CN106056208A - Bio-geographic optimization algorithm-oriented constraint handling method and device - Google Patents

Abstract

The present invention provides a constraint processing method and device for biogeographic optimization algorithms, wherein the method includes: improving the migration step: capturing individuals selected from the target population; extracting the target dimension elements of the selected individuals; based on the individual emigration rate , according to the analog binary crossover operator, the weighted fusion of the target dimension elements of the selected individuals is performed to generate new elements to be immigrated; the mutation step is improved: update the target subpopulation according to the new elements to be immigrated and use Gaussian distribution for disturbance, Obtain the excellent ones in the target population; the feasibility constraint processing step: determine the excellent ones in the target population and determine the optimal individual, and update the variation parameters with the differential evolution algorithm. By combining the information search ability of the differential evolution algorithm and the information utilization ability of the biogeography algorithm, the global optimization ability of the processing scheme is improved and balanced.

Description

Constraint processing method and device for biogeographical optimization algorithm

technical field

The present invention relates to the field of biogeography optimization algorithms, more specifically, to a constraint processing method and device for biogeography optimization algorithms.

Background technique

The biogeography optimization algorithm is a new type of swarm intelligence algorithm proposed by Simon in 2008 based on the biogeography mathematical model. This algorithm simulates the migration mechanism of biological populations between different habitats to share population information and simulate habitats. The sudden phenomenon of the ground is used to explore new areas, so as to achieve the purpose of optimization. The biogeography algorithm has simple structure, few control parameters, fast convergence speed, and excellent information utilization ability, and has been applied in different fields of engineering.

However, the biogeography optimization algorithm maximizes the use of the existing information in the population through the migration operation, sacrificing the exploration of new areas; although it uses random mutation operations to obtain new elements, explore unknown spaces, and increase population diversity, Exploration is not strong enough.

Therefore, the information exploration ability and information utilization ability of the biogeographical optimization algorithm are unbalanced. Therefore, biogeographical algorithms are prone to fall into local optimal solutions and prematurely mature.

Contents of the invention

The invention discloses a constraint processing method and system oriented to a biogeographical optimization algorithm. By combining the information search capability of a differential evolution algorithm and the information utilization capability of a biogeographical algorithm, the global optimization capability of the processing scheme is improved and balanced. , and introduce biogeography algorithms into the field of constrained optimization.

To achieve the above object, the present invention discloses:

A Constraint Handling Method for Biogeographical Optimization Algorithms,

Improve migration steps:

capture individuals selected from the target population;

extracting target dimension elements of the selected individual;

Based on the individual emigration rate, the target dimension elements of the selected individual are weighted and fused according to the simulated binary crossover operator to generate new elements to be immigrated;

Improve the mutation step: update the target subpopulation according to the new element to be immigrated and use the Gaussian distribution for disturbance to obtain the outstanding ones in the target population;

Feasibility constraint processing step: determine the outstanding person in the target population and determine the optimal individual, and update the variation parameters with the differential evolution algorithm.

Preferably, said capturing individuals selected from the target population includes:

According to the roulette mechanism, two different individuals are randomly selected from the population X.

Preferably, before the step of improving migration, it also includes:

Judging the current number of iterations, if it is determined to be less than the set value, then perform feasibility constraint processing, which includes:

The target population is sorted according to the individual serial number according to the outstanding person first, and the mapping from the individual fitness value to the number of species is completed;

Calculate the in-migration rate and out-migration rate of each individual in the target population to update the existence probability, and calculate the variation parameter.

Preferably, when judging the current number of iterations, if it is determined to be greater than the set value, the optimal individual in the population X and the corresponding fitness value and constraint violation value are output.

Preferably, the step of improving mutation includes:

Correct the individuals that meet the first mutation condition in the target population, calculate the fitness value and total constraint violation value of the new individual, and store the excellent ones in the first population; The target population, sub-population, and the first population are compared, and the best ones are stored in the target population. .

