CN107403035A - A kind of moon high ladder overall plan optimization method - Google Patents
A kind of moon high ladder overall plan optimization method Download PDFInfo
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- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
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Abstract
The present invention provides a kind of as follows based on the moon high ladder overall plan optimization method for improving resampling particle swarm optimization, step：One：Establish the Optimized model of moon high ladder overall plan；Two：Initialize particle populations；Three：Calculate population concentration class and re-sampling operations are carried out to particle populations；Four：Update particle position and speed；Five：Update the history optimal location and colony's optimal location of each particle；Six：Calculate particle active value go forward side by side row variation operation；Seven：Carry out vibrations operation；Eight：If being unsatisfactory for required precision and not yet reaching maximum iteration, iterations adds one, return to step three, otherwise records simultaneously output result；By above flow and step, moon high ladder overall plan optimization design problem can be efficiently and reliably handled, and because invention introduces become easy to operate and vibrations operation, on the one hand solving speed is accelerated, efficiency is improved, the ability of global search is on the other hand improved, improves optimization precision.
Description
Technical field
The present invention provides a kind of moon high ladder overall plan optimization method, and it is related to a kind of based on improvement resampling population
The moon high ladder overall plan optimization method of method, can quickly and efficiently realize moon high ladder overall plan optimization design, belong to
Aerospace field.
Background technology
The mankind explore space whole engineering technology system in, delivery technology always in occupation of and its consequence,
The power of carrying capacity directly determines the scale of construction of spacecraft.From exploration space is started so far, carrier rocket is always main
Delivery vehicle, and moon high ladder targeted in the present invention is a kind of new ideas delivery technology.Moon high ladder can be understood as
The space elevator established on the moon, its main body are a hawsers, and one end is fixedly connected on lunar surface platform, the other end with space-ward with
Breeding is connected, and whole hawser keeps tight.Climbing device can be run on hawser, can be transported between moonscape and space station
Delivery thing and personnel.Moon high ladder has relative to the advantages of traditional means of conveyance：Cost of transportation is extremely low, by preresearch estimates,
1kg goods feeding space is only needed 100 dollars using high ladder, less than the 1% of carrier rocket；Conevying efficiency is high, substantially can be real
Now run without interruption.Construction of the construction of moon high ladder for lunar base has great significance, or other celestial bodies
The construction of high ladder provides experience, and it will further facilitate exploration and utilization of the mankind to space.
In the design and building course of moon high ladder, the evaluation of its overall plan and the optimization of overall plan are crucial
Step.Evaluation method and system to moon high ladder overall plan have been applied for a patent in addition, and this patent proposes a kind of moon day
The Optimization Design of terraced overall plan.
The optimization design of so-called moon high ladder overall plan, it is exactly using aids such as computers, using numerical computations
The optimization design scheme for meeting to require is found with the method for analysis.Moon high ladder is a very huge and complicated engineering department
System, there may be many locally optimal solutions, while its design parameter excursion is very big, so traditional optimization method, such as ox
The solution effect of method, Sequential Quadratic Programming method etc. is general.Therefore need to use modern intelligence optimization algorithm, modern intelligent optimization
Algorithm refers to simulate natural phenomena by computer programming, imitates the social action and evolutionary mechanism of animal or even the mankind, so as to
Realize the general designation of the major class algorithm solved to complicated optimum problem.Wherein resampling particle swarm optimization algorithm, it is simulation birds
Population foraging behavior and a kind of modern intelligence optimization algorithm for having merged resampling technique in particle filter field.Its advantage is former
Reason is simple, and it is easy to realize, and it has embodied good effect in heavy construction optimization problem, but total in moon high ladder
In the optimization design of body scheme, resampling particle group optimizing method can not solve the optimal solution for meeting to require, calculate sometimes
Time is very long, is absorbed in local optimum region sometimes so as to obtain optimal design.
In order to solve the above problems, the present invention introduces mutation operation in resampling particle group optimizing method and vibrations are grasped
Make, and define population concentration class and particle active value two indices, it is proposed that a kind of moon high ladder overall plan optimization method.
The content of the invention
1st, purpose
The present invention provides a kind of moon high ladder overall plan optimization method, to overcome traditional optimal design method in certain journey
Calculating speed is slow on degree, and the shortcomings that be easily trapped into locally optimal solution, it is overall so as to efficiently and reliably complete moon high ladder
The optimization design of scheme.
2nd, technical scheme
In order to realize foregoing invention purpose, the present invention uses following technical scheme.
The present invention provides a kind of moon high ladder overall plan optimization method, i.e., a kind of based on improving resampling particle swarm optimization
Moon high ladder overall plan optimization method, mainly including following steps：
Step 1：Establish the Optimized model of moon high ladder overall plan
The moon high ladder overall plan contains the ginseng such as the shape to each major part of moon high ladder, material, performance
Several selections and calculating, and may finally abstract expression be one group of mathematical formulae and multistage software program set；
" Optimized model " mainly includes design variable, constraints and optimization aim；
It is somebody's turn to do " design variable " and refers to the parameter such as the shape of each major part, material, performance in moon high ladder overall plan,
The length of such as hawser, the cross-sectional area of hawser, the stress of hawser.Optimal design variable is come out by Optimization Method
, obtain optimal overall plan once optimal design variable is obtained also.
