CN105976018A - Discrete pigeon flock algorithm for structure health monitoring sensor optimal layout - Google Patents

Abstract

The invention belongs to sensor optimal layout in the field of civil engineering structure health monitoring, and provides a discrete pigeon flock algorithm for structure health monitoring sensor optimal layout. The method comprises a coding and initializing process, a take-off process, a flight process and a homing process. The coding and initializing process adopts a dual-coding mode, and is used to discretize a continuous variable and initialize pigeon flock position and velocity vectors. The take-off process consists of a soaring sub process and a rising sub process, and is used to homogenize the pigeon flock position vector and to look for the direction of optimal solution. The flight process includes a level flight sub process, a turning sub process and a chasing sub process, and is used to look for a local optimal solution and a global optimal solution and improve a global worst solution. The homing process prevents the algorithm from being trapped into a local optimal solution. The algorithm of the invention can be used to solve a discrete optimization problem with high efficiency, and has the advantages of good global convergence, fewer cycles and strong stability.

Description

Discrete Columba livia group's algorithm 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 a kind of sensor excellent Change the discrete Columba livia group's algorithm laid.

Background technology

Sensors location is the primary link in monitoring structural health conditions.Sensors location is exactly to treat numerous Survey in node, lay a number of sensor, optimize certain object function or Optimality Criteria so that Function Optimization.Mesh Before mainly have three classes for the optimized algorithm of sensors location: a class is traditional optimized algorithm, such as KEM method, The determinant of bigization Fisher information battle array and sensors location algorithm based on simplified model etc..Equations of The Second Kind is then sequence Method, such as gradual exclusion and progressively method of cumulative scale, its target is exactly to make the maximum nondiagonal element of MAC minimum.3rd class is based on life The colony intelligence optimized algorithm of thing, physics and Artificial Intelligence Development, such as genetic algorithm, particle cluster algorithm, ant group algorithm, harmony Algorithm, fish-swarm algorithm and monkey group's algorithm etc..Such method can preferably solve the restriction of constraints in combinatorial optimization problem, and It is difficult to be absorbed in locally optimal solution, can perform well in sensors location carries out optimizing to object function.

Be applied at present the colony intelligence optimized algorithm of sensors location mainly have simulated annealing, genetic algorithm, Neural network algorithm, particle cluster algorithm, monkey group's algorithm and wolf pack algorithm etc..These algorithms have ten in concrete model example Dividing outstanding performance, have has been applied in Practical Project, uses new swarm intelligence algorithm to have become as trend, and has huge Research Prospects and construction value.

Summary of the invention

The present invention proposes discrete Columba livia group's algorithm of a kind of sensors location, can effectively solve sensors location this Plant integer programming problem.Discrete Columba livia group's algorithm have when processing higher-dimension, multi-peak, challenge stronger global convergence, Less cycle-index and higher stability, can be carried out Optimality Criteria in the sensor of large-scale multinode is laid entirely Office's optimizing.

One, encode and initialize

(x c) represents that pigeon is individual, the feasible solution that respective sensor is arranged to utilize ordered pair.Wherein, x is the position of pigeon Putting vector, c is binary vector, for representing the position of sensor.Then for monitoring structural health conditions sensor optimization cloth If the coding of discrete Columba livia group's algorithm and initialization procedure as follows:

Step 1: all point positions contained by each for structure first order mode are as the candidate resource of preferred arrangement, it is assumed that all The sensor of candidate be numbered be 1～sum integer.

Step 2: with in Columba livia group i-th (i=1,2 ..., N, N are pigeon quantity in Columba livia group) as a example by a pigeon, its correspondence Solution can be expressed as X_i=X (x_i,c_i)={ (x_i,1,c_i,1),(x_i,2,c_i,2),…,(x_i,sum,c_i,sum), position vector x_iBe from Interval [x_down,x_upThe real number array randomly generated between], X_iIt is the current location of every pigeon.Wherein, the most one-dimensional point Amount can be expressed as:

x_i,j=rand × (x_up-x_down)+x_down (1)

In formula: rand is the random number in [0,1].Y_i=Y (y_i,c_i)={ (y_i,1,c_i,1)_,(y_i,2,c_i,2),…, (y_i,sum,c_i,sum) it is the current optimal location of every pigeon i；P_b=P (p_b,c_b)={ (p_b,1,c_b,1),(p_b,2,c_b,2),…, (p_b,sum,c_b,sum) it is the current optimal location of Columba livia group；P_w=P (p_w,c_w)={ (p_w,1,c_w,1),(p_w,2,c_w,2),…,(p_w,sum, c_w,sum) it is the current worst position of Columba livia group.

c_i,jFor x_i,jThe binary coding vector changed by sig function and obtain:

$c_{i,j}=sig\left(x_{i,j}\right)=\frac{1}{1+e^{-x_{i,j}}}---\left(2\right)$

When using above formula, need judgment threshold ε and interval [x_down,x_up], if sig is (x_i,j) > ε, then corresponding c_i,jTake 1, Represent and lay sensor in this position；If sig is (x_i,j)≤ε, then the value of this component is 0, shows on the position of this node Do not lay sensor.In this article, take ε=0.5, found by calculating, work as x_i,jWhen value is between [-5,5], 0_.0067≤ sig(x_i,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, the initialization individual due to Columba livia group is Random, when laying sensor it is possible that be not equal to the situation of sp, it is unsatisfactory for sensor and lays the requirement of number.Then need Step 2 to be repeated, re-starts the initialization that Columba livia group is individual, until meeting sensor to lay number sp, herein below During such as run into similar situation and all do same process.

Owing to Columba livia group individuality is all random initializtion, the sensor number of the initialization laying to be met that whole Columba livia group is individual Amount sp, therefore, the generation of Columba livia group individuality is not necessarily all effective.It is introduced into a kind of side based on probabilistic method decision threshold ε herein Method improves the initialized generation efficiency of Columba livia group.With Columba livia group individuality p_iJth dimension component p_i,jAs a example by, s_i,jThe probability of=1 is sp/ Sum so that s_i,jThe probability of=0 is 1-sp/sum, so so that Columba livia group's individuality initializes statistically disclosure satisfy that coding Requirement.Therefore, it can set value x_w, work as x_i,j∈[x_down,-x_w] time, s_i,j=0, and x_i,jProbability in this interval is 1-sp/sum；Work as x_i,j∈(-x_w,x_up] time, s_i,j=1, and x_i,jProbability in this interval is sp/sum.So x_wValue Can be:

x_w=(sp/num) × (x_up-x_down)-x_up (3)

I.e. pass through x_wBy interval [x_down,x_up] split, therefore the value of ε should beThreshold epsilon is according to this Plant obtaining value method and can accelerate the product of initial Columba livia group on the basis of the uniformity that ensure that Columba livia group each component individual Raw speed.

Step 3: Columba livia group's sensitivity initializes

Same, need to initialize the sensitivity coefficient α of every pigeon when Columba livia group being introduced_i, α_iProduce at random from [0,1] Raw.

Step 4: Columba livia group velocity initializes

Vector V_i=(v_i,1,v_i,2,…,v_i,j,…v_i,sum) it is the flight speed of pigeon i, [-V_max,V_max] it is flight speed Scope, v_ijTherefrom randomly generating, its expression formula is:

v_i,j=δ V_max (4)

In formula: δ is the random number in [-1,1].

Two, take off

(1) soar

Columba livia group is when taking off, and the height pedaling ground is different.According to this characteristic, homogenization initial value, define [down, Up] it is the interval of soaring of Columba livia group.

Step 1: set Δ X_i=(Δ x_i,1,Δx_i,2,…,Δx_i,j,…,Δx_i,sum) it is the height of arch of pigeon i, Δ X_i In every one-dimensional component randomly generate from the scope of soaring, its expression formula:

Δx_i,j=κ (up-down)+down (5)

In formula: κ is the random number in [0,1].

Step 2: update the current location X (x of every pigeon_i,c_i), its expression formula

X(x_i,c_i)=Y (y_i,c_i)+α_i*ΔX_i (6)

If X is (x_i,c_i) it is better than current optimal location Y (y_i,c_i), then by current location X (x_i,c_i) it is assigned to current optimal location Y(y_i,c_i), i.e. Y (y_i,c_i)=X (x_i,c_i), if X_iIt is better than Columba livia group current optimal location P (p_b,c_b), then make P (p_b,c_b)=X (x_i,c_i)。

Note 1: in step 2, at Y (y_i,c_i)+α_i*ΔX_iTime, due to Y (y_i,c_i)={ (y_i,1,c_i,1),(y_i,2, c_i,2),…,(y_i,sum,c_i,sum), Δ X_i=(Δ x_i,1,Δx_i,2,…,Δx_i,j,…,Δx_i,sum), it practice, in concrete phase Added-time, is every one-dimensional component y_i,j+α_i*Δx_i,jIt is added, and component c new after being added_Newi,jIt is still new component y_i,jPass through The binary coding vector that sig function is changed and obtained, such as runs into the addition phase of phase position vector in later step herein When subtracting situation, all first individually position vector is added and subtracted, calculate binary vector by the position vector of each dimension c_Newi,j.But calculating every one-dimensional component y_i,j+α_i*Δx_i,jTime, the new component obtained can produce the situation of " spilling ", super Go out interval [x_down,x_up], therefore specify, if beyond upper limit x_up, then value is x_up；If less than lower limit x_down, then value is x_down。 Flight course after this paper and during going back to the nest, if running into analogue, all needs to do same treatment.

