CN105740949A - Group global optimization method based on randomness best strategy - Google Patents

Abstract

The group global optimization method based on randomness best strategy comprises steps of performing ascending order ranking according to the error between the each individual target function value and each optimal individual object function value in the current group, calculating the selection probability of each individual according to the ranking, wherein if the error of the individual is great, the probability of being chosen is great too, using the roulette gambling method to randomly choose m individuals to execute a DE/best/1 mutation strategy on m individuals and execute the DE/rand/1 mutation strategy on the other individuals by targeting all the individuals in the current group and according to the individual selection probability, and comprehensively using the global detection capability of the DE/rank/1 strategy and the DE/best/1 local searching capability to improve the DE algorithm performance in order to balance the algorithm global searching capability and the local searching capability.

Description

A kind of colony's global optimization method based on randomness best strategy

Technical field

The present invention relates to a kind of intelligent optimization, computer application field, in particular, a kind of colony's global optimization method based on randomness best strategy.

Background technology

It is frequently encountered by some Global Optimal Problems in fields such as economy, science and engineerings, in global optimization, algorithm needs to find out a globally optimal solution from numerous locally optimal solutions, but, the problem that these global optimization approaches are maximum is likely to be absorbed in local optimum and cannot try to achieve globally optimal solution exactly.Increasingly sophisticated along with engineering optimization, the condition of the object function of optimization problem also becomes to become increasingly complex, it is common that discontinuous, non-differentiability, nonlinearity, it does not have clear and definite analytical expression, and has multiple peak value, multiobject feature.Therefore, traditional optimization method (method as based on gradient) is not used to and solves challenge.

Evolution algorithm (EAs) is the randomness searching algorithm of the evolutionary process of a kind of mimic biology circle, what is common is that of these algorithms produces a candidate solution population by the evolutionary process of hereditary material in simulation organism, such as, natural selection and biological evolution.Evolution algorithm characteristic based on population is prevented from being absorbed in local optimum such that it is able to bigger chance find globally optimal solution.Evolution algorithm should with having solved of various problems by success, for instance pattern recognition, bioinformatics, engineering design and image procossing etc..The most frequently used evolution algorithm includes evolutional programming, evolution strategy, genetic algorithm, particle cluster algorithm and differential evolution algorithm (DE).

Evolution algorithm generally first initializes the candidate solution (individuality) of a population, and the quality of each individuality is evaluated by a fitness function, then in each iteration, new individuality by the body recombination in population or mutation operation are produced new individuality, can be carried out selection finally by selection course and produces population of future generation by algorithm.Said process is repeated iteration, until reaching end condition, then the optimal solution of gained is the approximate solution of required problem.

Differential evolution algorithm (DE), as a kind of randomness algorithm, has proved to be global optimization approach simple and powerful in evolution algorithm.The same with other evolution algorithms, DE algorithm also comprises variation, intersects and selects three operations.Algorithm by producing variation individuality based on the regularity of distribution solved in current population, and variation individuality individual then in conjunction with corresponding parent produces new individuality.When new individual fitness value is better than parent individuality, then new individual replacement parent is individual.It is general that DE algorithm has algorithm, does not rely on problem information, and principle is simple, it is easy to accomplish, memory individual optimal solution and population internal information are shared and the feature such as stronger global convergence ability.Therefore, DE algorithm has shown the advantage of its uniqueness in the extensive use in the fields such as communication, power system, optics, chemical industry and mechanical engineering, but also exposes some weakness in theory and application.Such as, the overall detectivity of DE algorithm is stronger, it is possible to the region at globally optimal solution place, location quickly, but local search ability is more weak, causes that late convergence is slower.The overall detectivity of algorithm and local search ability are uneven.

Therefore, the existing global optimization method based on differential evolution algorithm also exists defect in the balance of overall situation detectivity and local search ability, it is necessary to improve.

