CN105976018B - Discrete dove group's method for monitoring structural health conditions sensors location - Google Patents

Discrete dove group's method for monitoring structural health conditions sensors location Download PDF

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CN105976018B
CN105976018B CN201610261698.1A CN201610261698A CN105976018B CN 105976018 B CN105976018 B CN 105976018B CN 201610261698 A CN201610261698 A CN 201610261698A CN 105976018 B CN105976018 B CN 105976018B
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pigeon
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伊廷华
温凯方
李宏男
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Dalian University of Technology
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Abstract

The invention belongs to the sensors locations in civil engineering works structure health monitoring field, propose a kind of discrete dove group's method for monitoring structural health conditions sensors location.The present invention includes coding and the four big processes that initialize, take off, fly and go back to the nest: coding and initialization procedure application dual coding mode are used for discretization continuous variable, and initialize dove group's position and speed vector；Take-off process includes emptying and rising two subprocess, for homogenizing dove group's position vector and finding the direction of optimal solution；Flight course includes putting down to fly, turn and chase three subprocess, for finding locally optimal solution, globally optimal solution and improving global worst solution；Process of going back to the nest then avoids algorithm from falling into locally optimal solution.Inventive algorithm can Efficient Solution discrete optimization problems of device, have preferable global convergence, less cycle-index, stronger stability.

Description

Discrete dove group's method for monitoring structural health conditions sensors location
Technical field
The invention belongs to the sensors location in civil engineering works structure health monitoring field, propose that a kind of sensor is excellent Change the discrete dove group's method laid.
Background technique
Sensors location is the primary link in monitoring structural health conditions.Sensors location be exactly it is numerous to It surveys in node, a certain number of sensors is laid, to optimize certain objective function or Optimality Criteria, so that Function Optimization.Mesh The preceding optimization algorithm for sensors location mainly has three classes: one kind is traditional optimization algorithm, such as KEM method, most The determinant of bigization Fisher information battle array and the sensors location algorithm based on simplified model etc..Second class is then sequence Method, such as gradual exclusion and gradually accumulative, target are exactly to make the maximum nondiagonal element of MAC minimum.Third class is based on life The colony intelligence optimization algorithm of object, physics and Artificial Intelligence Development, such as genetic algorithm, particle swarm algorithm, ant group algorithm, harmony Algorithm, fish-swarm algorithm and monkey group's algorithm etc..Such method can preferably solve the limitation of constraint condition in combinatorial optimization problem, and It is not easy to fall into locally optimal solution, can perform well in sensors location carrying out optimizing to objective function.
At present applied to sensors location colony intelligence optimization algorithm mainly have simulated annealing, genetic algorithm, Neural network algorithm, particle swarm algorithm, monkey group algorithm and wolf pack algorithm etc..These algorithms have ten in concrete model example Divide outstanding performance, some has been applied in Practical Project, has become trend using new swarm intelligence algorithm, and have huge Research Prospects and engineering value.
Summary of the invention
The present invention proposes a kind of discrete dove group's method of sensors location, can effectively solve sensors location this Kind integer programming problem.Discrete dove group's algorithm when handle higher-dimension, multi-peak, challenge with stronger global convergence, Less cycle-index and higher stability can carry out Optimality Criteria in the laying of the sensor of large-scale multinode complete Office's optimizing.
One, it encodes and initializes
Pigeon individual, the feasible solution of respective sensor arrangement are indicated using ordered pair (x, c).Wherein, x is the position of pigeon Vector is set, c is binary vector, for indicating the position of sensor.Then it is used for monitoring structural health conditions sensor optimization cloth If discrete dove group algorithm coding and initialization procedure it is as follows:
Step 1: all point positions that each first order mode of structure is contained are as the candidate resource of preferred arrangement, it is assumed that all The integer for 1~sum is numbered in candidate sensor.
