CN105095595A - Particle swarm optimization algorithm based on clustering degree of swarm - Google Patents

Abstract

The present invention discloses a particle swarm optimization algorithm based on a clustering degree of a swarm. The algorithm comprises the following steps of carrying out initialization; updating the swarm; judging whether a number of iterations is greater than a preset number of iterations and executing a corresponding step; judging whether a number of update iterations is greater than a preset number of times of stagnation and executing a corresponding step; calculating a particle clustering degree of each particle and a particle clustering degree of a swarm optimal position so as to acquire a distance between each particle and the swarm optimal position; according to a fitness of each particle, selecting a plurality of particles of which the number accords with a swarm scale to form a current swarm; and carrying out iterative optimization and updating until the maximum number of iterations is reached. According to the particle swarm optimization algorithm disclosed by the embodiment of the present invention, different evolutionary strategies can be adopted for different particles according to the progress of the optimizing process and the particle clustering degree so as to reduce the possibility of falling into the local minimum, improve the global searching ability of the algorithm and effectively avoid premature convergence.

Description

Particle swarm algorithm based on population aggregation degree

Technical Field

The invention relates to the technical field of optimization algorithms, in particular to a particle swarm algorithm based on a population clustering degree.

Background

The Particle Swarm Optimization (PSO) algorithm is a typical heuristic bionic algorithm, is derived from simulation of foraging movement behavior of a bird swarm, essentially realizes optimization according to information interaction between individuals and a collective, and is a typical swarm optimization algorithm.

Particle swarm optimization represents a solution of an optimization problem with particles, the corresponding objective function value of which is called the fitness of the particle, and a plurality of particles form a population. Each particle has a position and a speed, and in each iteration, each particle adjusts the position and the flight speed of the particle according to the best position found by the individual and the best position found by the population, so that the whole population continuously moves to a better solution, and the global optimal solution is hopefully reached finally.

The particle swarm algorithm is simple in principle, few in related parameters and easy to implement, but the biggest defect of the particle swarm algorithm is the premature convergence problem, so that the global optimal solution cannot be obtained. Among them, one important reason causing premature convergence of the particle swarm algorithm is: and in the whole evolution process, the guiding function of the optimal position of the population on the flight directions of all the particles is always kept. Although the mode can obtain a faster convergence speed, the population is easy to fall into a local extreme point, the global optimal solution is not favorably searched, particularly, in the later iteration stage, a large number of particles are gathered in a smaller search space, the unity of the whole population is strong, and the optimizing capability of other areas in the space is basically lost.

Disclosure of Invention

The present invention is directed to solving, at least to some extent, one of the technical problems in the related art described above.

Therefore, the invention aims to provide a particle swarm algorithm based on the population clustering degree, which can improve the global search capability of the algorithm and is simple and convenient.

In order to achieve the above object, an embodiment of an aspect of the present invention provides a particle swarm algorithm based on a population clustering degree, including the following steps: s1, initializing the population, wherein pbest is initialized to the current position of the particle, and gbest is initialized to the optimal position of the population; s2, initializing t to 0, t to iteration number, and initializing t _ status to 0, t _ status to update stop number of the population optimal position gbest; s3, initializing Flag _ gbest to 0, where Flag _ gbest to 0 indicates that the best location gbest of the population in the current iteration optimization has not been updated yet, and Flag _ gbest indicates the update times of the best location gbest of the population in the current iteration optimization; s4, updating the population; s5, judging whether the iteration time T is larger than the preset iteration time T, if so, executing a step S11, otherwise, executing a step S6; s6, judging whether the update iteration time T _ status is larger than the preset stagnation time T _ status, if so, executing the step S7, otherwise, executing the step S3; s7, calculating the particle aggregation degree of each particle in the population and the particle aggregation degree of the optimal position gbest of the population; s8, acquiring the distance between each particle and the optimal position gbest of the population according to the particle aggregation degree of each particle in the population; s9, selecting a plurality of particles with the same number as the population size according to the fitness of each particle to form a current population; s10, if Flag _ gbest is 0, setting t _ state to t _ state +1, and executing step S4; and S11, reaching the maximum iteration number and ending.

According to the particle swarm algorithm based on the population aggregation degree, provided by the embodiment of the invention, different evolutionary strategies are adopted for different particles according to the progress of the optimization process and the particle aggregation degree, and under a specific condition, the flight direction of the particles is possibly not guided by the optimal position of the population and even flies to the direction far away from the optimal position of the population, so that the possibility of trapping in a local extreme point is reduced, the global search capability of the algorithm is improved, and premature convergence is effectively avoided.

