CN102222266B - Normal cloud model-based moonlet cost optimization design method - Google Patents

Abstract

和k步时的位置

计算每个粒子k+1步的位置六、计算k+1步每个粒子pⁱ的自身最优位置和粒子群整体的最优位置G_k+1；七、比较k+1步粒子群整体的最优位置G_k+1的小卫星成本C(G_k+1)与k步粒子群整体的最优位置G_k的小卫星成本C(G_k)差的绝对值。本发明用于小卫星成本的计算。A small satellite cost optimization design method based on a normal cloud model, which involves a small satellite cost optimization method to solve the problem that the existing satellite cost optimization method uses an optimization algorithm based on gradient information, which requires high continuity of functions , slow convergence, unguaranteed stability, and low computational efficiency. Methods: 1. Establish an optimization model for the cost C of the small satellite; 2. Set the optimal design variable for the cost C of the small satellite; 4. Assuming that the optimization algorithm has completed k (k ≥ 1) steps, calculate the speed of k+1 steps of each particle; 5. Use the speed of particles k+1 steps

and the position at k steps

Calculate the position of each particle k+1 steps Sixth, calculate the optimal position of each particle p ⁱ in step k+1 and the optimal position G _k+1 of the overall particle swarm; Seventh, compare the small satellite cost C(G _{k+1 ) of the optimal position G k+ 1} of the overall optimal position of the particle swarm at k+1 steps with the optimal position of the overall k-step particle swarm The absolute value of the small satellite cost C(G _k ) difference at the optimal position G _k . The invention is used for calculating the cost of small satellites.

Description

A kind of cost optimization of moonlet based on normal cloud model method for designing

Technical field

The present invention relates to a kind of moonlet Cost Optimization Approach, be specifically related to a kind of particle swarm optimization algorithm of based on normal cloud model, constructing and optimize the cost of satellite.

Background technology

Moonlet generally is applied in communication, remote sensing, navigation and space science field, design of satellites is the design process of a multidisciplinary coupling, complexity, in design process, variation to design parameter is more responsive, in the design optimization problem of satellite, mainly face following difficulty: 1, the design optimization problem had both comprised continuous optimized variable, comprise again the discrete optimization variable, it is a hybrid variable optimization problem that comprises continuous variable and discrete variable, traditional efficiency of the Optimization Method based on gradient information is low, is not easy to obtain globally optimal solution; 2, the design of satellites optimization problem relates to a plurality of subjects, and stronger coupling is arranged between subject, and traditional optimized algorithm is difficult to process the coupling of design of satellites optimization problem, and convergence is difficult to guarantee; 3, due to the complicacy of design of satellites optimization problem, cause design error along with the carrying out of optimizing constantly accumulates, affected the precision and stability of optimum results.Therefore, design has improperly increased the cost of design of satellites, has reduced design efficiency, and the risk of mission failure is even arranged.In order to better meet the demand of design at detailed design phase, improve specific aim, the planned and efficiency of design, be necessary to design an efficient optimized algorithm cost of satellite is optimized calculating.The optimized algorithm that is based on gradient information that traditional satellite cost optimized algorithm adopts, the advantage of this algorithm is that the direction of algorithm convergence can be controlled, and its shortcoming is high to continuity of a function requirement, and convergence is slow, stability can not be guaranteed, easily be absorbed in local optimum point, and counting yield is low.

Summary of the invention

The objective of the invention is in order to solve the optimized algorithm of existing satellite cost optimization method employing based on gradient information, this algorithm requires high to the continuity of a function, convergence is slow, stability can not be guaranteed, easily be absorbed in local optimum point, the problem that counting yield is low, provide a kind of cost optimization of moonlet based on normal cloud model method for designing.

A kind of cost optimization of moonlet based on normal cloud model method for designing of the present invention realizes by following steps:

Step 1, set up moonlet cost C Optimized model: moonlet cost C comprises the cost C of satellite system _s, ground system cost C _gWith launch cost C _f, use C=C _s+ C _g+ C _fCalculate;

Step 2, set the optimal design variable of moonlet cost C: the optimal design variable of moonlet cost C comprises seven optimal design variablees altogether, is respectively the bottom surface radius, satellite altitude, the type of solar cell, type and the duty cycle of accumulator of charge-coupled device camera focal length, orbit altitude, cylindrical shape satellite;

Step 3, seven optimal design variablees in step 2 are carried out the initialization assignment: each particle p ⁱExpression, the population scale is elected 30 as, generates at random each particle p ⁱInitial position