Step 2: corresponding by taking i-th (i=1,2 ..., N, N are pigeon quantity in dove group) pigeon in dove group as an example Solution can be expressed as Xi=X (xi,ci)={ (xi,1,ci,1),(xi,2,ci,2),…,(xi,sum,ci,sum), position vector xiBe from Section [xdown,xup] between the real number array that is randomly generated, XiThe current location of as every pigeon.Wherein, per one-dimensional point Amount can indicate are as follows:
xi,j=rand × (xup-xdown)+xdown (1)
In formula: rand is the random number in [0,1].Yi=Y (yi,ci)={ (yi,1,ci,1),(yi,2,ci,2),…, (yi,sum,ci,sum) be every pigeon i current optimal location；Pb=P (pb,cb)={ (pb,1,cb,1),(pb,2,cb,2),…, (pb,sum,cb,sum) it is the current optimal location of dove group；Pw=P (pw,cw)={ (pw,1,cw,1),(pw,2,cw,2),…,(pw,sum, cw,sum) it is the current worst position of dove group.
ci,jFor xi,jBinary coding vector obtained from being converted as sig function:
When using above formula, judgment threshold ε and section [x are neededdown,xup], if sig (xi,j) > ε, then corresponding ci,j1 is taken, Sensor is laid in expression at this location；If sig (xi,j)≤ε, then the value of the component is 0, is shown on the position of the node Do not lay sensor.Herein, ε=0.5 is taken, is found by calculating, works as xi,jWhen value is between [- 5,5], 0.0067≤ sig(xi,j)≤0.9933, it can be seen that this obtaining value method is relatively reasonable.
Assuming that the number of sensors to be arranged is sp, in the operating process of algorithm, since the initialization of dove group's individual is Random, when laying sensor it is possible that the case where being not equal to sp, is unsatisfactory for the requirement that sensor lays number.Then need Step 2 is repeated, the initialization of dove group's individual is re-started, until laying number sp until meeting sensor, herein below During such as encounter similar situation and do same processing.
Since dove group's individual is all random initializtion, the initialization of entire dove group individual will meet the sensor number of laying Sp is measured, therefore, the generation of dove group's individual is not necessarily all effective.A kind of side based on probabilistic method decision threshold ε will be introduced herein Method come improve dove group initialization generation efficiency.With dove group's individual piJth tie up component pi,jFor, si,j=1 probability is sp/ Sum, so that si,j=0 probability is 1-sp/sum, and dove group's individual initialization can be made statistically to can satisfy coding in this way It is required that.Therefore, a value x can be setw, work as xi,j∈[xdown,-xw] when, si,j=0, and xi,jProbability in the section is 1-sp/sum；Work as xi,j∈(-xw,xup] when, si,j=1, and xi,jProbability in the section is sp/sum.So xwValue It can be with are as follows:
xw=(sp/num) × (xup-xdown)-xup (3)
Pass through xwBy section [xdown,xup] be split, therefore the value of ε should beThreshold epsilon is according to this Kind obtaining value method can accelerate the production of initial dove group on the basis of ensure that the uniformity of each component of dove group's individual Raw speed.
Step 3: dove group's susceptibility initialization
Need to initialize the sensitivity coefficient α of every pigeon when likewise, dove group being introducedi, αiIt is produced at random from [0,1] It is raw.
Step 4: the initialization of dove group velocity
Vector Vi=(vi,1,vi,2,…,vi,j,…vi,sum) be pigeon i flying speed, [- Vmax,Vmax] it is flying speed Range, vijIt is therefrom randomly generated, expression formula are as follows:
vi,j=δ Vmax (4)
In formula: δ is the random number in [- 1,1].
Two, it takes off
(1) it empties
For dove group when taking off, the height for pedaling ground is different.According to this characteristic, initial value is homogenized, define [down, Up] be dove group empty section.
Step 1: setting Δ Xi=(Δ xi,1,Δxi,2,…,Δxi,j,…,Δxi,sum) be pigeon i height of arch, Δ Xi In be randomly generated per one-dimensional component from emptying in range, expression formula:
Δxi,j=κ (up-down)+down (5)
In formula: κ is the random number in [0,1].