In addition, the particle swarm algorithm based on the population clustering degree according to the above embodiment of the present invention may further have the following additional technical features:

further, in an embodiment of the present invention, the step S4 further includes: updating the velocity and position of each particle; if the fitness is better than the particle current position pbest, updating the particle current position pbest to a current particle position; and if the fitness of the particles in the population is better than the population optimal position gbest, updating the population optimal position gbest to the current particle position, setting the update stagnation time t _ stop to be 0, Flag _ gbest to be 1, and otherwise t _ stop to be t _ stop + 1.

Further, in an embodiment of the present invention, the step S8 further includes: for a first percentage of particles for which the particles are most aggregated, calculating a distance between the first percentage of particles and the population optimal position gbest, comprising: if the distance between the two particles is smaller than the minimum distance threshold value, performing reverse search on the particle with preset probability; if the distance between the two particles is larger than the maximum distance threshold value, generating a small-scale population by taking the particle as a center particle, performing local search, and then adding a new particle into the whole population; updating pbest of each particle; if the fitness of the particles in the population is better than the optimal population position gbest, updating the optimal population position gbest to a current particle position, setting the update stagnation time t _ status to be 0, and setting Flag _ gbest to be 1; for a second percentage of particles with the smallest particle aggregation, calculating a distance between the second percentage of particles and the population optimal position gbest, including: if the distance between the two particles is smaller than the minimum distance threshold value, generating a small-scale population by taking the particle as a center particle, carrying out local search, and then adding a new particle into the whole population; if the distance between the two is greater than the maximum distance threshold, if the fitness is in the third percentage before the population, generating a small-scale population by taking the particle as a center particle, performing local search, then adding a new particle into the whole population, and if the fitness is in the fourth percentage after the population, directly and randomly generating a new particle to replace the particle; updating pbest of each particle; and if the fitness of the particles in the population is better than the population optimal position gbest, updating the population optimal position gbest to the current particle position, setting the update stagnation time t _ status to be 0, and setting Flag _ gbest to be 1.

Further, in an embodiment of the present invention, the calculating the particle aggregation degree of the population optimal position gbest further includes: if the aDtree _ gbest is smaller than the minimum threshold, generating a small-scale population by taking the optimal position gbest of the population as a central particle, performing local search, and then adding a new particle into the whole population; if the aDgrid _ gbest is larger than the maximum threshold value, calculating the sharing degree between the optimal position gbest of the population and all the particles in the population, randomly selecting a fifth percentage of particles from the particles with the sharing degree larger than 0 to execute reverse flight, and performing local search; updating pbest of each particle; and if the fitness of the particles in the population is better than the population optimal position gbest, updating the population optimal position gbest to the current particle position, setting the update stagnation time t _ status to be 0, and setting Flag _ gbest to be 1.

Further, in one embodiment of the present invention, the velocity of each particle is updated according to the following formula:

$v_{id}^{k+1}={\mathrm{wv}}_{id}^k+c_1{r}_1({\mathrm{pbest}}_{id}-x_{id}^k)+c_2{r}_2({\mathrm{gbest}}_d-x_{id}^k),$

updating the position of each particle according to the following formula:

$x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1},$

wherein w is an inertia factor, c₁、c₂Is a learning factor, r₁、r₂Is [0, 1 ]]A random number in between.

Further, in one embodiment of the present invention, the particle X_iThe degree of aggregation of the particles of (a) is defined by the formula:

<math> <mrow> <mi>a</mi> <mi>D</mi> <mi>g</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>

the particle aggregation degree of the population optimal position gbest is defined as follows:

<math> <mrow> <mi>a</mi> <mi>D</mi> <mi>g</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

further, in one embodiment of the present invention, the particle velocity is amplified when performing a direction search on the particle.

Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.

Drawings

The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:

FIG. 1 is a flow diagram of a particle swarm algorithm based on population clustering according to one embodiment of the invention;

FIG. 2 is a schematic diagram of a particle reverse search according to an embodiment of the present invention.

Detailed Description

Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention.

Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the present invention, "a plurality" means two or more unless specifically defined otherwise.