And initial velocity

Wherein $x_0^i=(x_0^{i1},x_0^{i2},x_0^{i3},x_0^{i4},x_0^{i5},x_0^{i6},x_0^{i7}),$ In formula

With

The bottom surface radius, satellite altitude, the type of solar cell, the type of accumulator and the initial value of duty cycle that represent respectively charge-coupled device camera focal length, orbit altitude, cylindrical shape satellite, wherein

In formula

With

Expression respectively

With

Corresponding speed initial value,

Utilize two pairs of population of formula one and formula to carry out the initialization assignment:

Formula one: $x_0^{\mathrm{ij}}=x_{\min }+s_1(x_{\max }-x_{\min })(j=\mathrm{1,2},...,7)$

Formula two: $v_0^{\mathrm{ij}}=\frac{x_{\min }+s_2(x_{\max }-x_{\min })}{\mathrm{\Δt}}(j=\mathrm{1,2},...,7)$

In formula one and formula two, S ₁And S ₂The random number between 0,1, x _minThe lower limit of design variable value, x _maxIt is the upper limit of design variable value;

Each particle p ⁱSelf optimal location L ⁱRepresent L ⁱInitial value

The optimal location of whole population particle represents with G, the initial value G of G ₀According to following step assignment:

A, calculating population are that 30 particles are at each particle self optimal location

Corresponding satellite cost

B, 30 moonlet costs of comparison

Size, filter out wherein minimum moonlet cost, suppose that minimum moonlet cost is The particle corresponding with it is p ^m, corresponding particle p ^mSelf optimal location be

Step 4, suppose that optimized algorithm completed k (k 〉=1) step, below calculate the speed in the k+1 step of each particle:

Suppose that algorithm calculates k (k 〉=1) during the step, each the particle p that has obtained ⁱSelf optimal location be

The optimal location of population integral body is G _k, each particle p ⁱPosition when k goes on foot

For:

Speed

For: $v_k^i=(v_k^{i1},v_k^{i2},...,v_k^{i7});$

When k+1 goes on foot, each particle p ⁱIn the k+1 speed in step

Calculate according to formula three, four, five:

Formula three: $v_{k+1}^{\mathrm{ij}}={\mathrm{\ωv}}_k^{\mathrm{ij}}+\frac{c_1{\mathrm{CP}}_k^{\mathrm{ij}}}{\mathrm{\Δt}}+\frac{c_2{\mathrm{CP}}_{\mathrm{gk}}^{\mathrm{ij}}}{\mathrm{\Δt}}$

Formula four: ${\mathrm{CP}}_k^{\mathrm{ij}}=\mathrm{cloud}(L_k^{\mathrm{ij}}-x_k^{\mathrm{ij}},E_n,H_e)$

Formula five: ${\mathrm{CP}}_{\mathrm{gk}}^{\mathrm{ij}}=\mathrm{cloud}(G_k^j-x_k^{\mathrm{ij}},E_n,H_e)$

Parameter ω in formula three is inertial coefficient, c ₁And c ₂For confidence factor, inertial coefficient ω span is [0.8,1.2], confidence factor c ₁And c ₂Span be [0,2];

In the k step, by the particle p of cloud model generation ⁱCurrent location

With respect to it self current optimal location Relative distance;

In the k step, by the particle p of cloud model generation ⁱCurrent location

Optimal location G with respect to whole population _kRelative distance, E _nThe entropy coefficient of cloud model, H _eThe super entropy coefficient of cloud model, E in optimizing process _nAnd H _eAll get the constant greater than zero, its E _nAnd H _eValue need to meet formula six:

Formula six: ${E_n}^2+{H_e}^2<\frac{1}{3}\min \{L_k^{\mathrm{ij}}-x_k^{\mathrm{ij}},G_k^j-x_k^{\mathrm{ij}}\}$

Normal cloud model cloud (E _x, E _n, H _e) computing method as follows:

Formula seven: E ' _n=randn (E _n, H _e)

Formula eight: cloud (E _x, E _n, H _e)=randn (E _x, E ' _n)

Wherein, E ' _nFor the intermediate variable in computation process, randn (E _n, H _e) expression generation E _nFor expectation, H _eFor variance with normal random number; Randn (E _x, E ' _n) represent to generate with E ' _nFor expectation, H _eFor variance with normal random number;

Step 5, the speed of utilizing particle k+1 to go on foot Position while with k, going on foot

