CN105005820A - Target assignment optimizing method based on particle swarm algorithm of population explosion - Google Patents

Abstract

The invention provides a target assignment optimizing method based on a particle swarm algorithm of population explosion, and belongs to the field of intelligent algorithm optimization. In the optimizing method, according to aggregation situation of population in a process of optimization searching, a "population explosion operator" is introduced; divergent treatment of particles is performed under a restricted condition based on partial principles of chaos searching and self-adapting; and parameter adjustment is performed at the same time. The population is prevented against prematurely falling into local optimization, and the problem of target assignment of a battle between intelligent tanks in a virtual battlefield is solved. The method comprises: step 1, performing real number coding of an own side and an opposite side, and generating excellent initial population by utilizing chaos searching; step 2, adjusting initial parameters of the algorithm; step 3, performing iterative optimization searching by adopting the particle swarm algorithm based on the "population explosion operator"; and step 4, ending iteration when the iteration number reaches a set number, and obtaining an optimal scheme. Compared to a method based on an original algorithm, the method increases the total optimization searching ability of particles, and satisfies the requirement of high timeliness.

Description

A kind of Target Assignment optimization method based on population blast particle cluster algorithm

Technical field

The invention belongs to intelligent algorithm and optimize field, particularly relate to a kind of Target Assignment optimization method based on population blast particle cluster algorithm.

Background technology

Target Assignment in virtual battlefield environment is CGF (Computer Generated Forces, CGF) real behavior simulation an importance, Target Assignment is a joint act of many CGF operation entities, and the accuracy of its simulation directly affects other operation behavior of CGF and the authenticity of CGF simulation.

The Research Significance of " Target Assignment " is not only the confidence level that can promote simulated effect in CGF analogue system, gives well " feeling of immersion ".Meanwhile, the research of " Target Assignment " also can play huge effect in actual operation, can be combatant and provides quick, hit scheme efficiently.

In virtual battlefield environment, the Target Assignment of CGF is a very important problem in modern war.But, the increase of exponentially level along with weapon sum and the increase of target sum of its solution space, become a multiparameter, multiple constraint " np complete problem ".Its optimum solution is obtained so can only solve by complete enumerative technique.Obviously be unpractical when larger, therefore must be solved by certain intelligent algorithm.For addressing this problem, people propose many algorithms, such as, and neural net method, genetic algorithm, particle cluster algorithm etc.These algorithms respectively have quality, but also mostly have certain limitation, and such as speed of convergence is comparatively slow, be difficult to realize etc. in practical operation.

Particle cluster algorithm (PSO algorithm) equals nineteen ninety-five proposition by Kennedy the earliest, and this algorithm is subject to the inspiration of flock of birds foraging behavior, and for solving optimization problem.Compare with genetic algorithm, PSO algorithm not only has the global optimizing ability of genetic algorithm, also has stronger local optimal searching ability.Because PSO algorithm concept is simple, realizes easily, fast convergence rate, the advantage PSO such as extensive model can be adapted to be widely used in multiple field.But PSO algorithm is often restrained too fast at the initial stage of search, when there is multiple extreme point in solution space (in the region namely near this point, allocative decision representated by this point is best) time, population is easily converged in Near The Extreme Point, therefore be easily absorbed in locally optimal solution the later stage population of optimizing, cause being difficult to obtain optimum solution.

Summary of the invention

For solving the problem, the invention provides a kind of Target Assignment optimization method based on population blast particle cluster algorithm, it specifically comprises the following steps:

Step 1, one's own side and the other side are all adopted real coding, and the other side is designated as 1,2 ... q ... N, one's own side is designated as 1,2 ... k ... M, then the solution space in searching process is (x ¹, x ²x ⁱx ^m), represent allocative decision, and random generation original allocation scheme, wherein, x ⁱspan be integer between 1 ~ N, x ⁱ=q represents that q the other side distributes to i-th one's own side, and N is the other side's sum, and M is one's own side's sum;

Step 11, random generation first primary the component value that particle position is respectively tieed up belongs to interval (0,1);