In the present invention, unless otherwise expressly specified or limited, the terms "mounted," "connected," "secured," and the like are to be construed broadly and can, for example, be fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood by those skilled in the art according to specific situations.

In the present invention, unless otherwise expressly stated or limited, "above" or "below" a first feature means that the first and second features are in direct contact, or that the first and second features are not in direct contact but are in contact with each other via another feature therebetween. Also, the first feature being "on," "above" and "over" the second feature includes the first feature being directly on and obliquely above the second feature, or merely indicating that the first feature is at a higher level than the second feature. A first feature being "under," "below," and "beneath" a second feature includes the first feature being directly under and obliquely below the second feature, or simply meaning that the first feature is at a lesser elevation than the second feature.

A particle swarm algorithm based on the degree of population clustering proposed according to an embodiment of the present invention is described below with reference to the accompanying drawings. Referring to fig. 1, the PSO-AD (particle swarm algorithm based on the population clustering degree) includes the following steps:

and S1, initializing the population, wherein pbest is initialized to the current position of the particle, and gbest is initialized to the optimal position of the population, namely the population is initialized randomly.

S2, initializing t to 0, t to iteration number, and initializing t _ status to 0, t _ status to update stop number of population optimum position gbest.

S3, initializing Flag _ gbest to 0, where Flag _ gbest to 0 indicates that the best location gbest of the population in the current iteration is not updated yet, and Flag _ gbest indicates the update frequency of the best location gbest of the population in the current iteration.

And S4, updating the population.

Further, in an embodiment of the present invention, the step S4 further includes: updating the velocity and position of each particle; if the fitness is better than the current particle position pbest, updating the current particle position pbest to the current particle position; and if the fitness of the particles in the population is better than the optimal population position gbest, updating the optimal population position gbest to the current particle position, setting the update stagnation time t _ status to be 0, setting Flag _ gbest to be 1, and otherwise, setting t _ status to be t _ status + 1.

Further, in one embodiment of the present invention, the velocity of each particle is updated according to the following formula:

$v_{id}^{k+1}={\mathrm{wv}}_{id}^k+c_1{r}_1({\mathrm{pbest}}_{id}-x_{id}^k)+c_2{r}_2({\mathrm{gbest}}_d-x_{id}^k),---\left(1\right)$

the position of each particle is updated according to the following formula:

$x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1},---\left(2\right)$

wherein w is an inertia factor, c₁、c₂Is a learning factor, r₁、r₂Is [0, 1 ]]A random number in between.

S5, judging whether the iteration time T is larger than the preset iteration time T, if so, executing the step S11, otherwise, executing the step S6.

S6, judging whether the update iteration time T _ status is larger than the preset stagnation time T _ status, if yes, executing step S7, otherwise executing step S3. The preset number of times of stagnation may be a maximum number of times of stagnation.

And S7, calculating the particle aggregation degree of each particle in the population and the particle aggregation degree of the optimal position gbest of the population.

Further, in an embodiment of the present invention, calculating the particle aggregation degree of the population optimal position gbest further includes: if the aDtree _ gbest is smaller than the minimum threshold, generating a small-scale population by taking the optimal position of the population gbest as a central particle, performing local search, and then adding a new particle into the whole population; if the aDgrid _ gbest is larger than the maximum threshold value, calculating the sharing degree between the optimal position gbest of the population and all the particles in the population, randomly selecting a fifth percentage of particles from the particles with the sharing degree larger than 0 to execute reverse flight, and performing local search; updating pbest of each particle; and if the fitness of the particles in the population is better than the optimal population position gbest, updating the optimal population position gbest to the current particle position, setting the update stagnation times t _ status to be 0, and setting Flag _ gbest to be 1.

Wherein, in an embodiment of the present invention, the fifth percentage may be 50%.

Further, in one embodiment of the present invention, the particle X_iThe degree of aggregation of the particles of (a) is defined by the formula:

<math> <mrow> <mi>a</mi> <mi>D</mi> <mi>g</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>

the particle aggregation degree of the population optimal position gbest is defined as:

<math> <mrow> <mi>a</mi> <mi>D</mi> <mi>g</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>.</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>

and S8, acquiring the distance between each particle and the optimal position gbest of the population according to the particle aggregation degree of each particle in the population.