Calculate the position in each particle k+1 step

Utilize present speed

With nine positions of upgrading each particle by formula, original position

Formula nine: $x_{k+1}^{\mathrm{ij}}=x_k^{\mathrm{ij}}+v_{k+1}^{\mathrm{ij}}(i=\mathrm{1,2},...,30;j=\mathrm{1,2},...,7)$

Step 6, calculating k+1 go on foot each particle p ⁱSelf optimal location Optimal location G with population integral body _k+1:

Each particle p ⁱSelf optimal location

By formula ten calculate:

Formula ten: $L_{k+1}^i=\begin{array}{}\end{array}\left\{\begin{array}{cc}{L}_k^i& C\left(L_k^i\right)\&le;C\left(x_{k+1}^i\right)\\ x_{k+1}^i& C\left(L_k^i\right)>C\left(x_{k+1}^i\right)\end{array}\right.$

The optimal location G of population integral body _k+1Computation process as follows:

Calculating k+1 each particle self optimal location during the step

Corresponding moonlet cost

Filter out wherein minimum moonlet cost, suppose that minimum moonlet cost is

Corresponding optimal location is

G _k+1By formula 11 calculate:

Formula 11 $G_{k+1}=\left\{\begin{array}{cc}{G}_k& C\left(G_k\right)\&le;C\left(L_{k+1}^s\right)\\ L_{k+1}^s& C\left(G_k\right)>C\left(L_{k+1}^s\right)\end{array}\right.$

The optimal location G of step 7, comparison k+1 step population integral body _k+1Moonlet cost C (G _k+1) with the optimal location G of k step population integral body _kMoonlet cost C (G _k) poor absolute value: if | C (G _k+1)-C (G _k) |＜0.01, algorithm is restrained, and optimizes and finishes, G _k+1The optimum solution of trying to achieve exactly, if | C (G _k+1)-C (G _k) | 〉=0.01, not convergence of algorithm, the G that the k+1 step is asked _k+1Not optimum solution, come back to step 4,, according to step 4～step 6, obtain according to k+1 step

And G _k+1The calculating k+2 step

And G _k+2, until the absolute value of difference of moonlet cost corresponding to population optimal locations that meets adjacent two steps is less than 0.01.

The present invention has following beneficial effect:

The present invention is directed to this structure of satellite cost Optimized model, particle swarm optimization algorithm based on normal cloud model has been proposed, when having solved in the satellite cost optimal design hybrid variable that not only comprises continuous variable but also comprise discrete variable and optimize convergence is slow, the problem that precision is not high.The inventive method is to build on the basis of normal cloud model, has inherited the determinacy and the characteristic that randomness merges mutually of cloud model, has improved speed of convergence and the Global Optimality of optimized algorithm, and is faster than traditional algorithm convergence based on gradient information, precision is high.

Embodiment

Embodiment one: present embodiment realizes by following steps:

Step 1, set up moonlet cost C Optimized model: moonlet cost C comprises the cost C of satellite system _s, ground system cost C _gWith launch cost C _f, use C=C _s+ C _g+ C _fCalculate;

Step 2, set the optimal design variable of moonlet cost C: the optimal design variable of moonlet cost C comprises seven optimal design variablees altogether, is respectively the bottom surface radius, satellite altitude, the type of solar cell, type and the duty cycle of accumulator of charge-coupled device camera focal length, orbit altitude, cylindrical shape satellite;

Step 3, seven optimal design variablees in step 2 are carried out the initialization assignment: each particle p ⁱExpression, the population scale is elected 30 as, generates at random each particle p ⁱInitial position

And initial velocity

Wherein $x_0^i=(x_0^{i1},x_0^{i2},x_0^{i3},x_0^{i4},x_0^{i5},x_0^{i6},x_0^{i7}),$ In formula

With The bottom surface radius, satellite altitude, the type of solar cell, the type of accumulator and the initial value of duty cycle that represent respectively charge-coupled device camera focal length, orbit altitude, cylindrical shape satellite, wherein

In formula

With

Expression respectively

With

Corresponding speed initial value,

Utilize two pairs of population of formula one and formula to carry out the initialization assignment:

Formula one: $x_0^{\mathrm{ij}}=x_{\min }+s_1(x_{\max }-x_{\min })(j=\mathrm{1,2},...,7)$

Formula two: $v_0^{\mathrm{ij}}=\frac{x_{\min }+s_2(x_{\max }-x_{\min })}{\mathrm{\&Delta;t}}(j=\mathrm{1,2},...,7)$