It is somebody's turn to do " constraints " and refers to the condition that moon high ladder overall plan must is fulfilled for, if cost is no more than on some
Limit, carrying capacity necessarily be greater than some lower limit etc..
It is somebody's turn to do " optimization aim " and refers to the good and bad evaluation score of moon high ladder overall plan, the evaluation score of scheme is higher, side
Case is better.The method for solving and system of scheme evaluation score are applied for a patent in addition, are not explained in detail here, and the present invention is main
It is the optimization method to above-mentioned Optimized model；
Above-mentioned Optimized model may finally be expressed as：
max F(x)
s.t.G(x)≤0
Wherein, x is design variable, and G (x) is constraints, and F (x) is optimization aim, that is, the evaluation score of scheme；
Step 2：Initialize particle populations
The initialization particle populations include：Determine the particle number N in particle populations, generate the initial bit of each particle
Put coordinate x and initial velocity vector v and each particle of initialization history optimal location pbest and the optimal location of colony
gbest；
" particle number N " value is relevant with specific optimization problem, typically takes 10~30 for this；
Should " initial position co-ordinates x " generation method be：
xid=xmin(d)+rand1id·(xmax(d)-xmin(d))
Wherein, xidIt is the coordinate value of i-th particle d dimension, xminAnd x (d)max(d) it is respectively particle d dimensional coordinate values
Lower and upper limit, rand1 are the random numbers between one group 0~1.
Should " initial velocity vector v " generation method be：
vid=xmin(d)+rand2id·(xmax(d)-xmin(d))-xid
Wherein, vidIt is the velocity amplitude of i-th particle d dimension, xminAnd x (d)maxAnd x (d)idImplication be same as above, rand2
It is the random number between one group 0~1；
Should " the history optimal location pbest " of each particle initial method be：The initial position for remembering particle is particle
History optimal location pbest initial value, i.e. pbest=x.Target function value, referred to as history optimal value are obtained simultaneously, is designated as
pbest_f；
Should " the optimal location gbest " of colony initial method be：The history optimal value of more above-mentioned each particle, its
The initial value that the position of the minimum particle of middle history optimal value is colony optimal location gbest, the history optimal value are current
Global optimum, it is designated as gbest_f；
Step 3：Calculate population concentration class and re-sampling operations are carried out to particle populations
" the population concentration class " is to be planted defined in the present invention for describing the multifarious macro-indicators of particle in population
The higher explanation particle distribution of clustering intensity is more concentrated, and population diversity is poorer；The lower explanation particle distribution of population concentration class is overstepping the bounds of propriety
Dissipate, population diversity is better；The calculation formula of population concentration class is：
In formula, N is particle number, and D is dimension, DISiFor the distance of i-th of particle to center,It is all grains
Son arrives the average distance of center, xijIt is the coordinate value of i-th of particle jth dimension,It is the coordinate value of center jth dimension,
Center randomly generates in search space；The implication of above formula is：Population concentration class be in population all particles to one
The inverse of the variance of the distance of the individual center randomly generated；
With the propulsion of calculating, the diversity of population gradually reduces, and particle buildup degree improves constantly, when particle buildup degree is big
In critical value, i.e. AD ＞ ADthWhen, re-sampling operations are carried out to particle populations；
It is to overcome particle swarm optimization algorithm in processing moon high ladder overall plan optimization design to be somebody's turn to do " re-sampling operations "
The special operational that existing convergence rate is carried out slowly and the shortcomings that be easily absorbed in local optimum during problem, its specific implementation process
For：
Weights distribution is carried out according to the rule of Gaussian Profile to each particle first, it is nearer apart from current group optimal location
Particle weights it is bigger, more remote particle weights are smaller, distribution formula be：
Wherein qiFor the weights assigned to i-th of particle, F (xi) it is fitness function, gbest is the optimal position of current group
Put, σ is with F (xi)-gbest be sample calculate gained variance, QiWeights after being normalized for i-th of particle；
Then the weights of each particle are judged, when the weights of some particle are less than given threshold values qtWhen, just with
Pr probability randomly generates new particle and substitutes it：
Work as Qi＜ qtWhen,
Wherein,It is new particle position coordinate, its determination method is：
Wherein, t is current iteration number, xminAnd xmaxIt is the lower and upper limit of particle coordinate value respectively, rand3 is one group
Random number between 0~1；
Simultaneously according to the velocity of the adaptive speed correction formula amendment particle：
Wherein T is maximum iteration, and t is current iteration number,For the particle rapidity newly introduced；
Wherein, the determination method of the particle rapidity newly introduced is：
Wherein, xminAnd xmaxIt is the lower and upper limit of particle coordinate value respectively, rand4 is random between one group 0~1
Number,It is particle position new caused by previous step；
Step 4：Update particle position and speed
The renewal particle position and speed are：Each particle is in the optimal position of respective history optimal location pbest and colony
Put under the influence of gbest and be according to the new position coordinates of given law generation and velocity, the update mode of velocity：
vi(t+1)=χ { vi(t)+c1r1[pbesti-xi(t)]+c2r2[gbest-xi(t)]}
" velocity more new formula " is somebody's turn to do to be formed by three, Section 1 vi(t) it is former speed, Section 2 c1r1[pbesti-xi
(t) it is] influence of the individual history optimal location to speed, Section 3 c2r2[pg-xi(t)] for colony's optimal location to speed
Influence；
Wherein c1、c2For acceleration factor, represent individual history optimal location and colony's optimal location influences to make on speed
Size, its value are relevant with specific optimization problem；r1、r2It is the random number between 0~1 for random factor；χ be compression because
Son, its determination method are：
The mode of location updating is：
xi(t+1)=xi(t)+vi(t+1)
Above formula is formed by two, Section 1 xi(t) it is original position, Section 2 vi(t+1) it is according to above-mentioned speed more new formula
Obtained new speed；
Step 5：Update the history optimal location and colony's optimal location of each particle
By the operation of step 3 and step 4, the location updating of particle, cause the history optimal location of each particle
Pbest and colony optimal location gbest are varied from, so to update history optimal location pbest and the colony of each particle
Optimal location gbest；
It is described that " the history optimal location pbest " of each particle renewal process is：
First, the target function value F (x corresponding to each particle current location are obtainedi(t+1))；
Then, F (x are comparedi(t+1)) and the particle history optimal value pbest_fi；
if F(xi(t+1)) ＜ pbest_fi
then pbesti=xi(t+1)
pbest_fi=F(xi(t+1))
In above formula, footnote i represents i-th of particle；The implication of above formula is, when target function value corresponding to particle current location
During less than the particle history optimal value, by the use of current location as the history optimal location of the particle, by the use of the target function value as
The history optimal value of the particle；Otherwise, pbest and pbest_f retains initial value.