Further, in an embodiment of the present invention, the step S8 further includes: for a first percentage of particles with the greatest degree of particle aggregation, calculating a distance between the first percentage of particles and the optimal location of the population, gbest, comprising: if the distance between the two particles is smaller than the minimum distance threshold value, performing reverse search on the particle with preset probability; if the distance between the two particles is larger than the maximum distance threshold value, generating a small-scale population by taking the particle as a center particle, performing local search, and then adding a new particle into the whole population; updating pbest of each particle; if the fitness of the particles in the population is better than the optimal population position gbest, updating the optimal population position gbest to the current particle position, setting the update stagnation time t _ status to be 0, and setting Flag _ gbest to be 1; for the second percentage of particles with the smallest particle aggregation, calculating the distance between the second percentage of particles and the optimal position gbest of the population, including: if the distance between the two particles is smaller than the minimum distance threshold value, generating a small-scale population by taking the particle as a center particle, carrying out local search, and then adding a new particle into the whole population; if the distance between the two is larger than the maximum distance threshold value, if the fitness is in the third percentage before the population, generating a small-scale population by taking the particle as a central particle, performing local search, then adding a new particle into the whole population, and if the fitness is in the fourth percentage after the population, directly and randomly generating a new particle to replace the particle; updating pbest of each particle; and if the fitness of the particles in the population is better than the optimal population position gbest, updating the optimal population position gbest to the current particle position, setting the update stagnation times t _ status to be 0, and setting Flag _ gbest to be 1.

In one embodiment of the present invention, the first percentage may be 10%, the preset probability may be 50%, the second percentage may be 10%, the third percentage may be 10%, and the fourth percentage may be 30%.

Preferably, in one embodiment of the invention, the particle velocity is amplified when performing a direction search on the particle.

Specifically, when performing a reverse search on the particle, the particle velocity is still updated according to equation (1), and according to the analysis, the particle velocity may be small, and in order to increase the probability that the particle will fly out of the local extremum region, the particle velocity is amplified according to equation (5).

$\{\begin{array}{c}{v}_{id}^{k+1}=K_i^{k+1}{v}_{id}^{k+1}\\ K_i^{k+1}=\max \left(0.2\min \left(\frac{V_1^{\max }}{\left|v_{i1}^{k+1}\right|},\frac{V_2^{\max }}{\left|v_{i2}^{k+1}\right|},\mathrm{...},\frac{V_D^{\max }}{\left|v_{iD}^{k+1}\right|}\right),1\right)\end{array},---\left(5\right)$

Wherein,respectively represents the maximum speed and the amplification factor of the particle speed of each dimension of the particleIt is ensured that the particle velocity is at least 0.2 times the maximum velocity without a change in direction.

S9, selecting a plurality of particles with the same number as the population size according to the fitness of each particle to form a current population;

s10, if Flag _ gbest is 0, setting t _ state to t _ state +1, and executing step S4; and

and S11, reaching the maximum iteration number and ending.

Further, in one embodiment of the present invention, the particle position is updated according to equation (6), and the new position and the old position are symmetric about the gbest center.

$x_{id}^{k+1}=2{\mathrm{gbest}}_d-x_{id}^k.---\left(6\right)$

Further, in an embodiment of the present invention, when performing a local search after performing a reverse search on a particle, an update formula of a position and a velocity defining the local search is as follows:

$v_{id}^{k+1}={\mathrm{wv}}_{id}^k+c_1(2r_1-1)({\mathrm{pbest}}_{id}-x_{id}^k)-c_2{r}_2({\mathrm{gbest}}_d-x_{id}^k),---\left(7\right)$

$x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1}.---\left(8\right)$

further, in one embodiment of the present invention, for the population { X }₁,X₂,...,X_N}, define particle X_i＝(x_i1,x_i2,...,x_iD) And X_j＝(x_j1,x_j2,...,x_jD) The distance between them is as in formula (9), defining the particle X_i＝(x_i1,x_i2,...,x_iD) And gbest is as in equation (10).

<math> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>D</mi> </mfrac> <msqrt> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>D</mi> </munderover> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>j</mi> <mi>d</mi> </mrow> </msub> </mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>D</mi> </mfrac> <msqrt> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>D</mi> </munderover> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>gbest</mi> <mi>d</mi> </msub> </mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>.</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

Further, in one embodiment of the present invention, to enhance the search for the peripheral regions of the better performing particles far from the gbest or less aggregated, the particles are respectively used as the center particles, and several new particles are randomly generated around the center particles to join the whole population. The new particle position and velocity initialization formula is shown as formulas (11) and (12), and pbest of the new particle is initialized to the current position of the new particle.