Summary of the invention

In order to overcome the existing global optimization method based on differential evolution algorithm deficiency in the balance of overall situation detectivity and local search ability, the present invention provides a kind of colony's global optimization method based on randomness best strategy taking into account overall situation detectivity and local search ability.

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

A kind of colony's global optimization method based on randomness best strategy, described optimization method comprises the following steps:

1) initialize: 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 ..., N_PRepresent that g is individual for the i-th in population, if g=0, then it represents that initial population；

3) the optimum individual x in current population is found out^best,g, according to each individual x^i,gTarget function value f (x^i,g) with the target function value f (x of optimum individual^best,g) error | f (x^i,g)-f(x^best,g) | carry out ascending order arrangement, and write down the ranking F of each individuality^i,g, wherein, F^i,gRepresent that g is for the value ranking of i-th individuality in population；

4) the select probability p of each individuality is calculated according to formula (1)^i,g；

$p^{i,g}=\frac{F^{i,g}}{0.5({N_P}^2+N_P)}---\left(1\right)$

Wherein, p^i,gRepresent that g is in populationiThe select probability of individuality, N_PFor population scale；

5) the select probability p according to each individuality^i,gUtilize roulette method to choose m individuality from current population and be DE/best/1 variation, m < N_P:

5.1) the decimal rand0 between stochastic generation one (0,1)；

5.2) ifAnd t is different from selecting individuality, then the t individuality is selected to make a variation according to formula (2):

$v_j^{t,g}=x_j^{best,g}+F\&CenterDot;(x_j^{a,g}-x_j^{b,g}),---\left(2\right)$

Wherein, j=1,2 ..., N, N is problem dimension, and g is evolutionary generation, a, b ∈ 1,2 ..., N_P, a ≠ b ≠ t, t is the index of currently selected target individual,It is that g ties up element for the jth that the variation of t target individual selected in population is individual,Respectively g is in population a, b individual jth dimension element,For the current g jth dimension element for the optimum individual in population, F represents gain constant；

6) for remaining N_P-m individuality carries out DE/rand/1 variation:

$v_j^{i,g}=x_j^{best,g}+F\&CenterDot;(x_j^{a,g}-x_j^{b,g})---\left(3\right)$

Wherein, j=1,2 ..., N, N is problem dimension, and g is evolutionary generation, a, b, c ∈ 1,2 ..., N_P, a ≠ b ≠ c ≠ i, i is remaining N_PThe index of target individual in-m individuality,It is that g ties up element for the jth that the variation of the i-th target individual in population is individual,Respectively g is in population a, b, c individual jth dimension element, and F represents gain constant；

7) according to formula (4), each variation individuality is carried out intersection and generate new individual trialⁱ, g:

${\mathrm{trial}}_j^{i,g}=\left\{\begin{array}{cc}{v}_j^{i,g}& \begin{array}{ccc}if\left(randb\right(0,1)\&le;C_R& or& j=rnbr\left(j\right)\end{array}\\ x_j^{i,g}& otherwise\end{array}\right.---\left(4\right)$

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 decimal randomly generating between 0 to 1, and rnbr (j) represents and randomly generates integer between 1 to N, C_RRepresent crossover probability；

8) according to formula (5), each new individuality is carried out population recruitment:

$x^{i,g+1}=\left|\begin{array}{cc}{\mathrm{trial}}^{i,g},& \begin{array}{cc}if& f\left({\mathrm{trial}}^{i,g}\right)\&le;f\left(x^{i,g}\right)\end{array}\\ x^{i,g},& otherwise\end{array}\right.---\left(5\right)$

Wherein, ${\mathrm{trial}}^{i,g}=({\mathrm{trial}}_1^{i,g},{\mathrm{trial}}_2^{i,g},...,{\mathrm{trial}}_N^{i,g}),x^{i,g+1}=(x_1^{i,g+1},x_2^{i,g+1},...,x_N^{i,g+1}),$ $x^{i,g}=$ $(x_1^{i,g},x_2^{i,g},\mathrm{...},x_N^{i,g}),$ Formula (5) shows, if new individuality is better than target individual, then new individual replacement target individual, otherwise keeps target individual constant；

9) judge whether to meet end condition, if it is satisfied, then preserve result and exit, otherwise return step 3).