In formula one and formula two, S ₁And S ₂The random number between 0,1, x _minThe lower limit of design variable value, x _maxIt is the upper limit of design variable value;

Each particle p ⁱSelf optimal location L ⁱRepresent L ⁱInitial value

The optimal location of whole population particle represents with G, the initial value G of G ₀According to following step assignment:

A, calculating population are that 30 particles are at each particle self optimal location

Corresponding satellite cost

B, 30 moonlet costs of comparison

Size, filter out wherein minimum moonlet cost, suppose that minimum moonlet cost is

The particle corresponding with it is p ^m, corresponding particle p ^mSelf optimal location be

Step 4, suppose that optimized algorithm completed k (k 〉=1) step, below calculate the speed in the k+1 step of each particle:

Suppose that algorithm calculates k (k 〉=1) during the step, each the particle p that has obtained ⁱSelf optimal location be

The optimal location of population integral body is G _k, each particle p ⁱPosition when k goes on foot

For:

Speed

For: $v_k^i=(v_k^{i1},v_k^{i2},...,v_k^{i7});$

When k+1 goes on foot, each particle p ⁱIn the k+1 speed in step

Calculate according to formula three, four, five:

Formula three: $v_{k+1}^{\mathrm{ij}}={\mathrm{\&omega;v}}_k^{\mathrm{ij}}+\frac{c_1{\mathrm{CP}}_k^{\mathrm{ij}}}{\mathrm{\&Delta;t}}+\frac{c_2{\mathrm{CP}}_{\mathrm{gk}}^{\mathrm{ij}}}{\mathrm{\&Delta;t}}$

Formula four: ${\mathrm{CP}}_k^{\mathrm{ij}}=\mathrm{cloud}(L_k^{\mathrm{ij}}-x_k^{\mathrm{ij}},E_n,H_e)$

Formula five: ${\mathrm{CP}}_{\mathrm{gk}}^{\mathrm{ij}}=\mathrm{cloud}(G_k^j-x_k^{\mathrm{ij}},E_n,H_e)$

Parameter ω in formula three is inertial coefficient, c ₁And c ₂For confidence factor, inertial coefficient ω span is [0.8,1.2], confidence factor c ₁And c ₂Span be [0,2];

In the k step, by the particle p of cloud model generation ⁱCurrent location

With respect to it self current optimal location

Relative distance;

In the k step, by the particle p of cloud model generation ⁱCurrent location

Optimal location G with respect to whole population _kRelative distance, E _nThe entropy coefficient of cloud model, H _eThe super entropy coefficient of cloud model, E in optimizing process _nAnd H _eAll get the constant greater than zero, its E _nAnd H _eValue need to meet formula six:

Formula six: ${E_n}^2+{H_e}^2<\frac{1}{3}\min \{L_k^{\mathrm{ij}}-x_k^{\mathrm{ij}},G_k^j-x_k^{\mathrm{ij}}\}$

Normal cloud model cloud (E _x, E _n, H _e) computing method as follows:

Formula seven: E ' _n=randn (E _n, H _e)

Formula eight: cloud (E _x, E _n, H _e)=randn (E _x, E ' _n)

Wherein, E ' _nFor the intermediate variable in computation process, randn (E _n, H _e) expression generation E _nFor expectation, H _eFor variance with normal random number; Randn (E _x, E ' _n) represent to generate with E ' _nFor expectation, H _eFor variance with normal random number;

Step 5, the speed of utilizing particle k+1 to go on foot

Position while with k, going on foot

Calculate the position in each particle k+1 step

Utilize present speed

With nine positions of upgrading each particle by formula, original position

Formula nine: $x_{k+1}^{\mathrm{ij}}=x_k^{\mathrm{ij}}+v_{k+1}^{\mathrm{ij}}(i=\mathrm{1,2},...,30;j=\mathrm{1,2},...,7)$

Step 6, calculating k+1 go on foot each particle p ⁱSelf optimal location

Optimal location G with population integral body _k+1:

Each particle p ⁱSelf optimal location

By formula ten calculate:

Formula ten: $L_{k+1}^i=\begin{array}{}\end{array}\left\{\begin{array}{cc}{L}_k^i& C\left(L_k^i\right)\&le;C\left(x_{k+1}^i\right)\\ x_{k+1}^i& C\left(L_k^i\right)>C\left(x_{k+1}^i\right)\end{array}\right.$

The optimal location G of population integral body _k+1Computation process as follows:

Calculating k+1 each particle self optimal location during the step

Corresponding moonlet cost

Filter out wherein minimum moonlet cost, suppose that minimum moonlet cost is

Corresponding optimal location is

G _k+1By formula 11 calculate:

Formula 11 $G_{k+1}=\left\{\begin{array}{cc}{G}_k& C\left(G_k\right)\&le;C\left(L_{k+1}^s\right)\\ L_{k+1}^s& C\left(G_k\right)>C\left(L_{k+1}^s\right)\end{array}\right.$

The optimal location G of step 7, comparison k+1 step population integral body _k+1Moonlet cost C (G _k+1) with the optimal location G of k step population integral body _kMoonlet cost C (G _k) poor absolute value: if | C (G _k+1)-C (G _k) |＜0.01, algorithm is restrained, and optimizes and finishes, G _k+1The optimum solution of trying to achieve exactly, if | C (G _k+1)-C (G _k) | 〉=0.01, not convergence of algorithm, the G that the k+1 step is asked _k+1Not optimum solution, come back to step 4,, according to step 4～step 6, obtain according to k+1 step

And G _k+1The calculating k+2 step

And G _k+2, until the absolute value of difference of moonlet cost corresponding to population optimal locations that meets adjacent two steps is less than 0.01.

Claims (1)

1. the cost optimization of the moonlet based on normal cloud model method for designing, it is characterized in that: described method realizes by following steps:

Step 1, set up moonlet cost C Optimized model: moonlet cost C comprises the cost C of satellite system _s, ground system cost C _gWith launch cost C _f, use C=C _s+ C _g+ C _fCalculate;

Step 2, set the optimal design variable of moonlet cost C: the optimal design variable of moonlet cost C comprises seven optimal design variablees altogether, is respectively the bottom surface radius, satellite altitude, the type of solar cell, type and the duty cycle of accumulator of charge-coupled device camera focal length, orbit altitude, cylindrical shape satellite;

Step 3, seven optimal design variablees in step 2 are carried out the initialization assignment: each particle p ⁱExpression, the population scale is elected 30 as, generates at random each particle p ⁱInitial position And initial velocity

Wherein $x_0^i=(x_0^{i1},x_0^{i2},x_0^{i3},x_0^{i4},x_0^{i5},x_0^{i6},x_0^{i7}),$ In formula

With

The bottom surface radius, satellite altitude, the type of solar cell, the type of accumulator and the initial value of duty cycle that represent respectively charge-coupled device camera focal length, orbit altitude, cylindrical shape satellite, wherein $v_0^i=(x_0^{i1},v_0^{i2},v_0^{i3},v_0^{i4},v_0^{i5},v_0^{i6},v_0^{i7}),$ In formula

With

Expression respectively

With

Corresponding speed initial value,

Utilize two pairs of population of formula one and formula to carry out the initialization assignment:

Formula one: $x_0^{\mathrm{ij}}=x_{\min }+s_1(x_{\max }-x_{\min })(j=\mathrm{1,2},...,7)$

Formula two: $v_0^{\mathrm{ij}}=\frac{x_{\min }+s_2(x_{\max }-x_{\min })}{\mathrm{\&Delta;t}}(j=\mathrm{1,2},...,7)$

In formula one and formula two, s ₁And s ₂The random number between 0,1, x _minThe lower limit of design variable value, x _maxIt is the upper limit of design variable value;

Each particle p ⁱSelf optimal location L ⁱRepresent L ⁱInitial value

The optimal location of whole population particle represents with G, the initial value G of G ₀According to following step assignment:

A, calculating population are that 30 particles are at each particle self optimal location

Corresponding satellite cost

B, 30 moonlet costs of comparison Size, filter out wherein minimum moonlet cost, suppose that minimum moonlet cost is

The particle corresponding with it is p ^m, corresponding particle p ^mSelf optimal location be

Step 4, suppose that optimized algorithm completed k (k 〉=1) step, below calculate the speed in the k+1 step of each particle:

Suppose that algorithm calculates k (k 〉=1) during the step, each the particle p that has obtained ⁱSelf optimal location be

The optimal location of population integral body is G _k, each particle p ⁱPosition when k goes on foot For:

Speed

For: $v_k^i=(v_k^{i1},v_k^{i2},...,v_k^{i7});$

When k+1 goes on foot, each particle p ⁱIn the k+1 speed in step

Calculate according to formula three, four, five:

Formula three: $v_{k+1}^{\mathrm{ij}}=\mathrm{\&omega;}{v}_k^{\mathrm{ij}}+\frac{c_{1}C{P}_k^{\mathrm{ij}}}{\mathrm{\&Delta;t}}+\frac{c_2{\mathrm{CP}}_{\mathrm{gk}}^{\mathrm{ij}}}{\mathrm{\&Delta;t}}$

Formula four: ${\mathrm{CP}}_k^{\mathrm{ij}}=\mathrm{cloud}(L_k^{\mathrm{ij}}-x_k^{\mathrm{ij}},E_n,H_e)$

Formula five: ${\mathrm{CP}}_{\mathrm{gk}}^{\mathrm{ij}}=\mathrm{cloud}(G_k^j-x_k^{\mathrm{ij}},E_n,H_e)$

Parameter ω in formula three is inertial coefficient, c ₁And c ₂For confidence factor, inertial coefficient ω span is [0.8,1.2], confidence factor c ₁And c ₂Span be [0,2];

In the k step, by the particle p of cloud model generation ⁱCurrent location

With respect to it self current optimal location Relative distance;

In the k step, by the particle p of cloud model generation ⁱCurrent location

Optimal location G with respect to whole population _kRelative distance, E _nThe entropy coefficient of cloud model, H _eThe super entropy coefficient of cloud model, E in optimizing process _nAnd H _eAll get the constant greater than zero, its E _nAnd H _eValue need to meet formula six:

Formula six: ${E_n}^2+{H_e}^2<\frac{1}{3}\min \{L_k^{\mathrm{ij}}-x_k^{\mathrm{ij}},G_k^j-x_k^{\mathrm{ij}}\}$

Normal cloud model cloud (E _x, E _n, H _e) computing method as follows:

Formula seven: E ' _n=randn (E _n, H _e)

Formula eight: cloud (E _x, E _n, H _e)=randn (E _x, E ' _n)

Wherein, E ' _nFor the intermediate variable in computation process, randn (E _n, H _e) expression generation E _nFor expectation, H _eFor variance with normal random number; Randn (E _x, E ' _n) represent to generate with E ' _nFor expectation, H _eFor variance with normal random number;

Step 5, the speed of utilizing particle k+1 to go on foot Position while with k, going on foot Calculate the position in each particle k+1 step $x_{k+1}^i:$

Utilize present speed

With nine positions of upgrading each particle by formula, original position

Formula nine: $x_{k+1}^{\mathrm{ij}}=x_k^{\mathrm{ij}}+v_{k+1}^{\mathrm{ij}}(i=\mathrm{1,2},...,30;j=\mathrm{1,2},...,7)$

Step 6, calculating k+1 go on foot each particle p ⁱSelf optimal location

Optimal location G with population integral body _k+1:

Each particle p ⁱSelf optimal location

By formula ten calculate:

Formula ten: $L_{k+1}^i=\left\{\begin{array}{cc}{L}_k^i& C\left(L_k^i\right)\&le;C\left(x_{k+1}^i\right)\\ x_{k+1}^i& C\left(L_k^i\right)>C\left(x_{k+1}^i\right)\end{array}\right.$

The optimal location G of population integral body _k+1Computation process as follows:

Calculating k+1 each particle self optimal location during the step

Corresponding moonlet cost

Filter out wherein minimum moonlet cost, suppose that minimum moonlet cost is

Corresponding optimal location is

G _k+1By formula 11 calculate:

Formula 11 $G_{k+1}=\left\{\begin{array}{cc}{G}_k& C\left(G_k\right)\&le;C\left(L_{k+1}^s\right)\\ L_{k+1}^s& C\left(G_k\right)>C\left(L_{k+1}^s\right)\end{array}\right.$

The optimal location G of step 7, comparison k+1 step population integral body _k+1Moonlet cost C (G _k+1) with the optimal location G of k step population integral body _kMoonlet cost C (G _k) poor absolute value: if | C (G _k+1)-C (G _k) |＜0.01, algorithm is restrained, and optimizes and finishes, G _k+1The optimum solution of trying to achieve exactly, if | C (G _k+1)-C (G _k) | 〉=0.01, not convergence of algorithm, the G that the k+1 step is asked _k+1Not optimum solution, come back to step 4,, according to step 4～step 6, obtain according to k+1 step

And G _k+1The calculating k+2 step

And G _k+2, until the absolute value of difference of moonlet cost corresponding to population optimal locations that meets adjacent two steps is less than 0.01.