It is described that " the optimal location gbest " of colony renewal process is：The history optimal value of more above-mentioned each particle, its
The position of the minimum particle of middle history optimal value is colony optimal location gbest, and the history optimal value is current global optimum
Value, is designated as gbest_f；
Step 6：Calculate particle active value go forward side by side row variation operation
" the particle active value " is the Microscopic Indexes for describing each particle active degree, if in certain iteration
The target function value of particle increased, then the particle is active particle, and its active value resets to maximum, is designated as AC=
ACmax；If the target function value of particle does not increase in certain iteration, then the active value of the particle subtracts 1；When certain particle
Active value when being equal to 0, the particle be inactive particle, and now the particle is carried out mutation operation while to reset its active value；
" mutation operation " refers near particle current location and the midpoint of current group optimal location with normal state point
Cloth form randomly generates new particle and substitutes it, and its formula calculated is:
Wherein x*Represent the optimal solution that is found so far, norm (μ, σ) represent average is μ, variance is σ Gauss with
Machine number；
Step 7：Carry out vibrations operation
Whenever population finds more excellent position, with regard to carrying out small range vibrations operation, its effect is by current optimum point
Vibrations find its more excellent position nearby, so as to improve the local exploring ability of algorithm；Its detailed process is：First randomly choose
K is tieed up, and k is 1 to arrive k set in advancemaxOn random number, select it is every it is one-dimensional on produce a vibrations point x '
X ' (d)=x (d)+norm (0,1) β L (d)
Wherein β is vibrations coefficient；If it is more excellent not shake a current optimum point of ratio, retain current optimum point, otherwise
Current optimum point, which is replaced, by the use of more excellent vibrations point is used as new optimum point；
Step 8：If being unsatisfactory for required precision and not yet reaching maximum iteration, iterations adds one, return to step
Three, otherwise record simultaneously output result；
" result " mainly includes the optimal design point and target letter of the moon high ladder overall plan optimization design problem
Number optimal value；" the optimal design point " is current colony's optimal location, and it is the optimal case of moon high ladder master-plan,
" the object function optimal value " is current global optimum, and it is the evaluation score of the optimal case.
By above flow and step, moon high ladder overall plan optimization design problem can be efficiently and reliably handled,
And due to invention introduces easy to operate and vibrations operation is become, on the one hand accelerating solving speed, improving efficiency, on the other hand change
It has been apt to the ability of global search, has improved optimization precision.
Wherein, " Optimized model for establishing moon high ladder overall plan " described in step 1, the process that it is established is such as
Under：
First according to the general requirement of moon high ladder scheme, the design variable of Optimized model, length, cable such as hawser are determined
The cross-sectional area of rope, stress of hawser etc.；
Then according to the total demand of moon high ladder scheme, the optimization aim of Optimized model is determined, optimization aim is one
Or multiple crucial indexs, optimization aim is exactly that the scheme obtained according to moon high ladder overall plan evaluation method is commented herein
Valency fraction, it is somebody's turn to do " moon high ladder overall plan evaluation method " and has applied for a patent in addition, be not described in detail herein；
Finally according to the general requirement of moon high ladder scheme, the constraints of Optimized model is determined, it is that we are designing
In the condition that must is fulfilled for, its specific targets is provided by user, as cost must be high no more than some upper limit, carrying capacity
In some lower limit etc..
Wherein, " the initialization particle populations " described in step 2, the practice that it is initialized are as follows：
Particle number N is first determined, typically takes 10~30；
Then initial position co-ordinates x is generated, its method is：
xid=xmin(d)+rand1id·(xmax(d)-xmin(d))
Wherein, xidIt is the coordinate value of i-th particle d dimension, xminAnd x (d)max(d) it is respectively particle d dimensional coordinate values
Lower and upper limit, rand1 are the random numbers between one group 0~1.