Further, described step 9) in, end condition is that function evaluates number of times.It is of course also possible to be other end conditions.

The technology of the present invention is contemplated that: first, carries out ascending order ranking according to the error between target function value and the target function value of optimum individual of individuality each in current population；Then, calculating the select probability of each individuality according to ranking, if the error of certain individuality is more big, then its selected probability is then more big；Then, for all individualities in current population, the select probability according to each individuality, utilize roulette method, randomly choose out m individual execution DE/best/1 Mutation Strategy, DE/rand/1 Mutation Strategy is then performed for other individuality；Thus comprehensively utilizing the DE/best/1 local search ability of overall detectivity sum of DE/rand/1 strategy to improve the performance of DE algorithm, to reach the effect of balanced algorithm ability of searching optimum and local search ability.

The local search ability of the present invention overall detectivity in conjunction with DE/rand/1 Mutation Strategy and DE/best/1 Mutation Strategy, ascending order ranking is carried out with the target function value error of optimum individual in current population according to each individuality, then the select probability of each individuality is calculated according to ranking, thus utilizing the mode of roulette to perform DE/best/1 Mutation Strategy according to the select probability selected part individuality in each generation of each individuality, thus realizing algorithm to detect seamlessly transitting of Local Search from the overall situation, to reach to balance the effect of overall situation detectivity and local search ability.

Beneficial effects of the present invention shows: the DE/best/1 local search ability of the overall detectivity sum of comprehensive utilization DE/rand/1 strategy is to improve the performance of DE algorithm, in every generation population at individual, the select probability drawn according to the functional value error ranking between each individuality and currently most individuality, only choose m individuality and carry out DE/best/1 variation, the local search ability of algorithm can not only be improved, and it can be avoided that be absorbed in local optimum, effectively achieve algorithm and detect seamlessly transitting of Local Search from the overall situation.

Accompanying drawing explanation

Fig. 1 is based on the basic flow sheet of colony's global optimization method of randomness best strategy.

Convergence in mean curve chart when Fig. 2 is based on colony's global optimization method of randomness best strategy to 30 dimension Ackey Optimization Solution.

Detailed description of the invention

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

See figures.1.and.2, a kind of colony's global optimization method based on randomness best strategy, comprise the following steps:

1) initialize: 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 ..., N_PRepresent that g is individual for the i-th in population, if g=0, then it represents that initial population；

3) the optimum individual x in current population is found out^best,g, according to each individual x^i,gTarget function value f (x^i,g) with the target function value f (x of optimum individual^best,g) error | f (x^i,g)-f(x^best,g) | carry out ascending order arrangement, and write down the ranking F of each individuality^i,g, wherein, F^i,gRepresent that g is for the value ranking of i-th individuality in population；

4) the select probability p of each individuality is calculated according to formula (1)^i,g；

$p^{i,g}=\frac{F^{i,g}}{0.5({N_P}^2+N_P)}---\left(1\right)$

Wherein, p^i,gRepresent that g is in populationiThe select probability of individuality, N_PFor population scale；

5) the select probability p according to each individuality^i,gUtilize roulette method to choose m individuality from current population and be DE/best/1 variation, m < N_P:

5.1) the decimal rand0 between stochastic generation one (0,1)；

5.2) ifAnd t is different from selecting individuality, then the t individuality is selected to make a variation according to formula (2):

$v_j^{t,g}=x_j^{best,g}+F\&CenterDot;(x_j^{a,g}-x_j^{b,g}),---\left(2\right)$

Wherein, j=1,2 ..., N, N is problem dimension, and g is evolutionary generation, a, b ∈ 1,2 ..., N_P, a ≠ b ≠ t, t is the index of currently selected target individual,It is that g ties up element for the jth that the variation of t target individual selected in population is individual,Respectively g is in population a, b individual jth dimension element,For the current g jth dimension element for the optimum individual in population, F represents gain constant；