Step 12, with first primary X ₁based on, according to $x_{n+1}^i=\left\{\begin{array}{cc}{x}_n^i/0.4& 0<x_n^i\&le;0.4\\ (1-x_n^i)/0.6& 0.4<x_n^i<1\end{array}\right.$ Generate other primaries X ₂~ X _d; Wherein, D is population scale, represent the i-th dimension component of the n-th particle position;

Step 13, by all primary X generated _nby round (X _n× (N-1)+1) round, obtain original allocation scheme, wherein n=1,2 ... D;

Step 2, utilizes formula $\begin{array}{cc}\max & f\left(X_n\right)=\underset{q=1}{\overset{N}{\mathrm{\&Sigma;}}}[t_q\&times;[1-\underset{k=1}{\overset{M}{\mathrm{\&Pi;}}}(1-p_{\mathrm{kq}}\&times;y_{\mathrm{kq}})\left]\right]\end{array}$ Calculate initial population X ₁~ X _din the fitness value of each particle, and the fitness value setting each particle individual optimal solution pbest that to be each particle current; The minimum globally optimal solution gbest as initial population is selected from the individual optimal solution pbest of each particle;

Wherein, t _qbe the threat angle value of q the other side, p _kqfor one's own side k is to the hit rate of the other side q, y _kqvalue be 0 or 1, if 1 one's own side k attacks the other side q, otherwise one's own side k does not attack the other side q;

Step 3, adopts iterative process to carry out optimizing search:

Step 31, if current particle population meets following three conditions simultaneously, then performs step 32; Otherwise, directly perform 35;

1) iterate between current iteration from the m time and keep the sustained iterations of globally optimal solution gbest (t-m) to be greater than the first setting threshold value;

2) set t as current iteration number of times, t is less than the second setting threshold value;

3) the non-conductively-closed of population blast operator, initial population blast operator is defaulted as non-conductively-closed;

Step 32, judges the degree of convergence of particle:

A convergence border c_boundary is calculated by c_boundary=((MaxDT-t)/MaxDT+0.05) × dis_BANG according to current iterations t, and calculate the Euclidean distance DIS of each particle to globally optimal solution gbest, if DIS< restrains border c_boundary, then particle converges on globally optimal solution gbest;

After having judged the degree of convergence of all particles, if perform step 33 when the particle in convergence border c_boundary reaches set amount, otherwise directly perform step 35;

Wherein, maxDT is maximum iteration time, and dis_BANG is constant, represents maximum convergence border;

Step 33, performs step 34 after performing population blast operator, performs population blast operator and comprises:

Step 331, utilize BANG=((MaxDT-t)/MaxDT+0.02) × (N/3)+1 to calculate brisance BANG, wherein, MaxDT is maximum iteration time, and t is current iteration number of times; ,

Step 332, according to calculate the blast direction matrix f of i-th particle _i, then result of calculation is expressed as: rand represent get 0 ~ 1 between an equally distributed random number, represent that the jth dimension of i-th particle will be subject to " gravitation ", represent that the jth dimension of i-th particle will be subject to " repulsion ", described " repulsion " is even if particle is away from the power in globally optimal solution direction; " gravitation " is even if particle is close to the power in globally optimal solution direction;

Step 333, uses v _i+ f _i× BANG upgrades particle rapidity v _i, use X _i+ v _iupgrade particle position X _i;

Step 34, with (w+w_1) × v _i+ c ₁× rand × (pbest-X _i)+(c ₂+ c_2) × rand × (gbest-X _i) upgrade particle rapidity v _i, then perform step 36, wherein w_1 and c_2 is the adjustment parameter introduced, and upgrades after terminating in iteration each time, w_1 w_1+ (-0.3/40) real-time update, c_2 c_2+ (1/40) real-time update;

Wherein, w is the weighted value of speed more new formula Central Plains speed, c ₁, c ₂be respectively the speed more weighted value of locally optimal solution and globally optimal solution in new formula;

Step 35, if do not satisfy condition 3):