Initial velocity vector v is regenerated, its method is：
vid=xmin(d)+rand2id·(xmax(d)-xmin(d))-xid
Wherein, vidIt is the velocity amplitude of i-th particle d dimension, xminAnd x (d)maxAnd x (d)idImplication be same as above, rand2
It is the random number between one group 0~1；
Then the history optimal location pbest of each particle is initialized, its method is：The initial position for remembering particle is particle
History optimal location pbest initial value, i.e. pbest=x.Target function value, referred to as history optimal value are obtained simultaneously, is designated as
pbest_f；
The optimal location gbest of colony is finally initialized, its method is：The history optimal value of more above-mentioned each particle,
The initial value that the position of the wherein minimum particle of history optimal value is colony optimal location gbest, the history optimal value is current
Global optimum, be designated as gbest_f；
Wherein, " calculate particle active value go forward side by side row variation operation " described in step 6, its practice is as follows：
First, the active value AC of each particle is calculatedi,
Then, AC is judgediWhether 0 is equal to, if ACiIt is not 0, then without any operation, if ACiEqual to 0, then root
Particle of the particle after mutation operation is obtained according to below equation.
。
3rd, advantage and effect
A kind of moon high ladder overall plan optimization method provided by the invention, it is related to a kind of based on improvement resampling particle
The moon high ladder overall plan optimization method of group's method, its major advantage are：The diversity of population and each grain can be monitored in real time
The active degree of son simultaneously makes respective handling, so as to reasonable distribution computing capability, improves computational efficiency；Simultaneously by becoming easy to operate
Ability of searching optimum is improved, local exploring ability is improved by shaking operation；Final realize efficiently and reliably is completed
The purpose of the optimization design of moon high ladder overall plan.
Brief description of the drawings
Fig. 1 the method for the invention flow charts.
Fig. 2 re-sampling operations flow charts.
Fig. 3 mutation operation flow charts.
Fig. 4 shakes operational flowchart.
Fig. 5 moon high ladder schemes synthesis Optimizing Flow figures.
Embodiment
This method is further described below in conjunction with accompanying drawing and a moon high ladder global optimization design example, but this reality
Example is not limited to this method, and most moon high ladder optimization design problems can use this method Optimization Solution.
As seen from Figure 1, it is provided by the invention overall based on the moon high ladder for improving resampling particle swarm optimization algorithm
Scheme optimization method, mainly including following eight steps：
Step 1：Establish the Optimized model of moon high ladder overall plan
In order to illustrate the logical process of method, this method is made here in conjunction with a moon high ladder global optimization design example
It is described in detail, the complex optimum flow of the example is as shown in Figure 5.
The design variable of this example has three：The length of high ladder hawser, the initial cross sectional of high ladder hawser product, high ladder hawser
Stress.
The constraints of this example has five：High ladder cable length is between 1000000km to 3000000km, high ladder cable
The initial cross sectional product of rope is in 20mm2To 50mm2Between, the stress of high ladder hawser is between 20Gpa to 43.3Gpa, and totle drilling cost is not
More than 200,000,000,000 dollars, carrying capacity is not less than 5000 tons.
The optimization aim of this example is the evaluation score of scheme.The method for solving and system of scheme evaluation score are in addition
Apply for a patent, be not explained in detail here, the present invention is mainly to the optimization method of above-mentioned Optimized model.
Above-mentioned Optimized model may finally be expressed as：
Wherein, R is the evaluation score of scheme, and l is cable length, A0It is the initial cross sectional product of hawser, σ is that hawser should
Power, C are totle drilling costs, and M is carrying capacity.lminAnd lmaxIt is the bound of cable length, AminAnd AmaxIt is hawser initial cross sectional
Long-pending bound, [σ]min[σ]maxIt is the bound of hawser stress, CmaxIt is maximum cost, MminIt is minimum carrying capacity.And
lmin=1000000km, lmax=3000000km, Amin=20mm2, Amax=50mm2, [σ]min=20Gpa, [σ]max=
43.3Gpa Cmax=2,000 hundred million dollars, Mmin=5000t.
Step 2：Initialize particle populations
The initialization particle populations include：Determine the particle number N in particle populations, generate the initial bit of each particle
Put coordinate x and initial velocity vector v and each particle of initialization history optimal location pbest and the optimal location of colony
gbest。
" particle number N " value is relevant with specific optimization problem, typically takes 10~30, takes N=20 in this example for this.This
The dimension of example is D=3.
Should " initial position co-ordinates x " generation method be：
xid=xmin(d)+rand1id·(xmax(d)-xmin(d))
Wherein, xidIt is the coordinate value of i-th particle d dimension, xminAnd x (d)max(d) it is respectively particle d dimensional coordinate values
Lower and upper limit, rand1 are the random numbers between one group 0~1.
Should " initial velocity vector v " generation method be：
vid=xmin(d)+rand2id·(xmax(d)-xmin(d))-xid
Wherein, vidIt is the velocity amplitude of i-th particle d dimension, xminAnd x (d)maxAnd x (d)idImplication be same as above, rand2
It is the random number between one group 0~1.
Should " the history optimal location pbest " of each particle initial method be：The initial position for remembering particle is particle
History optimal location pbest initial value, i.e. pbest=x.Target function value, referred to as history optimal value are obtained simultaneously, is designated as
pbest_f。
Should " the optimal location gbest " of colony initial method be：The history optimal value of more above-mentioned each particle, its
The initial value that the position of the minimum particle of middle history optimal value is colony optimal location gbest, the history optimal value are current
Global optimum, it is designated as gbest_f.