6) for remaining N_P-m individuality carries out DE/rand/1 variation:

$v_j^{i,g}=x_j^{best,g}+F\&CenterDot;(x_j^{a,g}-x_j^{b,g})---\left(3\right)$

Wherein, j=1,2 ..., N, N is problem dimension, and g is evolutionary generation, a, b, c ∈ 1,2 ..., N_P, a ≠ b ≠ c ≠ i, i is remaining N_PThe index of target individual in-m individuality,It is that g ties up element for the jth that the variation of the i-th target individual in population is individual,Respectively g is in population a, b, c individual jth dimension element, and F represents gain constant；

7) according to formula (4), each variation individuality is carried out intersection and generate new individual trial^i,g:

${\mathrm{trial}}_j^{i,g}=\left\{\begin{array}{cc}{v}_j^{i,g}& \begin{array}{ccc}if\left(randb\right(0,1)\&le;C_R& or& j=rnbr\left(j\right)\end{array}\\ x_j^{i,g}& otherwise\end{array}\right.---\left(4\right)$

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 decimal randomly generating between 0 to 1, and rnbr (j) represents and randomly generates integer between 1 to N, C_RRepresent crossover probability；

8) according to formula (5), each new individuality is carried out population recruitment:

$x^{i,g+1}=\left|\begin{array}{cc}{\mathrm{trial}}^{i,g},& \begin{array}{cc}if& f\left({\mathrm{trial}}^{i,g}\right)\&le;f\left(x^{i,g}\right)\end{array}\\ x^{i,g},& otherwise\end{array}\right.---\left(5\right)$

Wherein, ${\mathrm{trial}}^{i,g}=({\mathrm{trial}}_1^{i,g},{\mathrm{trial}}_2^{i,g},\mathrm{...},{\mathrm{trial}}_N^{i,g}),x^{i,g+1}=(x_1^{i,g+1},x_2^{i,g+1},\mathrm{...},x_N^{i,g+1}),$ $x^{i,g}=$ $(x_1^{i,g},x_2^{i,g},\mathrm{...},x_N^{i,g}),$ Formula (5) shows, if new individuality is better than target individual, then new individual replacement target individual, otherwise keeps target individual constant；

9) judge whether to meet end condition, if it is satisfied, then preserve result and exit, otherwise return step 3).

Further, described step 9) in, end condition is that function evaluates number of times.It is of course also possible to be other end conditions.

The present embodiment ties up Ackey functions for embodiment with classical 30, a kind of colony's global optimization method based on randomness best strategy, wherein comprises the steps of

1) initialize: population scale N is set_P=50, 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 ..., N_PRepresent that g is individual for the i-th in population, if g=0, then it represents that initial population；

3) the optimum individual x in current population is found out^best,g, according to each individual x^i,gTarget function value f (x^i,g) with the target function value f (x of optimum individual^best,g) error | f (x^i,g)-f(x^best,g) | carry out ascending order arrangement, and write down the ranking F of each individuality^i,g, wherein, F^i,gRepresent that g is for the value ranking of i-th individuality in population；

4) the select probability p of each individuality is calculated according to formula (1)^i,g；

$p^{i,g}=\frac{F^{i,g}}{0.5({N_P}^2+N_P)}---\left(1\right)$

Wherein, p^i,gRepresent that g is in populationiThe select probability of individuality, N_PFor population scale；

5) the select probability p according to each individuality^i,gRoulette method is utilized to choose m=5 (m < N from current population_P) individuality be DE/best/1 variation:

5.1) the decimal rand0 between stochastic generation one (0,1)；

5.2) ifAnd t is different from selecting individuality, then the t individuality is selected to make a variation according to formula (2):