Then according to (w+w_1) × v _i+ c ₁× rand × (pbest-X _i)+(c ₂+ c_2) × rand × (gbest-X _i) upgrade particle rapidity v _i, then perform step 36;

If satisfy condition 3):

Then according to w × v _i+ c ₁× rand × (pbest-X _i)+c ₂× rand × (gbest-X _i) upgrade particle rapidity v _i, then perform step 36;

Whether step 36, detect particle rapidity and cross the border: particle rapidity v _ithe value of any one dimension outside [-N/4, N/4], is then crossed the border, otherwise is not crossed the border; If cross the border, the velocity amplitude of this dimension gets boundary value, and speed of not crossing the border is constant; Perform step 37;

Step 37, according to X _i+ v _iupgrade particle position X _i, perform step 38;

Whether step 38, detect particle position and cross the border: the value of any one dimension of particle for outside [1, N], is then crossed the border, otherwise, do not cross the border; If cross the border, the value of this dimension gets the random value near boundary value in certain limit, and do not cross the border invariant position;

Step 39, upgrades globally optimal solution and individual optimal solution

If the fitness of the particle reposition of t iteration generation is less than the fitness of the individual optimal solution pbest of this particle, then the individual optimal solution upgrading this particle is particle reposition, otherwise constant; If the fitness of the individual optimal solution of particle reposition is less than the fitness of globally optimal solution, then replace globally optimal solution with the individual optimal solution of this particle, otherwise constant; Perform step 40 and step 41 simultaneously;

Step 40, if performed population blast operator in current iteration process, then will generate shadow population: the initial position of shadow population is the personal best particle of the particle position that is finished of t-1 iteration or each particle; If do not perform population blast operator in current iteration process, then directly performed step 4;

Carry out interlace operation successively affecting in algebraically t+1 to t+U of operator of population blast, until the t+U time iteration terminates, obtain the globally optimal solution of shadow population;

U is population blast shield amount, and namely t+1 to t+U gives tacit consent to population blast operator is conductively-closed, and is subject to the impact of population blast operator, performs step 42;

Step 41, in t+1 to t+U iteration, virtual population directly performs step 34,36,37,38 and 39, until the t+U time iteration terminates, obtains the globally optimal solution of virtual population, performs step 42;

Step 42, shadow population and virtual population are merged: if the fitness of the globally optimal solution of shadow population is less than the fitness value of the globally optimal solution of virtual population, by the globally optimal solution assignment of shadow population to the globally optimal solution of virtual population, an optional particle simultaneously, the globally optimal solution assignment of shadow population is given the individual optimal solution of this particle, then perform step 4;

Step 4, judges whether the maximum iteration time of population reaches set point number, if reach, iteration terminates, and iteration terminates the final globally optimal solution of rear acquisition virtual population, and this final globally optimal solution is converted to allocative decision; Otherwise return and perform step 3.

Beneficial effect:

Compared to former algorithm, after optimizing, algorithm is by introducing population blast operator, prevents population to be absorbed in locally optimal solution, therefore strengthens the global optimizing ability of algorithm; By introducing shadow population, strengthen the optimizing ability near current global extremum.Therefore, by this optimized algorithm, can greatly increase the probability finding optimum solution.Owing to enhancing global optimizing ability, the possibility obtaining inferior solution (solution that fitness is obviously poor) also reduces greatly.

Realize simple, the time cost (time namely increased on former algorithm time basis) of Optimum Operation is lower.Only introduce several parameter in this method, calculated amount is few, and performing the population blast time complexity of operator and basic particle group algorithm, to perform the time complexity that generation optimizing operates identical; Every generation of shadow population upgrades also identical with the time complexity that the optimizing of an execution generation operates.Due to the restriction effect to population blast operator, population blast operator can not be performed frequently, the requirement of high real-time can be met.

Accompanying drawing explanation

Fig. 1 a is 6 × 5 scale result figure of the present invention;

Fig. 1 b is 10 × 10 scale result figure of the present invention;

Fig. 1 c is 15 × 20 scale result figure of the present invention.

