase III, then make a variation according to formula (4):

$v_j^{i,g}=\left\{\begin{array}{cc}{x}_j^{best,g}+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& ifrandn(1,3)=1\\ x_j^{a,g}+F_i^g\·(x_j^{best,g}-x_j^{a,g})+F_i^g\·(x_j^{b,g}-x_j^{c,g}),& ifrandn(1,3)=2\\ x_j^{i,g}+F_i^g\·(x_j^{best,g}-x_j^{i,g})+F_i^g\·(x_j^{a,g}-x_j^{b,g}),& otherwise\end{array}\right.---\left(4\right)$

In situation 5.1) ~ 5.3) in, j=1,2 ..., N, N are problem dimension, and g is evolutionary generation, and randn (1,3) represents stochastic generation integer between interval [1,3], a, b, c, d, e ∈ 1,2 ..., N _p, a ≠ b ≠ c ≠ d ≠ e ≠ i, i is the index of current goal individuality, be the jth dimension element of g for the variation individuality of i-th target individual in population, be respectively the jth dimension element of g for a, b, c, d, e individuality in population, for the jth dimension element of the optimum individual in 0.5NP*randb (0, the 1) individuality of random selecting, randb (0,1) represents the random decimal produced between 0 to 1, for current g is for the jth dimension element of the optimum individual in population, represent i-th individual gain constant in g generation, represent that average is standard deviation is the normal distribution random number of 0.1, wherein calculate according to formula (5):

${\mathrm{\μ}}_F^g={\mathrm{\μ}}_F^{g-1}\·c+(1-c)\·S_F^{g-1},g>1---\left(5\right)$

Wherein, during g=0, represent in g-1 generation all can successfully enter of future generation individual mean value, represent the normal distribution average in g-1 generation, c is the rate of change of distance, calculates according to formula (6):

$c=\frac{|d_{ave}^g-d_{ave}^{g-1}|}{d_{ave}^{g-1}},g>1---\left(6\right)$

Wherein, during g=0, c=0.1, represent that g-1 is for the mean distance between individuality each in population;

6) according to formula (7), intersection is carried out to each variation individuality and generate new individual trial ^i,g:

${\mathrm{trial}}_j^{i,g}=\left\{\begin{array}{cc}{v}_j^{i,g}& \begin{array}{ccc}if(randb\left(0,1\right)\≤C_{Ri}^g& or& j=rnbr\left(j\right)\end{array}\\ x_j^{i,g}& otherwise\end{array}\right.---\left(7\right)$

Wherein, j=1,2 ..., N, represent that g is for new individual trial corresponding to i-th target individual in population ^i,gjth dimension element, randb (0,1) is expressed as the random decimal produced between 0 to 1, and rnbr (j) represents the random integer produced between 1 to N, represent i-th individual crossover probability in g generation, represent with for average, the normal distribution random number being error with 0.1, wherein calculate according to formula (8):

${\mathrm{\μ}}_{C_R}^g={\mathrm{\μ}}_{C_R}^{g-1}\·c+(1-c)\·S_{C_R}^{g-1}---\left(8\right)$

Wherein, during g=0, represent in g-1 generation all can successfully enter of future generation individual mean value, distance standardized rate c calculates according to formula (6), represent g-1 generation normal distribution average;

7) according to formula (9), population recruitment is carried out to each new individuality:

$x^{i,g+1}=\left\{\begin{array}{cc}{\mathrm{trial}}^{i,g},& iff\left({\mathrm{trial}}^{i,g}\right)\≤f\left(x^{i,g}\right)\\ x^{i,g},& otherwise\end{array}\right.---\left(9\right)$

Wherein, ${\mathrm{trial}}^{i,g}=({\mathrm{trial}}_1^{i,g},{\mathrm{trial}}_2^{i,g},...,{\mathrm{trial}}_N^{i,g}),$ $x^{i,g+1}=(x_1^{i,g+1},x_2^{i,g+1},...,x_N^{i,g+1}),x^{i,g}=$ $(x_1^{i,g},x_2^{i,g},...,x_N^{i,g}),$ Formula (9) shows, if new individuality is better than target individual, then and new individual replacement target individual, otherwise keep target individual constant;

8) judge whether to meet end condition, if met, then saving result exiting, otherwise return step 4).

2. as claimed in claim 1 a kind of based on shifty interim colony global optimization method, it is characterized in that: described step 8) in, end condition is function evaluates number of times.