Step 2: updating the current location X (x of every pigeoni,ci), expression formula
X(xi,ci)=Y (yi,ci)+αi*ΔXi (6)
If X (xi,ci) it is better than current optimal location Y (yi,ci), then by current location X (xi,ci) it is assigned to current optimal location Y(yi,ci), i.e. Y (yi,ci)=X (xi,ci), if XiOptimal location P (p current better than dove groupb,cb), then enable P (pb,cb)=X (xi,ci)。
Note 1: in step 2, in Y (yi,ci)+αi*ΔXiWhen, due to Y (yi,ci)={ (yi,1,ci,1),(yi,2, ci,2),…,(yi,sum,ci,sum), Δ Xi=(Δ xi,1,Δxi,2,…,Δxi,j,…,Δxi,sum), in fact, in specific phase Added-time is per one-dimensional component yi,j+αi*Δxi,jIt is added, and component c new after being addedNewi,jIt is still new component yi,jPass through Binary coding vector obtained from the conversion of sig function, such as encounters the addition phase of phase position vector in the later step of this paper When subtracting situation, all first individually position vector is added and subtracted, binary vector is calculated by the position vector of each dimension cNewi,j.But it is calculating per one-dimensional component yi,j+αi*Δxi,jWhen, it is the case where obtained new component can generate " spilling ", i.e., super Section [x outdown,xup], therefore provide, if exceeding upper limit xup, then value is xup；If being less than lower limit xdown, then value is xdown。 During the flight course after this paper is with going back to the nest, if encountering similar situation, all need to do same treatment.
Note 2: to improve algorithm later period convergent accuracy and speed.Emptying section [down, up] can be current with dove group Optimal location P (pb,cb) variation and change, accuracy and P (pb,cb) in maximum value it is identical.For example, P (pb,cb)= {(pb,1,cb,1),(pb,2,cb,2),…,(pb,sum,cb,sum), work as pb,1,pb,2,…,pb,sumIn the accuracy of maximum value be When 0.1, empties section and keeps identical accuracy:
(2) rise
Dove group has uphill process after emptying, and dove group is made to fly towards more preferably direction.This characteristic is simulated, with pseudo- gradient side Method finds the direction of optimal solution, referred to as ascent direction f 'i,j(X(xi,ci))。
Step 1: by formula (8), vector Δ C is randomly generatedI=(Δci,1,Δci,2,…,Δci,j,…,Δci,sum)
In formula: ri is lifting height.
Step 2: calculating pigeon i in the ascent direction f ' of every dimension ji,j(Xi), expression formula:
Step 3: updating the current location X (x of every pigeoni,ci), expression formula:
xi,j=yi,j+ri*sign(f′i,j(X(xi,ci))) (10)
In formula: sign (x) is sign function, the sign (x)=1 as x > 0；The sign (x)=0 as x=0；As x < 0 Sign (x)=- 1.If X (xi,ci) it is better than current optimal location Y (yi,ci), then by current location X (xi,ci) be assigned to it is current optimal Position Y (yi,ci), i.e. Y (yi,ci)=X (xi,ci), if XiOptimal location P (p current better than dove groupb,cb), then enable P (pb,cb)= X(xi,ci)。
Step 4: step 1 of recycling to step 3.
Note: step 1-4 is only carried out twice, because dove group will not be constantly in ascent stage, which is used only to find More preferably heading.The upper life smaller then later period convergence precision of height ri is higher, but preconvergence speed can be slack-off.It is further Improve algorithm later period convergent accuracy and speed.The accuracy that lifting height ri ratio empties range [down, up] is one more, Such as when the accuracy of [down, up] is 0.1, the accuracy of ri is 0.01, i.e. ri=ri*0.01.
Three, it flies
(1) it puts down and flies and turn
The neighbor scope for defining pigeon i is M, i.e., neighbours of the M pigeon around pigeon as itself；AveiFor neighbours dove The mean place of group.Flat winged number is F1；Variable r, value range are [1, F1], it often puts down and flies once to add 1.
Step 1: calculating the mean place ave of pigeon ii, expression formula:
In the formula, M is a very important parameter, it will affect the optimizing of local optimum.When the value mistake of M When big, AveiValue can level off to global optimum, this will affect convergence speed of the algorithm；When the value of M is too small, algorithm is easy Premature Convergence influences the precision of algorithm.In the formulaIt is downward bracket function.