Embodiment

Target Assignment optimization method based on population blast particle cluster algorithm of the present invention, it comprises:

Step 1, one's own side and the other side are all adopted real coding, and the other side is designated as 1,2 ... q ... N, one's own side is designated as 1,2 ... k ... M, then the solution space in searching process is (x ¹, x ²x ⁱx ^m), represent allocative decision, and random generation original allocation scheme, wherein, x ⁱspan be integer between 1 ~ N, x ⁱ=q represents that q the other side distributes to i-th one's own side, and N is the other side's sum, and M is one's own side's sum;

Step 11, random generation first primary the component value that particle position is respectively tieed up belongs to interval (0,1);

Step 12, with first primary X ₁based on, according to $x_{n+1}^i=\left\{\begin{array}{cc}{x}_n^i/0.4& 0<x_n^i\&le;0.4\\ (1-x_n^i)/0.6& 0.4<x_n^i<1\end{array}\right.$ Generate other primaries X ₂~ X _d; Wherein, D is population scale, represent the i-th dimension component of the n-th particle position;

Step 13, by all primary X generated _nby round (X _n× (N-1)+1) round, obtain original allocation scheme, wherein n=1,2 ... D;

Step 2, utilizes formula $\begin{array}{cc}\max & f\left(X_n\right)=\underset{q=1}{\overset{N}{\mathrm{\&Sigma;}}}[t_q\&times;[1-\underset{k=1}{\overset{M}{\mathrm{\&Pi;}}}(1-p_{\mathrm{kq}}\&times;y_{\mathrm{kq}})\left]\right]\end{array}$ Calculate initial population X ₁~ X _din the fitness value of each particle, and the fitness value setting each particle individual optimal solution pbest that to be each particle current; The minimum globally optimal solution gbest as initial population is selected from the individual optimal solution pbest of each particle;

Wherein, t _qbe the threat angle value of q the other side, p _kqfor one's own side k is to the hit rate of the other side q, y _kqvalue be 0 or 1, if 1 one's own side k attacks the other side q, otherwise one's own side k does not attack the other side q;

Step 3, adopts iterative process to carry out optimizing search:

Step 31, if current particle population meets following three conditions simultaneously, then performs step 32; Otherwise, directly perform 35;

1) iterate between current iteration from the m time and keep the sustained iterations of globally optimal solution gbest (t-m) to be greater than the first setting threshold value;

2) set t as current iteration number of times, t is less than the second setting threshold value;

3) the non-conductively-closed of population blast operator, initial population blast operator is defaulted as non-conductively-closed;

Step 32, judges the degree of convergence of particle:

A convergence border c_boundary is calculated by c_boundary=((MaxDT-t)/MaxDT+0.05) × dis_BANG according to current iterations t, and calculate the Euclidean distance DIS of each particle to globally optimal solution gbest, if DIS< restrains border c_boundary, then particle converges on globally optimal solution gbest;

After having judged the degree of convergence of all particles, if perform step 33 when the particle in convergence border c_boundary reaches set amount, otherwise directly perform step 35;

Wherein, maxDT is maximum iteration time, and dis_BANG is constant, represents maximum convergence border;

Step 33, performs step 34 after performing population blast operator, performs population blast operator and comprises:

Step 331, utilize BANG=((MaxDT-t)/MaxDT+0.02) × (N/3)+1 to calculate brisance BANG, wherein, MaxDT is maximum iteration time, and t is current iteration number of times; ,

Step 332, according to calculate the blast direction matrix f of i-th particle _i, then result of calculation is expressed as: rand represent get 0 ~ 1 between an equally distributed random number, represent that the jth dimension of i-th particle will be subject to " gravitation ", represent that the jth dimension of i-th particle will be subject to " repulsion ", described " repulsion " is even if particle is away from the power in globally optimal solution direction; " gravitation " is even if particle is close to the power in globally optimal solution direction;

Step 333, uses v _i+ f _i× BANG upgrades particle rapidity v _i, use X _i+ v _iupgrade particle position X _i;