$x_d^{new}=(x_{id}^k-r_{id})+2r_1{r}_{id},---\left(11\right)$

$v_d^{new}=V_d^{\min }+r_2(V_d^{\max }-V_d^{\min }),---\left(12\right)$

Wherein,d-dimensional components of the position and velocity of the new particle, respectively;a d-dimensional component for the selected center particle position; r is_idTo allow the generation of a new particle region, take the radius of r_id＝0.1x_ref,d；Maximum and minimum limit values of d-dimensional speed of the particles respectively; r is₁、r₂Is [0, 1 ]]A random number in between.

In one embodiment of the present invention, when a local search is performed on a newly generated particle, the particle is updated according to equations (1) and (2).

And, in one embodiment of the invention, a particle X is defined_iAnd X_jDegree of sharing of (2), particle X_iThe sharing degrees of gbest and gbest are shown in formulas (13) and (14), respectively.

Wherein σ_shareIs the shared radius. Under this definition, for a particular particle, only particles that fall within the shared radius of the particle contribute to its degree of aggregation, and the closer the distance, the greater the contribution.

In the embodiment of the invention, the optimization process can be accelerated through local updating, so that higher convergence speed is obtained. The calculation example shows that early convergence occurs in the GA and the PSO in the optimizing process, and the PSO-AD can ensure stronger global searching capability by reversely searching and generating new particles far away from the local extreme point, improve the possibility of jumping out of the local extreme point and effectively avoid early convergence.

Details are given below with respect to a specific embodiment.

In one embodiment of the present invention, as shown with reference to fig. 1, an embodiment of the present invention comprises the steps of:

s1, randomly initializing a population. pbest is initialized to the current position of the particle, and gbest is initialized to the position of the optimal particle in the population;

s2, initializing t to be 0, representing the iteration times, initializing t _ status to be 0, and representing the update stagnation times of the optimal position gbest of the population;

s3, initializing a Flag _ gbest to be 0, and representing that the gbest is not updated in the iterative optimization;

s4, updating the population: updating the speed and the position of each particle, updating pbest to the current particle position if the particle fitness is better than pbest, updating gbest to the current particle position if the particle fitness in the population is better than gbest, and setting t _ status to 0, Flag _ gbest to 1, or t _ status to t _ status + 1;

s5, judging whether T is larger than the maximum iteration time T, if so, turning to S13, otherwise, turning to S6;

s6, judging whether T _ state is larger than the maximum stagnation time T _ state, if so, turning to S7, otherwise, turning to S3;

s7, calculating the particle aggregation degree of each particle and the particle aggregation degree of the gbest;

s8, for 10% of particles with the maximum aggregation degree, calculating the distance between the particles and the gbest, and executing the following operations: if the distance between the two particles is smaller than a minimum distance threshold value, performing reverse search on the particles with a probability of 50%, if the distance between the two particles is larger than a maximum distance threshold value, generating a small-scale population by taking the particles as center particles, performing local search, then adding new particles into the whole population, updating pbest of each particle, if the fitness of the particles existing in the population is superior to that of the gbest, updating the gbest to the current position of the particle, setting t _ status to be 0, and setting Flag _ gbest to be 1;

s9, for 10% of particles with the minimum particle aggregation degree, calculating the distance between the particles and the gbest, and executing the following operations: if the distance between the two particles is less than a minimum distance threshold value, generating a small-scale population by taking the particle as a center particle, carrying out local search, then adding a new particle into the whole population, if the distance between the two particles is more than the maximum distance threshold value, if the fitness of the particle is 10% before the population, generating the small-scale population by taking the particle as the center particle, carrying out local search, then adding the new particle into the whole population, if the fitness of the particle is 30% after the population, directly and randomly generating the new particle to replace the particle, updating pbest of each particle, if the fitness of the particle in the population is better than that of the gbest, updating the gbest to the current position of the particle, setting t _ status to 0, and setting Flag _ gbest to 1;

s10, calculating the particle aggregation degree of the gbest, and executing the following operations: if aDgree _ gbest is smaller than a minimum threshold value, generating a small-scale population by taking the gbest as a central particle, carrying out local search, then adding a new particle into the whole population, if the aDgree _ gbest is larger than the maximum threshold value, calculating the sharing degree between the gbest and all the particles in the population, randomly selecting 50% of the particles with the sharing degree larger than 0 to carry out reverse flight, carrying out local search, updating the pbest of each particle, if the fitness of the particles existing in the population is better than that of the gbest, updating the gbest to the current position of the particle, setting t _ status to be 0, and Flag _ gbest to be 1;

s11, randomly selecting a plurality of particles which are consistent with the population scale number according to the wheel roulette mode to form a current population based on the fitness of each particle;

s12, if Flag _ gbest is 0, setting t _ state to t _ state +1, and turning to S4;

and S13, reaching the maximum iteration times and ending.