Step 3：Calculate population concentration class and re-sampling operations are carried out to particle populations
The population concentration class be defined in the present invention be used for the multifarious macro-indicators of particle in population, population are described
The higher explanation particle distribution of concentration class is more concentrated, and population diversity is poorer；Population concentration class is lower, and the distribution of explanation particle is more scattered,
Population diversity is better.The calculation formula of population concentration class is：
In formula, N is particle number, and D is dimension, DISiFor the distance of i-th of particle to center,It is all grains
Son arrives the average distance of center, xijIt is the coordinate value of i-th of particle jth dimension,It is the coordinate value of center jth dimension.
Center randomly generates in search space.The implication of above formula is：Population concentration class be in population all particles to one
The inverse of the variance of the distance of the individual center randomly generated；
With the propulsion of calculating, the diversity of population gradually reduces, and particle buildup degree improves constantly, when particle buildup degree is big
In critical value, i.e. AD ＞ ADthWhen, re-sampling operations are carried out to particle populations；
It is to overcome particle swarm optimization algorithm in processing moon high ladder overall plan optimization design to be somebody's turn to do " re-sampling operations "
The special operational that existing convergence rate is carried out slowly and the shortcomings that be easily absorbed in local optimum during problem, its flow such as Fig. 2 institutes
Show, its specific implementation process is：
Weights distribution is carried out according to the rule of Gaussian Profile to each particle first, it is nearer apart from current group optimal location
Particle weights it is bigger, more remote particle weights are smaller, distribution formula be：
Wherein qiFor the weights assigned to i-th of particle, F (xi) it is fitness function, gbest is the optimal position of current group
Put, σ is with F (xi)-gbest be sample calculate gained variance.QiWeights after being normalized for i-th of particle.
Then the weights of each particle are judged, when the weights of some particle are less than given threshold values qtWhen, just with
Pr probability randomly generates new particle and substitutes it：
Work as Qi＜ qtWhen,
Wherein,It is new particle position coordinate, its determination method is：
Wherein, t is current iteration number, xminAnd xmaxIt is the lower and upper limit of particle coordinate value respectively, rand3 is one group
Random number between 0~1.
Simultaneously according to the velocity of the adaptive speed correction formula amendment particle：
Wherein T is maximum iteration, and t is current iteration number,For the particle rapidity newly introduced.
Wherein, the determination method of the particle rapidity newly introduced is：
Wherein, xminAnd xmaxIt is the lower and upper limit of particle coordinate value respectively, rand4 is random between one group 0~1
Number.It is particle position new caused by previous step
Step 4：Update particle position and speed
The renewal particle position and speed are：Each particle is in the optimal position of respective history optimal location pbest and colony
Put under the influence of gbest and be according to the new position coordinates of given law generation and velocity, the update mode of velocity：
vi(t+1)=χ { vi(t)+c1r1[pbesti-xi(t)]+c2r2[gbest-xi(t)]}
" velocity more new formula " is somebody's turn to do to be formed by three, Section 1 vi(t) it is former speed, Section 2 c1r1[pbesti-xi
(t) it is] influence of the individual history optimal location to speed, Section 3 c2r2[pg-xi(t)] for colony's optimal location to speed
Influence；
Wherein c1、c2For acceleration factor, represent individual history optimal location and colony's optimal location influences to make on speed
Size, its value are relevant with specific optimization problem；r1、r2It is the random number between 0~1 for random factor；χ be compression because
Son, its determination method are：
The mode of location updating is：
xi(t+1)=xi(t)+vi(t+1)
Above formula is formed by two, Section 1 xi(t) it is original position, Section 2 vi(t+1) it is according to above-mentioned speed more new formula
Obtained new speed；
Step 5：Update the history optimal location and colony's optimal location of each particle
By the operation of step 3 and step 4, the location updating of particle, cause the history optimal location of each particle
Pbest and colony optimal location gbest are varied from, so to update history optimal location pbest and the colony of each particle
Optimal location gbest；
It is described that " the history optimal location pbest " of each particle renewal process is：
First, the target function value F (x corresponding to each particle current location are obtainedi(t+1))；
Then, F (x are comparedi(t+1)) and the particle history optimal value pbest_fi；
if F(xi(t+1)) ＜ pbest_fi
then pbesti=xi(t+1)
pbest_fi=F (xi(t+1))
In above formula, footnote i represents i-th of particle.The implication of above formula is, when target function value corresponding to particle current location
During less than the particle history optimal value, by the use of current location as the history optimal location of the particle, by the use of the target function value as
The history optimal value of the particle.Otherwise, pbest and pbest_f retains initial value；
It is described that " the optimal location gbest " of colony renewal process is：The history optimal value of more above-mentioned each particle, its
The position of the minimum particle of middle history optimal value is colony optimal location gbest, and the history optimal value is current global optimum
Value, is designated as gbest_f.
Step 6：Calculate particle active value go forward side by side row variation operation
" the particle active value " is the Microscopic Indexes for describing each particle active degree, if in certain iteration
The target function value of particle increased, then the particle is active particle, and its active value resets to maximum, is designated as AC=
ACmax；If the target function value of particle does not increase in certain iteration, then the active value of the particle subtracts 1；When certain particle
Active value when being equal to 0, the particle be inactive particle, and now the particle is carried out mutation operation while to reset its active value.