Step 34, with (w+w_1) × v _i+ c ₁× rand × (pbest-X _i)+(c ₂+ c_2) × rand × (gbest-X _i) upgrade particle rapidity v _i, then perform step 36, wherein w_1 and c_2 is the adjustment parameter introduced, and upgrades after terminating in iteration each time, w_1 w_1+ (-0.3/40) real-time update, c_2 c_2+ (1/40) real-time update;

Wherein, w is the weighted value of speed more new formula Central Plains speed, c ₁, c ₂be respectively the speed more weighted value of locally optimal solution and globally optimal solution in new formula;

Step 35, if do not satisfy condition 3):

Then according to (w+w_1) × v _i+ c ₁× rand × (pbest-X _i)+(c ₂+ c_2) × rand × (gbest-X _i) upgrade particle rapidity v _i, then perform step 36;

If satisfy condition 3):

Then according to w × v _i+ c ₁× rand × (pbest-X _i)+c ₂× rand × (gbest-X _i) upgrade particle rapidity v _i, then perform step 36;

Whether step 36, detect particle rapidity and cross the border: particle rapidity v _ithe value of any one dimension outside [-N/4, N/4], is then crossed the border, otherwise is not crossed the border; If cross the border, the velocity amplitude of this dimension gets boundary value, and speed of not crossing the border is constant; Perform step 37;

Step 37, according to X _i+ v _iupgrade particle position X _i, perform step 38;

Whether step 38, detect particle position and cross the border: the value of any one dimension of particle for outside [1, N], is then crossed the border, otherwise, do not cross the border; If cross the border, the value of this dimension gets the random value near boundary value in certain limit, and do not cross the border invariant position;

Step 39, upgrades globally optimal solution and individual optimal solution

If the fitness of the particle reposition of t iteration generation is less than the fitness of the individual optimal solution pbest of this particle, then the individual optimal solution upgrading this particle is particle reposition, otherwise constant; If the fitness of the individual optimal solution of particle reposition is less than the fitness of globally optimal solution, then replace globally optimal solution with the individual optimal solution of this particle, otherwise constant; Perform step 40 and step 41 simultaneously;

Step 40, if performed population blast operator in current iteration process, then will generate shadow population: the initial position of shadow population is the personal best particle of the particle position that is finished of t-1 iteration or each particle; If do not perform population blast operator in current iteration process, then directly performed step 4;

Carry out interlace operation successively affecting in algebraically t+1 to t+U of operator of population blast, until the t+U time iteration terminates, obtain the globally optimal solution of shadow population;

U is population blast shield amount, and namely t+1 to t+U gives tacit consent to population blast operator is conductively-closed, and is subject to the impact of population blast operator, performs step 42;

Step 41, in t+1 to t+U iteration, virtual population directly performs step 34,36,37,38 and 39, until the t+U time iteration terminates, obtains the globally optimal solution of virtual population, performs step 42;

Step 42, shadow population and virtual population are merged: if the fitness of the globally optimal solution of shadow population is less than the fitness value of the globally optimal solution of virtual population, by the globally optimal solution assignment of shadow population to the globally optimal solution of virtual population, an optional particle simultaneously, the globally optimal solution assignment of shadow population is given the individual optimal solution of this particle, then perform step 4;

Step 4, judges whether the maximum iteration time of population reaches set point number, if reach, iteration terminates, and iteration terminates the final globally optimal solution of rear acquisition virtual population, and this final globally optimal solution is converted to allocative decision; Otherwise return and perform step 3.

For further illustrating above-mentioned algorithm, the improve PSO algorithm (M-PSO) that the present invention uses is emulated on target assignment problem with standard particle group algorithm (PSO).Consider 6 × 5 respectively, 10 × 10 and 15 × 20 3 kinds of scales, i.e. 65, friend side enemies, 10 10, friend side enemies, 15 20, friend side enemies, three kinds of scales.