In step S4, equation (1) is used when the velocity of each particle is updated, and equation (2) is used when the position of each particle is updated.

$v_{id}^{k+1}={\mathrm{wv}}_{id}^k+c_1{r}_1({\mathrm{pbest}}_{id}-x_{id}^k)+c_2{r}_2({\mathrm{gbest}}_d-x_{id}^k),---\left(1\right)$

$x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1},---\left(2\right)$

Wherein, w is inertia factor, and is w ═ w₀-Δw·k；c₁、c₂As a learning factor, there is c₁＝c₂＝2；r₁、r₂Is [0, 1 ]]A random number in between.

In steps S7 and S10, the particle X_iThe degree of aggregation of the particles of (a) is defined by the formula (3):

<math> <mrow> <mi>a</mi> <mi>D</mi> <mi>g</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>.</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>

the particle aggregation degree of the population optimum position gbest is defined as shown in formula (4):

<math> <mrow> <mi>a</mi> <mi>D</mi> <mi>g</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>.</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>

in steps S8 and S10, when the particle is searched reversely, the particle velocity is updated according to equation (1), and according to the analysis, the particle velocity may be small, and in order to increase the possibility that the particle flies out of the local extremum region, the particle velocity is amplified according to equation (5).

$\left\{\begin{array}{c}{v}_{id}^{k+1}=K_i^{k+1}{v}_{id}^{k+1}\\ K_i^{k+1}=\max \left(0.2\min \left(\frac{V_1^{\max }}{\left|v_{i1}^{k+1}\right|},\frac{V_2^{\max }}{\left|v_{i2}^{k+1}\right|},\mathrm{...},\frac{V_D^{\max }}{\left|v_{iD}^{k+1}\right|}\right),1\right)\end{array}\right.,---\left(5\right)$

In the formula,respectively represents the maximum speed and the amplification factor of the particle speed of each dimension of the particleIt is ensured that the particle velocity is at least 0.2 times the maximum velocity without a change in direction. The particle position is updated according to equation (6), and the new position and the old position are symmetric about the gbest center.

$x_{id}^{k+1}=2{\mathrm{gbest}}_d-x_{id}^k.---\left(6\right)$

Further, referring to fig. 2, the flight direction of the new particle is still guided by the original velocity, pbest and gbest, and then the particle position is updated to directly pass the gbest, so that the new particle at this time may fly away from the current local extreme point at a greater velocity to search other areas.

In step S8, when performing a local search after performing a reverse search on a particle, the update formula of the position and velocity defining the local search is as follows:

$v_{id}^{k+1}={\mathrm{wv}}_{id}^k+c_1(2r_1-1)({\mathrm{pbest}}_{id}-x_{id}^k)-c_2{r}_2({\mathrm{gbest}}_d-x_{id}^k),---\left(7\right)$

$x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1}.---\left(8\right)$

in steps S8 and S9, the population { X }is selected₁,X₂,...,X_N}, define particle X_i＝(x_i1,x_i2,...,x_iD) And X_j＝(x_j1,x_j2,...,x_jD) The distance between them is as in formula (9), defining the particle X_i＝(x_i1,x_i2,...,x_iD) And gbest is as in equation (10).

<math> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>D</mi> </mfrac> <msqrt> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>D</mi> </munderover> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>j</mi> <mi>d</mi> </mrow> </msub> </mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>D</mi> </mfrac> <msqrt> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>D</mi> </munderover> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>gbest</mi> <mi>d</mi> </msub> </mrow> <msub> <mi>x</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>f</mi> <mo>,</mo> <mi>d</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <mo>.</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow> </math>

In steps S8, S9, and S10, in order to enhance the search for the peripheral regions of some better-performing particles far away from the gbest or less aggregated, the particles are respectively used as the center particles, and several new particles are randomly generated around the center particles to join the whole population. The new particle position and velocity initialization formula is shown as formulas (11) and (12), and pbest of the new particle is initialized to the current position of the new particle.