$v_j^{t,g}=x_j^{best,g}+F\&CenterDot;(x_j^{a,g}-x_j^{b,g}),---\left(2\right)$

Wherein, j=1,2 ..., N, N is problem dimension, and g is evolutionary generation, a, b ∈ 1,2 ..., N_P, a ≠ b ≠ t, t is the index of currently selected target individual,It is that g ties up element for the jth that the variation of t target individual selected in population is individual,Respectively g is in population a, b individual jth dimension element,For the current g jth dimension element for the optimum individual in population, F represents gain constant；

6) for remaining N_P-m individuality carries out DE/rand/1 variation:

$v_j^{i,g}=x_j^{best,g}+F\&CenterDot;(x_j^{a,g}-x_j^{b,g})---\left(3\right)$

Wherein, j=1,2 ..., N, N is problem dimension, and g is evolutionary generation, a, b, c ∈ 1,2 ..., N_P, a ≠ b ≠ c ≠ i, i is remaining N_PThe index of target individual in-m individuality,It is that g ties up element for the jth that the variation of the i-th target individual in population is individual,Respectively g is in population a, b, c individual jth dimension element, and F represents gain constant；

7) according to formula (4), each variation individuality is carried out intersection and generate new individual trial^i,g:

${\mathrm{trial}}_j^{i,g}=\left\{\begin{array}{cc}{v}_j^{i,g}& \begin{array}{ccc}if\left(randb\right(0,1)\&le;C_R& or& j=rnbr\left(j\right)\end{array}\\ x_j^{i,g}& otherwise\end{array}\right.---\left(4\right)$

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 decimal randomly generating between 0 to 1, and rnbr (j) represents and randomly generates integer between 1 to N, C_RRepresent crossover probability；

8) according to formula (5), each new individuality is carried out population recruitment:

$x^{i,g+1}=\left|\begin{array}{cc}{\mathrm{trial}}^{i,g},& \begin{array}{cc}if& f\left({\mathrm{trial}}^{i,g}\right)\&le;f\left(x^{i,g}\right)\end{array}\\ x^{i,g},& otherwise\end{array}\right.---\left(5\right)$

Wherein, ${\mathrm{trial}}^{i,g}=({\mathrm{trial}}_1^{i,g},{\mathrm{trial}}_2^{i,g},...,{\mathrm{trial}}_N^{i,g}),x^{i,g+1}=(x_1^{i,g+1},x_2^{i,g+1},...,x_N^{i,g+1}),$ $x^{i,g}=$ $(x_1^{i,g},x_2^{i,g},\mathrm{...},x_N^{i,g}),$ Formula (5) shows, if new individuality is better than target individual, then new individual replacement target individual, otherwise keeps target individual constant；

9) judge that object function evaluates whether number of times reaches 150000, if reached, then preserve result and exit, otherwise returning step 3).

Ackey function is tieed up for embodiment with 30, the average success rate of 30 independent operatings is 100% (degree of accuracy of the optimal solution that regulation algorithm finds in 150000 object function evaluation number of times is successfully solve when being 0.00001), the meansigma methods of the solution tried to achieve in 150000 function evaluation number of times is 7.55E-15, and standard deviation is 0.00E+00.

The excellent effect of optimization that the embodiment that the present invention provides that described above is shows, the obvious present invention is not only suitable for above-described embodiment, and may apply to the every field in Practical Project (such as protein structure prediction, power system, the optimization problems such as path planning), simultaneously under not necessarily departing from essence spirit of the present invention and the premise without departing from content involved by flesh and blood of the present invention, it can be done many variations and be carried out.