C in 6 × 5 scales ₁=c ₂=2, w=0.7289, population scale is 50, and evolutionary generation is 1000; C in 10 × 10 scales ₁=c ₂=2, w=0.7289, population scale is 50, and evolutionary generation is 1000; C in 15 × 20 scales ₁=c ₂=2, w=0.7289, population scale is 50, and evolutionary generation is 1000.Carry out 30 experiments respectively, the Contrast on effect of certain experiment of random selecting two kinds of algorithms is as shown in Fig. 1 a to Fig. 1 c, and in 30 experiments, average effect result is as follows:

As can be seen from this result, after improving, algorithm relative standard particle cluster algorithm performance has good lifting, especially when scale is less, the performance boost of this optimized algorithm is remarkable.According to force search result, under 6 × 5 scales, 0.29295 is optimal value; Under 10 × 10 scales, 0.76350 is optimal value.When larger, although be difficult to find optimal value again, optimized algorithm still can the optimizing ability of the former algorithm of larger lifting.This optimized algorithm can make optimal time increase on a small quantity, but spent time still meets scene requirement.Therefore, this algorithm can obtain better effect compared to original algorithm, has good practical value.

Certainly; the present invention also can have other various embodiments; when not deviating from the present invention's spirit and essence thereof; those of ordinary skill in the art are when making various corresponding change and distortion according to the present invention, but these change accordingly and are out of shape the protection domain that all should belong to the claim appended by the present invention.

Claims (1)

1., based on a Target Assignment optimization method for population blast particle cluster algorithm, it is characterized in that, comprising:

Step 1, one's own side and the other side are all adopted real coding, and the other side is designated as 1,2 ... q ... N, one's own side is designated as 1,2 ... k ... M, then the solution space in searching process is (x ¹, x ²x ⁱx ^m), represent allocative decision, and random generation original allocation scheme, wherein, x ⁱspan be integer between 1 ~ N, x ⁱ=q represents that q the other side distributes to i-th one's own side, and N is the other side's sum, and M is one's own side's sum;

Step 11, random generation first primary the component value that particle position is respectively tieed up belongs to interval (0,1);

Step 12, with first primary X ₁based on, according to generate other primaries X ₂~ X _d; Wherein, D is population scale, represent the i-th dimension component of the n-th particle position;

Step 13, by all primary X generated _nby round (X _n× (N-1)+1) round, obtain original allocation scheme, wherein n=1,2 ... D;

Step 2, utilizes formula calculate initial population X ₁~ X _din the fitness value of each particle, and the fitness value setting each particle individual optimal solution pbest that to be each particle current; The minimum globally optimal solution gbest as initial population is selected from the individual optimal solution pbest of each particle;

Wherein, t _qbe the threat angle value of q the other side, p _kqfor one's own side k is to the hit rate of the other side q, y _kqvalue be 0 or 1, if 1 one's own side k attacks the other side q, otherwise one's own side k does not attack the other side q;

Step 3, adopts iterative process to carry out optimizing search:

Step 31, if current particle population meets following three conditions simultaneously, then performs step 32; Otherwise, directly perform 35;

1) iterate between current iteration from the m time and keep the sustained iterations of globally optimal solution gbest (t-m) to be greater than the first setting threshold value;

2) set t as current iteration number of times, t is less than the second setting threshold value;

3) the non-conductively-closed of population blast operator, initial population blast operator is defaulted as non-conductively-closed;

Step 32, judges the degree of convergence of all particles:

A convergence border c_boundary is calculated by c_boundary=((MaxDT-t)/MaxDT+0.05) × dis_BANG according to current iterations t, and calculate the Euclidean distance DIS of each particle to globally optimal solution gbest, if DIS < restrains border c_boundary, then particle converges on globally optimal solution gbest;

After having judged the degree of convergence of all particles, if perform step 33 when the particle in convergence border c_boundary reaches set amount, otherwise directly perform step 35;

Wherein, maxDT is maximum iteration time, and dis_BANG is constant, represents maximum convergence border;

Step 33, performs step 34 after performing population blast operator, performs population blast operator and comprises:

Step 331, utilize BANG=((MaxDT-t)/MaxDT+0.02) × (N/3)+1 to calculate brisance BANG, wherein, MaxDT is maximum iteration time, and t is current iteration number of times; ,