" mutation operation " refers near particle current location and the midpoint of current group optimal location with normal state point
Cloth form randomly generates new particle and substitutes it, and its flow is as shown in figure 3, variation formula is:
Wherein x*Represent the optimal solution that is found so far, norm (μ, σ) represent average is μ, variance is σ Gauss with
Machine number.
Step 7：Carry out vibrations operation
Whenever population finds more excellent position, with regard to carrying out small range vibrations operation, its effect is by current optimum point
Vibrations find its more excellent position nearby, so as to improve the local exploring ability of algorithm.Its detailed process is：First randomly choose
K is tieed up, and k is 1 to arrive k set in advancemaxOn random number, select it is every it is one-dimensional on produce one vibrations point x ', its flow as figure
Shown in 4, vibrations formula is:
X ' (d)=x (d)+norm (0,1) β L (d)
Wherein β is vibrations coefficient.If it is more excellent not shake a current optimum point of ratio, retain current optimum point, otherwise
Current optimum point, which is replaced, by the use of more excellent vibrations point is used as new optimum point.
Step 8：If being unsatisfactory for required precision and not yet reaching maximum iteration, iterations adds one, return to step
Three, otherwise record simultaneously output result.
" result " mainly includes the optimal design point and target letter of the moon high ladder overall plan optimization design problem
Number optimal value." the optimal design point " is current colony's optimal location, and it is the optimal case of moon high ladder master-plan,
" the object function optimal value " is current global optimum, and it is the evaluation score of the optimal case.
By numerical computations and analysis, the design that most has for obtaining this example is：L=204590km, A0=44.75mm2, σ
=43.06Gpa.
The quality scale of the program is 19.6 ten thousand tons, and L1 points year carrying capacity is 12180 tons, and construction-time is 19.9,
Construction cost is 200,000,000,000 dollars.
By above flow and step, the practical problem of moon high ladder overall plan optimization design can be effectively handled, and
And because invention introduces two indices：Population concentration class and particle active value, can monitor in real time population diversity and
The active degree of particle, so as to reasonable distribution computing resource；Simultaneously present invention introduces two operation：Mutation operation and vibrations are grasped
Make, on the one hand improve ability of searching optimum, avoid being absorbed in locally optimal solution, on the one hand improve local exploring ability, improve
Convergence rate.The final purpose for realizing the optimization design for efficiently and reliably completing moon high ladder overall plan.
The embodiment of this patent is explained in detail above, but this patent is not limited to above-mentioned embodiment,
In one of ordinary skill in the art's possessed knowledge, it can also be made on the premise of this patent objective is not departed from each
Kind change.
Claims (4)
1. a kind of moon high ladder overall plan optimization method, i.e., a kind of overall based on the moon high ladder for improving resampling particle swarm optimization
Scheme optimization method, it is characterised in that：Including following steps：
Step 1：Establish the Optimized model of moon high ladder overall plan
The moon high ladder overall plan contains the parameters such as the shape to each major part of moon high ladder, material, performance
Selection and calculating, and final abstract expression is the set of one group of mathematical formulae and multistage software program；
" Optimized model " includes design variable, constraints and optimization aim；
It is somebody's turn to do shape, material and performance that " design variable " refers to each major part in moon high ladder overall plan；Optimal sets
Meter variable is come out by Optimization Method, and optimal totality side has been obtained once optimal design variable is obtained also
Case；
It is somebody's turn to do " constraints " and refers to the condition that moon high ladder overall plan must is fulfilled for；
It is somebody's turn to do " optimization aim " and refers to the good and bad evaluation score of moon high ladder overall plan, the evaluation score of scheme is higher, and scheme is got over
It is good；
Above-mentioned Optimized model is ultimately expressed as：
max F(x)
s.t. G(x)≤0
Wherein, x is design variable, and G (x) is constraints, and F (x) is optimization aim, that is, the evaluation score of scheme；
Step 2：Initialize particle populations
The initialization particle populations include：Determine that the particle number N in particle populations, the initial position of each particle of generation are sat
Mark x and initial velocity vector v and each particle of initialization history optimal location pbest and the optimal location gbest of colony；
" particle number N " value is relevant with specific optimization problem, typically takes 10~30 for this；
Should " initial position co-ordinates x " generation method be：
xid=xmin(d)+rand1id·(xmax(d)-xmin(d))
Wherein, xidIt is the coordinate value of i-th particle d dimension, xminAnd x (d)max(d) be respectively particle d dimensional coordinate values lower limit
And the upper limit, rand1 are the random numbers between one group 0~1；
Should " initial velocity vector v " generation method be：
vid=xmin(d)+rand2id·(xmax(d)-xmin(d))-xid
Wherein, vidIt is the velocity amplitude of i-th particle d dimension, xminAnd x (d)maxAnd x (d)idImplication be same as above, rand2 is one
Random number between group 0~1；
Should " the history optimal location pbest " of each particle initial method be：The initial position for remembering particle is particle history
Optimal location pbest initial value, i.e. pbest=x；Target function value, referred to as history optimal value are obtained simultaneously, is designated as
pbest_f；
Should " the optimal location gbest " of colony initial method be：The history optimal value of more above-mentioned each particle, wherein going through
The initial value that the position of the minimum particle of history optimal value is colony optimal location gbest, the history optimal value is the current overall situation
Optimal value, it is designated as gbest_f；
Step 3：Calculate population concentration class and re-sampling operations are carried out to particle populations