Note 2: for improving degree of accuracy and the speed of the convergence of algorithm later stage.Soaring interval [down, up] can be current along with Columba livia group Optimal location P (p_b,c_b) change and change, its degree of accuracy and P (p_b,c_bMaximum in) is identical.Such as, P (p_b,c_b)= {(p_b,1,c_b,1),(p_b,2,c_b,2),…,(p_b,sum,c_b,sum), work as p_b,1,p_b,2,…,p_b,sumIn the degree of accuracy of maximum be When 0.1, the degree of accuracy that interval holding of soaring is identical:

$\left\{\begin{array}{c}{\mathrm{up}}_{new}=up*0.1\\ {\mathrm{down}}_{new}=down*0.1\end{array}\right.---\left(7\right)$

(2) rise

Columba livia group has uphill process after soaring, and makes Columba livia group towards more excellent direction flight.Simulate this characteristic, with pseudo-gradient side Method, finds the direction of optimal solution, referred to as ascent direction f '_i,j(X(x_i,c_i))。

Step 1: by formula (8), randomly generates vector Δ C_i=(Δ c_i,1,Δc_i,2,…,Δc_i,j,…,Δc_i,sum)

In formula: ri is lifting height.

Step 2: calculate the pigeon i ascent direction f ' at every dimension j_i,j(X_i), its expression formula:

$\begin{array}{ccc}{f}_{i,j}^{\′}\left(X\right(x_i,c_i\left)\right)=\frac{f\left(X\right(x_i,c_i)+{\mathrm{\ΔC}}_i)-f\left(X\right(x_i,c_i)-{\mathrm{\ΔC}}_i)}{2{\mathrm{\Δc}}_{i,j}},& i=1,2,\mathrm{...},N,& j=1,2,\mathrm{...},sum\end{array}---\left(9\right)$

Step 3: update the current location X (x of every pigeon_i,c_i), its expression formula:

x_i,j=y_i,j+ri*sign(f′_i,j(X(x_i,c_i))) (10)

In formula: sign (x) is sign function, as x > 0 time sign (x)=1；Sign (x)=0 as x=0；When x is < when 0 Sign (x)=-1.If X is (x_i,c_i) it is better than current optimal location Y (y_i,c_i), then by current location X (x_i,c_i) it is assigned to current optimum Position Y (y_i,c_i), i.e. Y (y_i,c_i)=X (x_i,c_i), if X_iIt is better than Columba livia group current optimal location P (p_b,c_b), then make P (p_b,c_b)= X(x_i,c_i)。

Step 4: step 1 of recirculation is to step 3.

Note: step 1-4 is only carried out twice, because Columba livia group will not be constantly in ascent stage, this stage is used only to find More excellent heading.Upper raw height ri convergence precision of the least then later stage is the highest, but preconvergence speed can be slack-off.For further Improve degree of accuracy and the speed of the convergence of algorithm later stage.More than the degree of accuracy of the scope of soaring [down, up] one of lifting height ri, Such as when the degree of accuracy of [down, up] is 0.1, the degree of accuracy of ri is 0.01, i.e. ri=ri*0.01.

Three, flight

(1) flat fly and turn

The neighbor scope of definition pigeon i is M pigeon around M, the i.e. pigeon neighbours as self；Ave_iFor neighbours Columba livia The mean place of group.It is flat that to fly number of times be F₁；Variable r, span is [1, F₁], often put down and fly once to add 1.

Step 1: calculate mean place ave of pigeon i_i, its expression formula:

In this formula, M is a very important parameter, and it can affect the optimizing of local optimum.Value mistake as M Time big, Ave_iValue can level off to global optimum, this can affect convergence of algorithm speed；When the value of M is too small, algorithm is easy Premature Convergence, affects the precision of algorithm.In this formulaIt it is downward bracket function.

Step 2: calculate flight speed V of pigeon i_i.As follows with formula

V_I=w*V_i+c₁*(Ave_i-X(x_i,c_i)) (12)

The value of w is as follows:

$w=0.9-\frac{0.5}{M_c-1}*(cn-1)---\left(13\right)$

The situation of " spilling " can be produced, i.e. beyond interval [-V when calculated new velocity vector_max,V_max], therefore Regulation, if beyond upper limit V_max, then value is V_max；If less than lower limit-V_max, then value is-V_max。

Step 3: update the current location of every pigeon, its expression formula is as follows:

X^r+1(x_i,c_i)=X^r(x_i,c_i)+V_i (14)

Step 4: repeat step 1 to step 3, until it reaches put down and fly cycle-index F₁。

(2) turn

Step 1: definition number of turns is F₂.Calculate flight speed V of pigeon i_i。

V_i=c₂*(P(p_b,c_b)-Y(y_i,c_i)) (15)

In formula: c₂It it is the overall situation flight factor.