Step 332, according to calculate the blast direction matrix f of i-th particle _i, then result of calculation is expressed as: rand represent get 0 ~ 1 between an equally distributed random number, represent that the jth dimension of i-th particle will be subject to " gravitation ", represent that the jth dimension of i-th particle will be subject to " repulsion ", described " repulsion " is even if particle is away from the power in globally optimal solution direction; " gravitation " is even if particle is close to the power in globally optimal solution direction;

Step 333, uses v _i+ f _i× BANG upgrades particle rapidity v _i, use X _i+ v _iupgrade particle position X _i;

Step 34, with (w+w_1) × v _i+ c ₁× rand × (pbest-X _i)+(c ₂+ c_2) × rand × (gbest-X _i) upgrade particle rapidity v _i, then perform step 36, wherein w_1 and c_2 is the adjustment parameter introduced, and upgrades after terminating in iteration each time, w_1 w_1+ (-0.3/40) real-time update, c_2 c_2+ (1/40) real-time update;

Wherein, w is the weighted value of speed more new formula Central Plains speed, c ₁, c ₂be respectively the speed more weighted value of locally optimal solution and globally optimal solution in new formula;

Step 35, if do not satisfy condition 3):

Then according to (w+w_1) × v _i+ c _i× rand × (pbest-X _i)+(c ₂+ c_2) × rand × (gbest-X _i) upgrade particle rapidity v _i, then perform step 36;

If satisfy condition 3):

Then according to w × v _i+ c ₁× rand × (pbest-X _i)+c ₂× rand × (gbest-X _i) upgrade particle rapidity v _i, then perform step 36;

Whether step 36, detect particle rapidity and cross the border: particle rapidity v _ithe value of any one dimension outside [-N/4, N/4], is then crossed the border, otherwise is not crossed the border; If cross the border, the velocity amplitude of this dimension gets boundary value, and speed of not crossing the border is constant; Perform step 37;

Step 37, according to X _i+ v _iupgrade particle position X _i, perform step 38;

Whether step 38, detect particle position and cross the border: the value of any one dimension of particle for outside [1, N], is then crossed the border, otherwise, do not cross the border; If cross the border, the value of this dimension gets the random value near boundary value in certain limit, and do not cross the border invariant position;

Step 39, upgrades globally optimal solution and individual optimal solution

If the fitness of the particle reposition of t iteration generation is less than the fitness of the individual optimal solution pbest of this particle, then the individual optimal solution upgrading this particle is particle reposition, otherwise constant; If the fitness of the individual optimal solution of particle reposition is less than the fitness of globally optimal solution, then replace globally optimal solution with the individual optimal solution of this particle, otherwise constant; Perform step 40 and step 41 simultaneously;

Step 40, if performed population blast operator in current iteration process, then will generate shadow population: the initial position of shadow population is the personal best particle of the particle position that is finished of t-1 iteration or each particle; If do not perform population blast operator in current iteration process, then directly performed step 4;

Carry out interlace operation successively affecting in algebraically t+1 to t+U of operator of population blast, until the t+U time iteration terminates, obtain the globally optimal solution of shadow population;

U is population blast shield amount, and namely t+1 to t+U gives tacit consent to population blast operator is conductively-closed, and is subject to the impact of population blast operator, performs step 42;

Step 41, in t+1 to t+U iteration, virtual population directly performs step 34,36,37,38 and 39, until the t+U time iteration terminates, obtains the globally optimal solution of virtual population, performs step 42;

Step 42, shadow population and virtual population are merged: if the fitness of the globally optimal solution of shadow population is less than the fitness value of the globally optimal solution of virtual population, by the globally optimal solution assignment of shadow population to the globally optimal solution of virtual population, an optional particle simultaneously, the globally optimal solution assignment of shadow population is given the individual optimal solution of this particle, then perform step 4;

Step 4, judges whether the maximum iteration time of population reaches set point number, if reach, iteration terminates, and iteration terminates the final globally optimal solution of rear acquisition virtual population, and this final globally optimal solution is converted to allocative decision; Otherwise return and perform step 3.