Step 2: calculating the flying speed V of pigeon ii.It is as follows with formula
Vi=w*Vi+c1*(Avei-X(xi,ci)) (12)
The value of w is as follows:
The case where " spilling " can be generated in the new velocity vector being calculated, exceeds section [- Vmax,Vmax], therefore Regulation, if exceeding upper limit Vmax, then value is Vmax；If being less than lower limit-Vmax, then value is-Vmax。
Step 3: the current location of every pigeon is updated, expression formula is as follows:
Xr+1(xi,ci)=Xr(xi,ci)+Vi (14)
Step 4: repeating step 1 to step 3, until reaching flat winged cycle-index F1。
(2) it turns
Step 1: definition number of turns is F2.Calculate the flying speed V of pigeon ii。
Vi=c2*(P(pb,cb)-Y(yi,ci)) (15)
In formula: c2It is the global flight factor.
Step 2: updating the current location of every pigeon, the same formula of expression formula (14).
If Xr+1(xi,ci) it is better than current optimal location Y (yi,ci), then enable Y (yi,ci)=Xr+1(xi,ci), if X (xi,ci) Optimal location P (p current better than dove groupb,cb), then enable P (pb,cb)=Xr+1(xi,ci)。
Step 3: repeating step 1 to step 2, until reaching turning cycle-index F2。
Note: since the sensor of every pigeon lays component ci,jIt is by location components xi,jDetermining, so turning P (p before processb,cb) and Y (yi,ci) value all determined respectively, and the corresponding binary coding for meeting number of sensors ci, the value after the two calculates is also definite value, but not necessarily meets sensing using the binary coding that new position vector calculates The arrangement number requirement of device, so needing further to improve dove group's algorithm herein, without position during flat fly Vector is set to binary coding sig (xi,j) conversion, but fly flat and after turning process is common, carry out sig (xi,j) Conversion, if being unsatisfactory for laying the requirement of quantity sp, repeat flat to fly over journey if being unsatisfactory for the coding requirement of sensor laying Step 2, until laying number until meeting.
(3) it chases
Step 1: an integer-bit cp is randomly generated between [n/2]~n dimension of n-dimensional space vector, is replaced as position Dai Dian:
Cp=[n/2]+[φ (n/2)] (16)
In formula: φ is the random number in [0,1].
Step 2: by Pb=P (pb,cb)={ (pb,1,cb,1),(pb,2,cb,2),…,(pb,cp,cb,cp),…,(pb,sum, cb,sum) in from the value of cp~sum be copied directly to Pw=P (pw,cw)={ (pw,1,cw,1),(pw,2,cw,2),…,(pw,cp, cw,cp),…,(pw,sum,cw,sum) in the corresponding position cp~sum, if the worst position P of updated groupwBetter than before most Poor position then retains update, otherwise without updating.Further, since needing to meet the number of sensor laying, so if more P after newwIt is not able to satisfy the number requirement of sensor laying, then without updating yet.
Four, it goes back to the nest
Step 1: for pigeon i, the coefficient r that goes back to the nest being randomly generated in [- rg, rg]i。
Step 2: according to the current optimal location of every pigeon, judging the difference of a body position and other pigeon mean places Away from.
Step 3: updating the current location of pigeon i.
X(xi,ci)=Y (yi,ci)+ΔHi (18)
If X (xi,ci) it is better than current optimal location Y (yi,ci), then enable Y (yi,ci)=X (xi,ci), if X (xi,ci) be better than The current optimal location P (p of dove groupb,cb), then enable P (pb,cb)=X (xi,ci)。
A complete algorithm flow is i.e.: coding and initializing, takes off, flying, four big processes of going back to the nest.Iterate this mistake Journey, until finding globally optimal solution or meeting termination condition.
Beneficial effects of the present invention:
Discrete dove group algorithm has preferable global convergence, algorithm circulation in higher-dimension, multi-peak complicated function The less and stronger stability of number can effectively solve the problems, such as this large space search of sensors location.
Detailed description of the invention
Fig. 1 is bridge benchmark model.
Fig. 2 is that discrete dove group's algorithm is made to lay result figure to the three dimension mode confidence criterion optimization for considering redundancy.
Fig. 3 is to compare figure according to the Method of Mode Fitting in 5 direction rank z of model for laying node location fitting.