$x_d^{new}=(x_{id}^k-r_{id})+2r_1{r}_{id},---\left(11\right)$

$v_d^{new}=V_d^{\min }+r_2(V_d^{\max }-V_d^{\min }),---\left(12\right)$

Wherein,d-dimensional components of the position and velocity of the new particle, respectively;a d-dimensional component for the selected center particle position; r is_idTo allow the generation of a new particle region, take the radius of r_id＝0.1x_ref,d；Maximum and minimum limit values of d-dimensional speed of the particles respectively; r is₁、r₂Is [0, 1 ]]A random number in between.

In steps S8, S9, and S10, when the newly generated particle is locally searched, the particle is updated according to expressions (1) and (2).

In step S10, a particle X is defined_iAnd X_jDegree of sharing of (2), particle X_iThe sharing degrees of gbest and gbest are shown in formulas (13) and (14), respectively.

<math> <mrow> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> <msub> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> <mtd> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>&gt;</mo> <msub> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow> </math>

<math> <mrow> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = '{' close = ''> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <msub> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mtd> <mtd> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&le;</mo> <msub> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>tan</mi> <mi>c</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&gt;</mo> <msub> <mi>&sigma;</mi> <mrow> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow> </math>

Wherein sigma_shareIs the shared radius. Under this definition, for a particular particle, only particles that fall within the shared radius of the particle contribute to its degree of aggregation, and the closer the distance, the greater the contribution.

According to the embodiment of the invention, operations such as reverse search, small-scale generation of new particles, local search and the like are introduced according to the change of the aggregation degree of the population near each particle in the optimization process, so that the strong global search capability is ensured, the possibility of jumping out of a local extreme point is improved, premature convergence is effectively avoided, and the method can be applied to 980 in the optimized scheduling and optimized control of each provincial power system and regional power system in China and has great economic and social benefits.

According to the particle swarm algorithm based on the population aggregation degree, provided by the embodiment of the invention, different evolutionary strategies are adopted for different particles according to the progress of the optimization process and the particle aggregation degree, and under a specific condition, the flight direction of the particles is possibly not guided by the optimal position of the population and even flies to the direction far away from the optimal position of the population, so that the possibility of trapping in a local extreme point is reduced, the global search capability of the algorithm is improved, and premature convergence is effectively avoided.

Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and alternate implementations are included within the scope of the preferred embodiment of the present invention in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present invention.

The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic device) having one or more wires, a portable computer diskette (magnetic device), a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium could even be paper or another suitable medium upon which the program is printed, as the program can be electronically captured, via for instance optical scanning of the paper or other medium, then compiled, interpreted or otherwise processed in a suitable manner if necessary, and then stored in a computer memory.

It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.

It will be understood by those skilled in the art that all or part of the steps carried by the method for implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and when the program is executed, the program includes one or a combination of the steps of the method embodiments.

In addition, functional units in the embodiments of the present invention may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a stand-alone product, may also be stored in a computer readable storage medium.

The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc.

In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made in the above embodiments by those of ordinary skill in the art without departing from the principle and spirit of the present invention.

Claims (7)

1. A particle swarm algorithm based on the population clustering degree is characterized by comprising the following steps:

s1, initializing the population, wherein pbest is initialized to the current position of the particle, and gbest is initialized to the optimal position of the population;

s2, initializing t to 0, t to iteration number, and initializing t _ status to 0, t _ status to update stop number of the population optimal position gbest;

s3, initializing Flag _ gbest to 0, where Flag _ gbest to 0 indicates that the best location gbest of the population in the current iteration optimization has not been updated yet, and Flag _ gbest indicates the update times of the best location gbest of the population in the current iteration optimization;

s4, updating the population;

s5, judging whether the iteration time T is larger than the preset iteration time T, if so, executing a step S11, otherwise, executing a step S6;

s6, judging whether the update iteration time T _ status is larger than the preset stagnation time T _ status, if so, executing the step S7, otherwise, executing the step S3;

s7, calculating the particle aggregation degree of each particle in the population and the particle aggregation degree of the optimal position gbest of the population;

s8, acquiring the distance between each particle and the optimal position gbest of the population according to the particle aggregation degree of each particle in the population;

s9, selecting a plurality of particles with the same number as the population size according to the fitness of each particle to form a current population;

s10, if Flag _ gbest is 0, setting t _ state to t _ state +1, and executing step S4; and

and S11, reaching the maximum iteration number and ending.