The present invention also discloses correspondingly:

A constraint processing device for biogeographical optimization algorithms,

Improve the migration module, its configuration is:

capture individuals selected from the target population;

extracting target dimension elements of the selected individual;

Based on the individual emigration rate, the target dimension elements of the selected individual are weighted and fused according to the simulated binary crossover operator to generate new elements to be immigrated;

Improve the mutation module, which is configured to update the subpopulation of the target according to the new element to be immigrated and use Gaussian distribution to perturb, so as to obtain the outstanding ones in the target population;

The feasibility constraint processing module is configured to determine the outstanding individuals in the target population and determine the optimal individual, and update the variation parameters with a differential evolution algorithm.

Preferably, the device also includes a judging module configured to:

Judging the current number of iterations, if it is determined to be less than the set value, then perform feasibility constraint processing, which includes:

The target population is sorted according to the individual serial number according to the outstanding person first, and the mapping from the individual fitness value to the number of species is completed;

Calculate the in-migration rate and out-migration rate of each individual in the target population to update the existence probability, and calculate the variation parameter.

Preferably, the judging module also realizes:

Judging the current number of iterations, when it is determined to be greater than the set value, output the optimal individual in the population X and the corresponding fitness value and constraint violation value.

Preferably, the improved variation module is configured as:

Correct the individuals that meet the first mutation condition in the target population, calculate the fitness value and total constraint violation value of the new individual, and store the excellent ones in the first population; The target population, sub-population, and the first population are compared, and the best ones are stored in the target population.

Through the constraint processing method and device oriented to biogeography optimization algorithm of the present invention, analog binary crossover operator, Gaussian distribution, adaptive differential evolution algorithm and feasibility-based constraint processing mechanism are introduced to improve and balance the information of biogeography algorithm Search ability and information utilization ability, so as to realize the solution of constrained optimization problems. The migration operator of the improved algorithm is based on the simulated binary crossover operator, randomly selects two individuals from the population, and combines the two individuals according to the preset weighting coefficient to obtain new feature elements; the improved variation element is based on Gaussian distribution Perturbation is performed to generate new individuals. In addition, in the improved algorithm, in addition to the evolution of some poor individuals according to the biogeographic algorithm, they are also updated according to the variation elements of two kinds of differential evolution, so as to improve the global optimization ability of the algorithm and speed up the convergence speed. Different individuals of the constraint processing method oriented to the biogeographical optimization algorithm follow the feasibility constraint processing mechanism when comparing each other. By combining the information search ability of the differential evolution algorithm and the information utilization ability of the biogeographical algorithm, the performance of the processing scheme is improved and balanced. Global optimization capability.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings that are required in the description of the embodiments or the prior art.

FIG. 1 is a flowchart of a constraint processing method oriented to a biogeographical optimization algorithm according to an embodiment of the present invention.

Fig. 2 is a flowchart of a constraint processing method oriented to a biogeographical optimization algorithm according to another embodiment of the present invention.

Fig. 3 is a flowchart of a constraint processing method oriented to a biogeographical optimization algorithm according to another embodiment of the present invention.

Fig. 4 is a schematic structural diagram of a constraint processing device oriented to a biogeographical optimization algorithm according to an embodiment of the present invention.

Fig. 5 is a schematic structural diagram of a constraint processing device oriented to a biogeographical optimization algorithm according to another embodiment of the present invention.

Specific implementation method

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. It should be noted that, in the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

The invention discloses a constraint processing method and system oriented to a biogeographical optimization algorithm. By combining the information search capability of a differential evolution algorithm and the information utilization capability of a biogeographical algorithm, the global optimization capability of the processing scheme is improved and balanced.

In order to realize the solutions in the embodiments, the following construction and initialization processes need to be implemented:

Step 1: Setting parameters: maximum immigrant rate I=1, maximum emigration rate E=1, maximum mutation rate mmax=1, distribution parameter η=10, upper boundary FL of variation range of differential evolution algorithm variation parameters =0.7 and the lower boundary FU=0.9, the population size NP, the upper boundary Ubound of the optimization variable, the lower boundary Lbound of the optimization variable, the preset maximum number of iterations Gmax, the violation tolerance δ of the inequality constraint; define the fitness value Fitness of the optimization problem and the total constraint violation function Constraint.