" the population concentration class " is to be used for describing the multifarious macro-indicators of particle in population, kind clustering defined in the present invention
The higher explanation particle distribution of intensity is more concentrated, and population diversity is poorer；Population concentration class is lower, and the distribution of explanation particle is more scattered, kind
Group's diversity is better；The calculation formula of population concentration class is：
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In formula, N is particle number, and D is dimension, DISiFor the distance of i-th of particle to center,It is all particles in
The average distance of heart position, xijIt is the coordinate value of i-th of particle jth dimension,It is the coordinate value of center jth dimension, centre bit
Put and randomly generated in search space；The implication of above formula is：Population concentration class is that all particles are random to one in population
The inverse of the variance of the distance of caused center；
With the propulsion of calculating, the diversity of population gradually reduces, and particle buildup degree improves constantly, and faces when particle buildup degree is more than
Dividing value, i.e. AD ＞ ADthWhen, re-sampling operations are carried out to particle populations；
It is to overcome particle swarm optimization algorithm in processing moon high ladder overall plan optimization design problem to be somebody's turn to do " re-sampling operations "
When the special operational that carries out slowly and the shortcomings that be easily absorbed in local optimum of existing convergence rate, its specific implementation process is：
Weights distribution, the grain nearer apart from current group optimal location are carried out according to the rule of Gaussian Profile to each particle first
Sub- weights are bigger, and more remote particle weights are smaller, and distribution formula is：
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Wherein qiFor the weights assigned to i-th of particle, F (xi) it is fitness function, gbest is current group optimal location, σ
For with F (xi)-gbest be sample calculate gained variance, QiWeights after being normalized for i-th of particle；
Then the weights of each particle are judged, when the weights of some particle are less than given threshold values qtWhen, just with the general of Pr
Rate randomly generates new particle and substitutes it：
Work as Qi＜ qtWhen,
Wherein,It is new particle position coordinate, its determination method is：
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Wherein, t is current iteration number, xminAnd xmaxIt is the lower and upper limit of particle coordinate value respectively, rand3 is one group 0~1
Between random number；
Simultaneously according to the velocity of the adaptive speed correction formula amendment particle：
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Wherein T is maximum iteration, and t is current iteration number,For the particle rapidity newly introduced；
Wherein, the determination method of the particle rapidity newly introduced is：
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Wherein, xminAnd xmaxIt is the lower and upper limit of particle coordinate value respectively, rand4 is the random number between one group 0~1,It is particle position new caused by previous step；
Step 4：Update particle position and speed
The renewal particle position and speed are：Each particle is in respective history optimal location pbest and colony's optimal location
It is according to the new position coordinates of given law generation and velocity, the update mode of velocity under the influence of gbest：
vi(t+1)=χ { vi(t)+c1r1[pbesti-xi(t)]+c2r2[gbest-xi(t)]}
" velocity more new formula " is somebody's turn to do to be formed by three, Section 1 vi(t) it is former speed, Section 2 c1r1[pbesti-xi(t)]
For influence of the individual history optimal location to speed, Section 3 c2r2[pg-xi(t)] it is influence of colony's optimal location to speed；
Wherein c1、c2For acceleration factor, individual history optimal location and colony's optimal location are represent to speed influence
Size, its value are relevant with specific optimization problem；r1、r2It is the random number between 0~1 for random factor；χ is compressibility factor,
Its determination method is：
The mode of location updating is：
xi(t+1)=xi(t)+vi(t+1)
Above formula is formed by two, Section 1 xi(t) it is original position, Section 2 vi(t+1) it is to be obtained according to above-mentioned speed more new formula
New speed；
Step 5：Update the history optimal location and colony's optimal location of each particle
By the operation of step 3 and step 4, the location updating of particle, cause each particle history optimal location pbest and
Colony optimal location gbest is varied from, so to update the history optimal location pbest and colony's optimal location of each particle
gbest；
It is described that " the history optimal location pbest " of each particle renewal process is：
First, the target function value F (x corresponding to each particle current location are obtainedi(t+1))；
Then, F (x are comparedi(t+1)) and the particle history optimal value pbest_fi；
if F(xi(t+1)) ＜ pbest_fi
then pbesti=xi(t+1)
pbest_fi=F (xi(t+1))
In above formula, footnote i represents i-th of particle；The implication of above formula is, when target function value corresponding to particle current location is less than
During the particle history optimal value, by the use of current location as the history optimal location of the particle, the grain is used as by the use of the target function value
The history optimal value of son；Otherwise, pbest and pbest_f retains initial value；
It is described that " the optimal location gbest " of colony renewal process is：The history optimal value of more above-mentioned each particle, wherein going through
The position of the minimum particle of history optimal value is colony optimal location gbest, and the history optimal value is current global optimum, note
For gbest_f；
Step 6：Calculate particle active value go forward side by side row variation operation
" the particle active value " is the Microscopic Indexes for describing each particle active degree, if the particle in certain iteration
Target function value increased, then the particle is active particle, and its active value resets to maximum, is designated as AC=ACmax；
If the target function value of particle does not increase in certain iteration, then the active value of the particle subtracts 1；When enlivening for certain particle
When value is equal to 0, the particle is inactive particle, and now carry out mutation operation to the particle resets its active value simultaneously；