Claims (2)

1. the colony's global optimization method based on randomness best strategy, it is characterised in that: described optimization method comprises the following steps:

1) initialize: 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 ..., N_PRepresent that g is individual for the i-th in population, if g=0, then it represents that initial population；

3) the optimum individual x in current population is found out^best,g, according to each individual x^i,gTarget function value f (x^i,g) with the target function value f (x of optimum individual^best,g) error | f (x^i,g)-f(x^best,g) | carry out ascending order arrangement, and write down the ranking F of each individuality^{i ,g}, wherein, F^i,gRepresent that g is for the value ranking of i-th individuality in population；

4) the select probability p of each individuality is calculated according to formula (1)^i,g；

$p^{i,g}=\frac{F^{i,g}}{0.5({N_P}^2+N_P)}---\left(1\right)$

Wherein, p^i,gRepresent that g is in populationiThe select probability of individuality, N_PFor population scale；

5) the select probability p according to each individuality^i,gUtilize roulette method to choose m individuality from current population and be DE/best/1 variation, m < N_P:

5.1) the decimal rand0 between stochastic generation one (0,1)；

5.2) ifAnd t is different from selecting individuality, then the t individuality is selected to make a variation according to formula (2):

$v_j^{t,g}=x_j^{best,g}+F\&CenterDot;(x_j^{a,g}-x_j^{b,g}),---\left(2\right)$

Wherein, j=1,2 ..., N, N is problem dimension, and g is evolutionary generation, a, b ∈ 1,2 ..., N_P, a ≠ b ≠ t, t is the index of currently selected target individual,It is that g ties up element for the jth that the variation of t target individual selected in population is individual,Respectively g is in population a, b individual jth dimension element,For the current g jth dimension element for the optimum individual in population, F represents gain constant；

6) for remaining N_P-m individuality carries out DE/rand/1 variation:

$v_j^{i,g}=x_j^{best,g}+F\&CenterDot;(x_j^{a,g}-x_j^{b,g})---\left(3\right)$

Wherein, j=1,2 ..., N, N is problem dimension, and g is evolutionary generation, a, b, c ∈ 1,2 ..., N_P, a ≠ b ≠ c ≠ i, i is remaining N_PThe index of target individual in-m individuality,It is that g ties up element for the jth that the variation of the i-th target individual in population is individual,Respectively g is in population a, b, c individual jth dimension element, and F represents gain constant；

7) according to formula (4), each variation individuality is carried out intersection and generate new individual trial^i,g:

${\mathrm{trial}}_j^{i,g}=\left\{\begin{array}{cc}{v}_j^{i,g}& \begin{array}{ccc}if(randb\left(0,1\right)\&le;C_R& or& j=rnbr\left(j\right)\end{array}\\ x_j^{i,g}& otherwise\end{array}\right.---\left(4\right)$

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 decimal randomly generating between 0 to 1, and rnbr (j) represents and randomly generates integer between 1 to N, C_RRepresent crossover probability；

8) according to formula (5), each new individuality is carried out population recruitment:

$x^{i,g+1}=\left\{\begin{array}{cc}{\mathrm{trial}}^{i,g},& \begin{array}{cc}if& f\left({\mathrm{trial}}^{i,g}\right)\&le;f\left(x^{i,g}\right)\end{array}\\ x^{i,g},& otherwise\end{array}\right.---\left(5\right)$

Wherein, ${\mathrm{trial}}^{i,g}=({\mathrm{trial}}_1^{i,g},{\mathrm{trial}}_2^{i,g},...,{\mathrm{trial}}_N^{i,g}),x^{i,g+1}=(x_1^{i,g+1},x_2^{i,g+1},...,x_N^{i,g+1}),x^{i,g}=$

$\left(x_1^{i,g},x_2^{i,g},\mathrm{...},x_N^{i,g}\right),$ Formula (5) shows, if new individuality is better than target individual, then new individual replacement target individual, otherwise keeps target individual constant；

9) judge whether to meet end condition, if it is satisfied, then preserve result and exit, otherwise return step 3).

2. as claimed in claim 1 a kind of based on randomness best strategy colony's global optimization method, it is characterised in that: described step 9) in, end condition be function evaluate number of times.