Step 2: The number of initialization iterations G=1, the target population X, the probability of habitat existence P and the variation parameter vector F, each row of the matrix X represents an individual, and each dimension element of the vector P represents the existence probability of an individual of the corresponding dimension, Each dimensional element of F corresponds to the differential evolution variation parameter of the corresponding individual in the population X, which is used to calculate the fitness value and the total constraint violation value of each habitat in the population X. Based on the feasibility constraint processing mechanism, it can be determined that best individual.

Fig. 1 is the constraint processing method oriented to the biogeography optimization algorithm of the embodiment of the present invention, including:

S101: Improve migration steps:

Referring to Figure 2, this step is specifically implemented as:

S201: capturing individuals selected from the target population;

Preferably, said capturing individuals selected from the target population includes:

According to the roulette mechanism, two different individuals are randomly selected from the population X.

S202: Extracting target dimension elements of the selected individual;

S203: Based on the individual emigration rate, the target dimension elements of the selected individuals are weighted and fused according to the simulated binary crossover operator to generate new elements to be immigrated;

Introduce the simulated binary crossover operator of the genetic algorithm to improve the basic migration operation. The update mechanism of the simulated binary crossover operator is as follows:

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; parent</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; parent</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&rsqb;</span>$

Among them, Parent1j and Parent2j represent the j-th dimension elements of two individuals randomly selected from the population X, C1j and C2j represent the new elements obtained after crossover, and β is calculated according to the following formula:

$\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}& \begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}& \mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; \&le;</span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\end{array}\\ \frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>}^{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}}& \begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}& \mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; ></span>\mathrm{<span\; class="notranslate">\; 0.5</span>}\end{array}\end{array}\right.$

In the improved migration operation, for the elements that need to perform migration operations in each dimension, based on the individual migration rate, two different individuals are randomly selected from the population X according to the roulette mechanism, and the simulated binary crossover operator pairs different The elements of outstanding individuals are weighted and fused to generate two new elements to be moved in. The new elements inherit the outstanding individuals, and at the same time explore new areas of the optimization space, thus improving the information exploration ability of the algorithm.

where η represents the distribution parameter of the simulated binary crossover operator, and u represents a random number between 0 and 1.

S102: Improve the mutation step: update the target sub-population according to the new element to be immigrated and use the Gaussian distribution for disturbance to obtain the outstanding ones in the target population;

Correct the individuals that are out of the optimal range in the population, and calculate the fitness value and total constraint violation value of all individuals in the population.

Gaussian distribution is introduced to improve the variable elements, and the probability density function of Gaussian distribution is as follows: $f_{\mathrm{\&mu;},{\mathrm{\&sigma;}}^2}\left(x\right)=\frac{1}{\mathrm{\&sigma;}\sqrt{2\mathrm{\&pi;}}}{e}^{\frac{(x-\mathrm{\&mu;})}{2{\mathrm{\&sigma;}}^2}}$

Where μ represents the mean value of the probability distribution, and σ represents the variance of the probability distribution. If the element Xij needs to perform a mutation operation, the improved mutation operation is as follows:

X' _ij =X _ij +N(0,1)

Among them, N(0, 1) represents a Gaussian distribution with a mean value of 1 and a variance of 0, and X′ _ij represents a new element obtained after X _ij performs an improved mutation operation. The element that improves the mutation abandons the blind random mutation method. For the element that needs to perform the mutation operation, it is perturbed based on the Gaussian distribution to realize the exploration of the surrounding area of the original individual, and it is more likely to obtain an excellent solution, so that The algorithm can quickly break away from the local optimal solution with greater possibility, which further improves and balances the global optimization ability of the processing scheme.

S103: Feasibility constraint processing step: determine the outstanding individuals in the target population and determine the optimal individual, and update the variation parameters with a differential evolution algorithm.

The feasibility constraint processing mechanism is introduced so that the algorithm can handle the constraints in the optimization problem. Taking the minimum optimization as an example, the specific principle of the mechanism is as follows: a feasible individual is better than an infeasible individual; when two infeasible individuals are compared with each other, the total constraint Individuals with small violations are excellent; when two feasible individuals are compared with each other, individuals with small fitness values are excellent.