Specific embodiment
Below in conjunction with attached drawing and technical solution, a specific embodiment of the invention is further illustrated.
Bridge model totally two across, it is 5.4864 meters long, it is 1.8288 meters wide.Bridge model is modeled using SAP2000, and the model is Through having imported into MTLAB.177 nodes are shared, each node there are 3 freedom degrees i.e. tri- directions x, y and z.The model Finite element model it is as shown in Fig. 1.
Optimality Criteria chooses the three dimension mode confidence criterion for considering redundancy, formula: f=max (TMAC-I)+ω g (R). In formula: TMAC is three dimension mode confidence Criterion Matrix, and I is unit matrix, and ω is that weight coefficient (adjusts the successive of TMAC and R optimization Sequentially), g (R) is redundancy function.TMAC formula are as follows:In formula: Fi,jTo be laid by sensor position The i-th row jth column element in the Fisher information battle array of corresponding node.TMACi,j∈ [0,1], TMACi,jFor the i-th row in TMAC Jth column element.
By the mass matrix and stiffness matrix of model, the available Mode Shape matrix of model analysis is carried out to model, It can be carried out the calculating of three dimension mode confidence criterion, and with method of the invention come to objective function optimizing.Parameter selection is pressed Chosen according to the term of reference that provides of dove group's algorithm, the pigeon quantity of dove group is N=60, empty range [down, up] be [- 1,1], lifting height ri takes 0.1, neighbor scope M=5, maximum flying speed Vmax=1, range of going back to the nest [- rg, rg] be [- 5, 5], winged number F equal with number of turns is put down1=F2=5, local flight coefficient c1=1 and global flight coefficient c2=1.Algorithm Termination condition is loop iteration 200 times.The node installation position of experimental result is as shown in Fig. 2.The adjacent feelings of sensor node Condition is less, and laying is more uniform, visual preferable.So the vibration information measured is also more.Fig. 3 is the node according to laying 5 direction rank z formation fitted figures being fitted with cubic spline interpolation.Fitting effect is preferable.

Claims (1)

1. a kind of discrete dove group's method for monitoring structural health conditions sensors location, it is characterised in that following steps:
(1) it encodes and initializes
Pigeon individual, the feasible solution of respective sensor installation position are indicated using ordered pair (x, c)；Wherein, x is the position of pigeon Vector, c are binary vector, for indicating the riding position of sensor；Coding and initialization procedure are as follows:
Step 1: using all nodes contained in the structural modal vibration shape as the position candidate of sensor arrangement, it is assumed that passed wait lay The integer that the number of sensor is 1~sum；
Step 2: using i-th pigeon in dove group as node, i=1,2 ..., N, N are pigeon quantity in dove group, homographic solution For Xi=X (xi,ci)={ (xi,1,ci,1),(xi,2,ci,2),…,(xi,sum,ci,sum), position vector xiIt is from section [xdown, xup] between the real number array that is randomly generated, XiAs every pigeon current location；Wherein per one-dimensional representation in components are as follows:
xi,j=rand × (xup-xdown)+xdown (1)
In formula: rand is the random number in [0,1]；Yi=Y (yi,ci)={ (yi,1,ci,1),(yi,2,ci,2),…,(yi,sum, ci,sum) be every pigeon i current optimal location；Pb=P (pb,cb)={ (pb,1,cb,1),(pb,2,cb,2),…,(pb,sum, cb,sum) it is the current optimal location of dove group；Pw=P (pw,cw)={ (pw,1,cw,1),(pw,2,cw,2),…,(pw,sum,cw,sum) be The current worst position of dove group；
ci,jFor xi,jBinary coding vector obtained from being converted as sig function:
The generation efficiency of dove group's initialization is improved using the method based on probabilistic method decision threshold ε；Assuming that the sensor to be arranged Number is sp, in the operating process of algorithm, due to dove group individual initialization be it is random, may when laying sensor There is the case where not equal to sp, be unsatisfactory for the requirement that sensor lays number, then need to repeat step 2, re-starts dove group The initialization of body, until laying number sp until meeting sensor；