2. The particle swarm algorithm based on the population clustering degree of claim 1, wherein the step S4 further comprises:

updating the velocity and position of each particle;

if the fitness is better than the particle current position pbest, updating the particle current position pbest to a current particle position;

and if the fitness of the particles in the population is better than the population optimal position gbest, updating the population optimal position gbest to the current particle position, setting the update stagnation time t _ stop to be 0, Flag _ gbest to be 1, and otherwise t _ stop to be t _ stop + 1.

3. The particle swarm algorithm based on the population clustering degree of claim 2, wherein the step S8 further comprises:

for a first percentage of particles for which the particles are most aggregated, calculating a distance between the first percentage of particles and the population optimal position gbest, comprising:

if the distance between the two particles is smaller than the minimum distance threshold value, performing reverse search on the particle with preset probability;

if the distance between the two particles is larger than the maximum distance threshold value, generating a small-scale population by taking the particle as a center particle, performing local search, and then adding a new particle into the whole population;

updating pbest of each particle;

if the fitness of the particles in the population is better than the optimal population position gbest, updating the optimal population position gbest to a current particle position, setting the update stagnation time t _ status to be 0, and setting Flag _ gbest to be 1;

for a second percentage of particles with the smallest particle aggregation, calculating a distance between the second percentage of particles and the population optimal position gbest, including:

if the distance between the two particles is smaller than the minimum distance threshold value, generating a small-scale population by taking the particle as a center particle, carrying out local search, and then adding a new particle into the whole population;

if the distance between the two is greater than the maximum distance threshold, if the fitness is in the third percentage before the population, generating a small-scale population by taking the particle as a center particle, performing local search, then adding a new particle into the whole population, and if the fitness is in the fourth percentage after the population, directly and randomly generating a new particle to replace the particle;

updating pbest of each particle;

and if the fitness of the particles in the population is better than the population optimal position gbest, updating the population optimal position gbest to the current particle position, setting the update stagnation time t _ status to be 0, and setting Flag _ gbest to be 1.

4. The particle swarm algorithm based on the population clustering degree of claim 3, wherein the calculating the particle clustering degree of the optimal location of the population gbest further comprises:

if the aDtree _ gbest is smaller than the minimum threshold, generating a small-scale population by taking the optimal position gbest of the population as a central particle, performing local search, and then adding a new particle into the whole population;

if the aDgrid _ gbest is larger than the maximum threshold value, calculating the sharing degree between the optimal position gbest of the population and all the particles in the population, randomly selecting a fifth percentage of particles from the particles with the sharing degree larger than 0 to execute reverse flight, and performing local search;

updating pbest of each particle;

and if the fitness of the particles in the population is better than the population optimal position gbest, updating the population optimal position gbest to the current particle position, setting the update stagnation time t _ status to be 0, and setting Flag _ gbest to be 1.

5. The particle swarm algorithm based on the population clustering degree of claim 2,

updating the velocity of each particle according to the following formula:

$v_{id}^{k+1}={\mathrm{wv}}_{id}^k+c_1{r}_1({\mathrm{pbest}}_{id}-x_{id}^k)+c_2{r}_2({\mathrm{gbest}}_d-x_{id}^k),$

updating the position of each particle according to the following formula:

$x_{id}^{k+1}=x_{id}^k+v_{id}^{k+1},$

wherein w is an inertia factor, c₁、c₂Is a learning factor, r₁、r₂Is [0, 1 ]]A random number in between.

6. The particle swarm algorithm based on the population clustering degree of claim 4,

particle X_iThe degree of aggregation of the particles of (a) is defined by the formula:

<math> <mrow> <mi>a</mi> <mi>D</mi> <mi>g</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math>

the particle aggregation degree of the population optimal position gbest is defined as follows:

<math> <mrow> <mi>a</mi> <mi>D</mi> <mi>g</mi> <mi>r</mi> <mi>e</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>s</mi> <mi>h</mi> <mi>a</mi> <mi>r</mi> <mi>e</mi> <mo>_</mo> <mi>g</mi> <mi>b</mi> <mi>e</mi> <mi>s</mi> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>

7. the particle swarm algorithm based on the population clustering degree of claim 4, wherein the particle velocity is amplified when performing a direction search on the particles.