As preferably, the step of improving variation includes:

Correct the individuals that meet the first mutation condition in the target population, calculate the fitness value and total constraint violation value of the new individuals, and save the excellent ones into the first population;

Preferably, the following technical solutions may be implemented to complete the above steps, but not limited thereto.

Each individual whose serial number in the population X is in the interval [0.7*NP+1, NP] evolves according to the rand/1 and rand to best/1 mutation methods of differential evolution, and obtains two new individuals. After the individual is corrected, the fitness value and the total constraint violation value of the new individual are calculated, and the excellent ones are stored in the population DEX.

For the individuals in the target population that meet the second variation condition, compare individuals based on the target population, subpopulation, and the first population, and save the excellent ones into the target population:

For the individuals whose serial numbers in population X are in the interval [1, 0.7*NP], compare the individuals in X with the corresponding individuals in NewX1 and NewX2, and the excellent ones will be stored in population X; for the serial numbers in population X in the interval [0.7 *NP+1, NP] Individuals in population X, NewX1, NewX2, and DEX are compared with each other, and the best ones are stored in population X.

To update the differential evolution variation parameter F, the update mechanism is as follows:

${\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; G</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}{\mathrm{<span\; class="notranslate">\; FL</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; rand</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; FU</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; FL</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>& \begin{array}{cc}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; f</span>}& \mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; no</span>}\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; 0.3</span>}\end{array}\\ {\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; G</span>}}& \mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; t</span>}\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; w</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; e</span>}\end{array}\right.$

in and respectively represent the differential evolution variation parameters of the i-th individual in the population X in the G-th iteration and the G+1-th iteration, FUi and FLi represent the upper and lower boundaries of the variation range of the variation parameter Fi, and rand and rand1 represent A random number between; G=G+1.

Differential evolutionary algorithm is a classic swarm intelligence optimization algorithm. It searches the optimization space by perturbing other individuals through the weighted difference between different individuals. It has excellent information search ability. Geographical algorithm, the new hybrid biogeographical algorithm adopts the following mixed mechanism: In addition to the evolution of the poorer 30% individuals in the population according to the improved migration operation and mutation operation, it also evolves according to the rand/1 and randto best/1 of the differential evolution algorithm way to update. Based on this method, poor individuals in the population can quickly evolve to excellent individuals, and the optimization space can be explored more effectively, so that the information search ability of the differential evolution algorithm and the information utilization ability of the biogeography algorithm can be reasonably combined to improve and The global optimization capability of the processing scheme is balanced.

Referring to Figure 3, on the basis of Embodiment 1,

Before the improved migration step S101, it also includes:

S301: Judging the current number of iterations, if it is determined that it is less than the set value, perform feasibility constraint processing, which includes:

S302: Sorting the target population according to the individual serial number according to the outstanding person first, and completing the mapping from the individual fitness value to the number of species;

303: Calculate the in-migration rate and out-migration rate of each individual in the target population to update the existence probability, and calculate the variation parameter.

and:

When determined to be greater than the set value, S304:

Output the optimal individual in the population X and the corresponding fitness value and constraint violation value.

When it is judged that the current number of iterations G is greater than Gmax, the optimal individual in the population X and the corresponding fitness value and constraint violation value are output, and no other steps are performed.

Based on the feasibility constraint processing mechanism, the individuals in the population X are sorted, the outstanding ones come first, and the mapping from the individual fitness value to the number of species is completed according to the individual serial number of the population. The mapping method is as follows: Xi represents the processing mechanism according to the feasibility constraint The number of species corresponding to the i-th individual in population X after sorting is Si=NP-i+1.

Calculate the in-migration rate λi and out-migration rate μi of each individual in the target population, update the existence probability P, and calculate the mutation rate mi:

${\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; )</span>$

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; P</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

${\stackrel{<span\; class="notranslate">\; \&Center\; Dot;</span>}{\mathrm{<span\; class="notranslate">\; P</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\left\{\begin{array}{cc}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ <span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& \mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; <</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; P</span>}\\ <span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}& {\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; P</span>}\end{array}\right.$

${\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; a</span>}\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; max</span>}}}<span\; class="notranslate">\; )</span>$

Where Pi represents the existence probability of individual Xi, Pmax=max(Pi).