With dove group's individual piJth tie up component pi,jFor, ci,j=1 probability is sp/sum, so that ci,j=0 probability is 1- Sp/sum, so that dove group's individual initialization meets coding requirement；Set xw, work as xi,j∈[xdown,-xw] when, ci,j=0, and xi,jProbability in the section is 1-sp/sum；Work as xi,j∈(-xw,xup] when, ci,j=1, and xi,jProbability in the section is sp/sum；So xwValue are as follows:
xw=(sp/sum) × (xup-xdown)-xup (3)
Pass through xwBy section [xdown,xup] be split, therefore the value of ε is
Step 3: dove group's susceptibility initialization
Need to initialize the sensitivity coefficient α of every pigeon when dove group is introducedi, αiIt is randomly generated from [0,1]；
Step 4: the initialization of dove group velocity
Vector Vi=(vi,1,vi,2,…,vi,j,…vi,sum) be pigeon i flying speed, [- Vmax,Vmax] be flying speed model It encloses, vijIt is therefrom randomly generated, expression formula are as follows:
vi,j=δ Vmax (4)
In formula: δ is the random number in [- 1,1]；
(2) it takes off
(1) it empties
For dove group when taking off, the height for pedaling ground is different；According to this characteristic, initial value is homogenized, defining [down, up] is Dove group's empties section；
Step 1: setting Δ Xi=(Δ xi,1,Δxi,2,…,Δxi,j,…,Δxi,sum) be pigeon i height of arch, Δ XiIn it is every One-dimensional component is randomly generated from emptying in range, expression formula:
Δxi,j=κ (up-down)+down (5)
In formula: κ is the random number in [0,1]；
Step 2: updating the current location X (x of every pigeoni,ci), expression formula
X(xi,ci)=Y (yi,ci)+αi*ΔXi (6)
If X (xi,ci) it is better than current optimal location Y (yi,ci), then by current location X (xi,ci) it is assigned to current optimal location Y (yi, ci), i.e. Y (yi,ci)=X (xi,ci), if XiOptimal location P (p current better than dove groupb,cb), then enable P (pb,cb)=X (xi,ci)；
In step 2, in Y (yi,ci)+αi*ΔXiWhen, due to Y (yi,ci)={ (yi,1,ci,1),(yi,2,ci,2),…,(yi,sum, ci,sum), Δ Xi=(Δ xi,1,Δxi,2,…,Δxi,j,…,Δxi,sum), in fact, being per one-dimensional point in specific be added Measure yi,j+αi*Δxi,jIt is added, and component c new after being addedNewi,jIt is still new component yi,jIt is converted by sig function The binary coding vector arrived, when encountering the addition of position vector in the next steps and subtracting each other situation, all first individually to position to Amount is added and subtracted, and binary vector c is calculated by the position vector of each dimensionNewi,j；But it is calculating per one-dimensional component yi,j+αi*Δxi,jWhen, there may be beyond section [x for obtained new componentdown,xup] the case where, it is specified that if exceed upper limit xup, Then value is xup；If being less than lower limit xdown, then value is xdown；During flight course is with going back to the nest, if encountering similar situation, Same mode is all made of to handle；
To improve algorithm later period convergent accuracy and speed；Section [down, up] is emptied with the current optimal location P of dove group (pb,cb) variation and change, accuracy and P (pb,cb) in maximum value it is identical；P(pb,cb)={ (pb,1,cb,1),(pb,2, cb,2),…,(pb,sum,cb,sum), work as pb,1,pb,2,…,pb,sumIn maximum value when being 0.1, empty section and keep identical essence Exactness:
(2) rise
Dove group has uphill process after emptying, and dove group is made to fly towards more preferably direction；This characteristic is simulated, with pseudo- gradient method, is sought Look for the direction of optimal solution, referred to as ascent direction fi,′j(X(xi,ci))；
Step 1: by formula (8), vector Δ C is randomly generatedi=(Δ ci,1,Δci,2,…,Δci,j,…,Δci,sum)
In formula: ri is lifting height；
Step 2: calculating pigeon i in the ascent direction f of every dimension ji,′j(Xi), expression formula:
Step 3: updating the current location X (x of every pigeoni,ci), expression formula:
xi,j=yi,j+ri*sign(fi,′j(X(xi,ci))) (10)
In formula: sign (x) is sign function, the sign (x)=1 as x > 0；The sign (x)=0 as x=0；The sign as x < 0 (x)=- 1；If X (xi,ci) it is better than current optimal location Y (yi,ci), then by current location X (xi,ci) it is assigned to current optimal location Y(yi,ci), i.e. Y (yi,ci)=X (xi,ci), if XiOptimal location P (p current better than dove groupb,cb), then enable P (pb,cb)=X (xi,ci)；
Step 4: step 1 of recycling to step 3；
(3) it flies
(1) it puts down and flies and turn
The neighbor scope for defining pigeon i is M, i.e., neighbours of the M pigeon around pigeon as itself；AveiFor neighbours dove group's Mean place；Flat winged number is F1；Variable r, value range are [1, F1], it often puts down and flies once to add 1；
Step 1: calculating the mean place ave of pigeon ii, expression formula:
In formula (11), M is a very important parameter, it influences the optimizing of local optimum；When the value of M is excessive When, AveiValue level off to global optimum, influence convergence speed of the algorithm；When the value of M is too small, algorithm is easy precocious receive It holds back, influences the precision of algorithm；In the formulaIt is downward bracket function；
Step 2: calculating the flying speed V of pigeon ii；Formula is as follows
Vi=w*Vi+c1*(Avei-X(xi,ci)) (12)
Wherein, c1Indicate local flight coefficient；
The value of w is as follows:
It can generate in the new velocity vector being calculated beyond section [- Vmax,Vmax] the case where, therefore provide, if beyond upper Limit Vmax, then value is Vmax；If being less than lower limit-Vmax, then value is-Vmax；
Step 3: the current location of every pigeon is updated, expression formula is as follows:
Xr+1(xi,ci)=Xr(xi,ci)+Vi (14)
Step 4: repeating step 1 to step 3, until reaching flat winged cycle-index F1；
(2) it turns
Step 1: definition number of turns is F2；Calculate the flying speed V of pigeon ii；
Vi=c2*(P(pb,cb)-Y(yi,ci)) (15)
In formula: c2It is the global flight factor；
Step 2: updating the current location of every pigeon, the same formula of expression formula (14)；
If Xr+1(xi,ci) it is better than current optimal location Y (yi,ci), then enable Y (yi,ci)=Xr+1(xi,ci), if X (xi,ci) be better than The current optimal location P (p of dove groupb,cb), then enable P (pb,cb)=Xr+1(xi,ci)；
Step 3: repeating step 1 to step 2, until reaching turning cycle-index F2；
(3) it chases
Step 1: an integer-bit cp is randomly generated between [n/2]~n dimension of n-dimensional space vector, as position alternative point:
Cp=[n/2]+[φ (n/2)] (16)
In formula: φ is the random number in [0,1]；
Step 2: by Pb=P (pb,cb)={ (pb,1,cb,1),(pb,2,cb,2),…,(pb,cp,cb,cp),…,(pb,sum,cb,sum)} In from the value of cp~sum copy to Pw=P (pw,cw)={ (pw,1,cw,1),(pw,2,cw,2),…,(pw,cp,cw,cp),…, (pw,sum,cw,sum) in the corresponding position cp~sum, if the worst position P of updated groupwBetter than worst position before, then Retain and update, otherwise without updating；Further, since needing to meet the number of sensor laying, so if updated Pw It is not able to satisfy the number requirement of sensor laying, then without updating yet；
(4) it goes back to the nest
Step 1: for pigeon i, the coefficient r that goes back to the nest being randomly generated in [- rg, rg]i；
Step 2: according to the current optimal location of every pigeon, judging the gap of a body position and other pigeon mean places；
Step 3: updating the current location of pigeon i；
X(xi,ci)=Y (yi,ci)+ΔHi (18)
If X (xi,ci) it is better than current optimal location Y (yi,ci), then enable Y (yi,ci)=X (xi,ci), if X (xi,ci) better than dove group Current optimal location P (pb,cb), then enable P (pb,cb)=X (xi,ci)；
A complete algorithm flow is i.e.: coding and initializing, takes off, flying, four big processes of going back to the nest；Iterate this process, Until finding globally optimal solution or meeting termination condition.
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