" mutation operation " refers near particle current location and the midpoint of current group optimal location with normal distribution shape
Formula randomly generates new particle and substitutes it, and its formula is:
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Wherein x*The optimal solution found so far is represented, norm (μ, σ) expression averages are μ, the Gauss number that variance is σ；
Step 7：Carry out vibrations operation
Whenever population finds more excellent position, with regard to carrying out small range vibrations operation, its effect is by the shake in current optimum point
It is dynamic to find position more excellent near it, so as to improve the local exploring ability of algorithm；Its detailed process is：K dimensions are first randomly choosed,
K is 1 to arrive k set in advancemaxOn random number, select it is every it is one-dimensional on produce a vibrations point x '
X ' (d)=x (d)+norm (0,1) β L (d)
Wherein β is vibrations coefficient；If it is more excellent not shake a current optimum point of ratio, retain current optimum point, otherwise with more
Excellent vibrations point replaces current optimum point as new optimum point；
Step 8：If being unsatisfactory for required precision and not yet reaching maximum iteration, iterations adds one, return to step three,
Otherwise record and output result；
" result " includes the optimal design point and object function optimal value of the moon high ladder overall plan optimization design problem；
" the optimal design point " is current colony's optimal location, and it is the optimal case of moon high ladder master-plan, " the target
Optimized value " is current global optimum, and it is the evaluation score of the optimal case；
By above flow and step, moon high ladder overall plan optimization design problem is efficiently and reliably handled, and due to
Invention introduces easy to operate and vibrations operation is become, on the one hand accelerate solving speed, improve efficiency, on the other hand improve the overall situation
The ability of search, improve optimization precision.
2. a kind of moon high ladder overall plan optimization method according to claim 1, i.e., a kind of based on improvement resampling grain
The moon high ladder overall plan optimization method of subgroup method, it is characterised in that：
" Optimized model for establishing moon high ladder overall plan " described in step 1, the process that it is established are as follows：
First according to the general requirement of moon high ladder scheme, the design variable of Optimized model is determined, the length, hawser such as hawser
The stress of cross-sectional area and hawser；
Then according to the total demand of moon high ladder scheme, the optimization aim of Optimized model is determined, optimization aim is one and multiple
Several crucial indexs, optimization aim is exactly the evaluation of the scheme obtained according to moon high ladder overall plan evaluation method herein
Fraction；
Finally according to the general requirement of moon high ladder scheme, the constraints of Optimized model is determined, it is that we in the design must
The condition that must meet, its specific targets are provided by user.
3. a kind of moon high ladder overall plan optimization method according to claim 1, i.e., a kind of based on improvement resampling grain
The moon high ladder overall plan optimization method of subgroup method, it is characterised in that：
" initialization particle populations " described in step 2, the practice that it is initialized are as follows：
Particle number N is first determined, typically takes 10~30；
Then initial position co-ordinates x is generated, its method is：
xid=xmin(d)+rand1id·(xmax(d)-xmin(d))
Wherein, xidIt is the coordinate value of i-th particle d dimension, xminAnd x (d)max(d) be respectively particle d dimensional coordinate values lower limit
And the upper limit, rand1 are the random numbers between one group 0~1；
Initial velocity vector v is regenerated, its method is：
vid=xmin(d)+rand2id·(xmax(d)-xmin(d))-xid
Wherein, vidIt is the velocity amplitude of i-th particle d dimension, xminAnd x (d)maxAnd x (d)idImplication be same as above, rand2 is one
Random number between group 0~1；
Then the history optimal location pbest of each particle is initialized, its method is：The initial position for remembering particle is particle history
Optimal location pbest initial value, i.e. pbest=x；Target function value, referred to as history optimal value are obtained simultaneously, is designated as
pbest_f；
The optimal location gbest of colony is finally initialized, its method is：The history optimal value of more above-mentioned each particle, wherein
The initial value that the position of the minimum particle of history optimal value is colony optimal location gbest, the history optimal value are currently complete
Office's optimal value, is designated as gbest_f.
4. a kind of moon high ladder overall plan optimization method according to claim 1, i.e., a kind of based on improvement resampling grain
The moon high ladder overall plan optimization method of subgroup method, it is characterised in that：
" calculate particle active value go forward side by side row variation operation " described in step 6, its practice is as follows：
First, the active value AC of each particle is calculatedi,
Then, AC is judgediWhether 0 is equal to, if ACiIt is not 0, then without any operation, if ACiEqual to 0, then according to
Lower formula obtains particle of the particle after mutation operation.
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5
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710531396.6A CN107403035A (en) | 2017-07-03 | 2017-07-03 | A kind of moon high ladder overall plan optimization method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
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| CN103164742A (en) * | 2013-04-02 | 2013-06-19 | 南京邮电大学 | Server performance prediction method based on particle swarm optimization nerve network |
| CN105893694A (en) * | 2016-04-21 | 2016-08-24 | 北京航空航天大学 | Complex system designing method based on resampling particle swarm optimization algorithm |
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| CN103164742A (en) * | 2013-04-02 | 2013-06-19 | 南京邮电大学 | Server performance prediction method based on particle swarm optimization nerve network |
| CN105893694A (en) * | 2016-04-21 | 2016-08-24 | 北京航空航天大学 | Complex system designing method based on resampling particle swarm optimization algorithm |
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