The constraint processing algorithm oriented to the biogeography optimization algorithm in the above embodiment is based on the improvement of the migration operator based on the simulated binary crossover operator, and the Gaussian distribution is introduced into the mutation operation, and the poorer individuals in the population evolve according to the differential evolution mutation operator. The above improvements The scheme balances the information exploration ability and information utilization ability of biogeographical algorithms.

The introduction of a feasible constraint processing mechanism enables the algorithm to handle constraint optimization, which provides a way to generalize biogeography algorithms to the field of constraint optimization, so that it can converge to the global optimal solution with greater possibility and faster speed .

The embodiment of the present invention also discloses: a constraint processing device oriented to a biogeographical optimization algorithm, comprising:

Improve migration module 401, its configuration is:

capture individuals selected from the target population;

extracting target dimension elements of the selected individual;

Based on the individual emigration rate, the target dimension elements of the selected individual are weighted and fused according to the simulated binary crossover operator to generate new elements to be immigrated;

Improve the mutation module 402, which is configured to update the target subpopulation according to the new elements to be imported and use Gaussian distribution for disturbance, so as to obtain the outstanding ones in the target population;

Feasibility constraint processing module 403, which is configured to determine the outstanding individuals in the target population and determine the optimal individual, and update the variation parameters with a differential evolution algorithm.

Preferably, the improved variation module is configured as:

Correct the individuals that meet the first mutation condition in the target population, calculate the fitness value and total constraint violation value of the new individuals, and save the excellent ones into the first population;

For individuals in the target population that meet the second variation condition, compare individuals based on the target population, sub-population, and the first population, and the outstanding ones are stored in the target population. .

Referring to Fig. 5, it also includes a judging module 501, which is configured as:

Judging the current number of iterations, if it is determined to be less than the set value, then perform feasibility constraint processing, which includes:

The target population is sorted according to the individual serial number according to the outstanding person first, and the mapping from the individual fitness value to the number of species is completed;

Calculate the in-migration rate and out-migration rate of each individual in the target population to update the existence probability, and calculate the variation parameter.

The judgment module also implements:

Judging the current number of iterations, when it is determined to be greater than the set value, output the optimal individual in the population X and the corresponding fitness value and constraint violation value.

Improve the mutation module configuration to

It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is a relationship between these entities or operations. There is no such actual relationship or order between them. Furthermore, the term "comprises", "comprises" or any other variation thereof is intended to cover a non-exclusive inclusion such that a process, method, article or apparatus comprising a set of elements includes not only those elements, but also includes elements not expressly listed. other elements of or also include elements inherent in such a process, method, article, or device. Without further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article or apparatus comprising said element.

In summary:

Through the constraint processing method and device oriented to biogeography optimization algorithm of the present invention, analog binary crossover operator, Gaussian distribution, adaptive differential evolution algorithm and feasibility-based constraint processing mechanism are introduced to improve and balance the information of biogeography algorithm Search ability and information utilization ability, so as to realize the solution of constrained optimization problems. The migration operator of the improved algorithm is based on the simulated binary crossover operator, randomly selects two individuals from the population, and combines the two individuals according to the preset weighting coefficient to obtain new feature elements; the improved variation element is based on Gaussian distribution Perturbation is performed to generate new individuals. In addition, in the improved algorithm, in addition to the evolution of some poor individuals according to the biogeographic algorithm, they are also updated according to the variation elements of two kinds of differential evolution, so as to improve the global optimization ability of the algorithm and speed up the convergence speed. Different individuals of the constraint processing method oriented to the biogeographical optimization algorithm follow the feasibility constraint processing mechanism when comparing each other. By combining the information search ability of the differential evolution algorithm and the information utilization ability of the biogeographical algorithm, the performance of the processing scheme is improved and balanced. Global optimization capability.

As for the system embodiment, since it basically corresponds to the method embodiment, the description is relatively simple, and for related parts, please refer to part of the description of the method embodiment. The device embodiments described above are only illustrative, and the units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in One place, or it can be distributed to multiple network elements. Part or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. It can be understood and implemented by those skilled in the art without creative effort.

Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be implemented through computer programs to instruct related hardware, and the programs can be stored in computer-readable storage media. During execution, it may include the processes of the embodiments of the above-mentioned methods. Wherein, the storage medium may be a magnetic disk, an optical disk, a read-only memory (Read-Only Memory, ROM) or a random access memory (Random Access Memory, RAM) and the like.

The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the embodiments of the present invention . Therefore, the embodiments of the present invention will not be limited to these embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims (9)

1. A constraint processing method for biogeography optimization algorithms, characterized in that: Improve migration steps: capture individuals selected from the target population; extracting target dimension elements of the selected individual; Based on the individual emigration rate, the target dimension elements of the selected individual are weighted and fused according to the simulated binary crossover operator to generate new elements to be immigrated; Improve the mutation step: update the target subpopulation according to the new element to be immigrated and use the Gaussian distribution for disturbance to obtain the outstanding ones in the target population; Feasibility constraint processing step: determine the outstanding person in the target population and determine the optimal individual, and update the variation parameters with the differential evolution algorithm. 2. the constraint processing method oriented to biogeography optimization algorithm according to claim 1, is characterized in that, the individuality that described capturing is selected from target population comprises: According to the roulette mechanism, two different individuals are randomly selected from the population X. 3. the constraint processing method oriented to biogeography optimization algorithm according to claim 1, is characterized in that, before described improvement migration step, also comprises: Judging the current number of iterations, if it is determined to be less than the set value, then perform feasibility constraint processing, which includes: The target population is sorted according to the individual serial number according to the outstanding person first, and the mapping from the individual fitness value to the number of species is completed; Calculate the in-migration rate and out-migration rate of each individual in the target population to update the existence probability, and calculate the variation parameter. 4. The constraint processing method oriented to biogeography optimization algorithm according to claim 3, characterized in that, judging the current number of iterations, when it is determined to be greater than the set value, the optimal individual and the corresponding adaptation in the output population X degree value and constraint violation degree value. 5. the constraint processing method facing biogeography optimization algorithm according to claim 3, is characterized in that, improving variation step comprises: Correct the individuals that meet the first mutation condition in the target population, calculate the fitness value and total constraint violation value of the new individuals, and save the excellent ones into the first population; For individuals in the target population that meet the second variation condition, compare individuals based on the target population, sub-population, and the first population, and the outstanding ones are stored in the target population. 6. A constraint processing device for biogeography optimization algorithms, characterized in that, Improve the migration module, its configuration is: capture individuals selected from the target population; extracting target dimension elements of the selected individual; Based on the individual emigration rate, the target dimension elements of the selected individual are weighted and fused according to the simulated binary crossover operator to generate new elements to be immigrated; Improve the mutation module, which is configured to update the subpopulation of the target according to the new elements to be immigrated and use Gaussian distribution to perturb, so as to obtain the excellent ones in the target population; The feasibility constraint processing module is configured to determine the outstanding individuals in the target population and determine the optimal individual, and update the variation parameters with a differential evolution algorithm. 7. the constraint processing system facing biogeography optimization algorithm according to claim 6, is characterized in that, also comprises judging module, and it is configured as: Judging the current number of iterations, if it is determined to be less than the set value, then perform feasibility constraint processing, which includes: The target population is sorted according to the individual serial number according to the outstanding person first, and the mapping from the individual fitness value to the number of species is completed; Calculate the in-migration rate and out-migration rate of each individual in the target population to update the existence probability, and calculate the variation parameter. 8. the constraint processing system facing biogeography optimization algorithm according to claim 7, is characterized in that, this judging module also realizes: Judging the current number of iterations, when it is determined to be greater than the set value, output the optimal individual in the population X and the corresponding fitness value and constraint violation value. 9. The constraint processing system oriented to biogeography optimization algorithm according to claim 7, the improved variation module is configured as: Correct the individuals that meet the first mutation condition in the target population, calculate the fitness value and total constraint violation value of the new individuals, and save the excellent ones into the first population; For individuals in the target population that meet the second variation condition, compare individuals based on the target population, sub-population, and the first population, and the outstanding ones are stored in the target population.