Step 2: update the current location of every pigeon, the same formula of its expression formula (14).

If X^r+1(x_i,c_i) it is better than current optimal location Y (y_i,c_i), then make Y (y_i,c_i)=X^r+1(x_i,c_i), if X is (x_i,c_i) It is better than Columba livia group current optimal location P (p_b,c_b), then make P (p_b,c_b)=X^r+1(x_i,c_i)。

Step 3: repeat step 1 to step 2, until it reaches turning cycle-index F₂。

Note: owing to component c laid by the sensor of every pigeon_i,jIt is by location components x_i,jDetermine, so turning P (p before process_b,c_b) and Y (y_i,c_i) value determine the most respectively, and correspondence meets the binary coding of number of sensors c_i, the value after both calculate also is definite value, but the binary coding using new position vector to calculate not necessarily meets sensing The layout number requirement of device, so here needing to improve Columba livia group's algorithm further, does not carry out position during flat flying Put vector and arrive binary coding sig (x_i,j) conversion, but fly and after turning process terminates jointly flat, carry out sig (x_i,j) Conversion, if being unsatisfactory for the coding requirement that sensor is laid, if being unsatisfactory for laying the requirement of quantity sp, then repeat flat to fly over journey Step 2, lays number until meeting.

(3) chase

Step 1: randomly generate integer-bit cp between [n/2]～the n dimension of n-dimensional space vector, replace as position Dai Dian:

Cp=[n/2]+[φ (n/2)] (16)

In formula: φ is the random number in [0,1].

Step 2: by P_b=P (p_b,c_b)={ (p_b,1,c_b,1),(p_b,2,c_b,2),…,(p_b,cp,c_b,cp),…,(p_b,sum, c_b,sum) in be copied directly to P from the value of cp～sum_w=P (p_w,c_w)={ (p_w,1,c_w,1),(p_w,2,c_w,2),…,(p_w,cp, c_w,cp),…,(p_w,sum,c_w,sum) in cp～sum relevant position, if the worst position P of the colony after Geng Xining_wBefore being better than Difference position, then retain renewal, be not updated.Additionally, due to need to meet the number that sensor is laid, if so more P after Xin_wThe number requirement that sensor is laid can not be met, be not updated.

Four, go back to the nest

Step 1: for pigeon i, randomly generates the coefficient r that goes back to the nest in [-rg, rg]_i。

Step 2: according to the current optimal location of every pigeon, it is judged that individual body position and the difference of other pigeon mean places Away from.

${\mathrm{\&Delta;H}}_i=r_i*\left(\right(\underset{i=1}{\overset{N}{\&Sigma;}}Y\left(y_i,c_i\right)-Y\left(y_i,c_i\right))/(N-1)-Y(y_i,c_i\left)\right)---\left(17\right)$

Step 3: update the current location of pigeon i.

X(x_i,c_i)=Y (y_i,c_i)+ΔH_i (18)

If X is (x_i,c_i) it is better than current optimal location Y (y_i,c_i), then make Y (y_i,c_i)=X (x_i,c_i), if X is (x_i,c_i) be better than Columba livia group current optimal location P (p_b,c_b), then make P (p_b,c_b)=X (x_i,c_i)。

A complete algorithm flow is i.e.: encodes and initializes, take off, fly, four big processes of going back to the nest.Iterate this mistake Journey, until finding globally optimal solution or meeting end condition.

Beneficial effects of the present invention:

Discrete Columba livia group's algorithm, in the case of higher-dimension, multi-peak complicated function, has preferable global convergence, and algorithm circulates The stability that number of times is less and stronger, can effectively solve sensors location this large space search problem.

Accompanying drawing explanation

Fig. 1 is bridge benchmark model.

Fig. 2 is to make discrete Columba livia group's algorithm that the three dimension mode confidence criterion optimization considering redundancy is laid result figure.

Fig. 3 is the Method of Mode Fitting comparison diagram according to the z direction, model 5 rank laying node location matching.

Detailed description of the invention

Below in conjunction with accompanying drawing and technical scheme, further illustrate the detailed description of the invention of the present invention.

Bridge model totally two across, long 5.4864 meters, wide 1.8288 meters.Bridge model uses SAP2000 modeling, and this model is Through having imported in the middle of MTLAB.Having 177 nodes, each node has 3 degree of freedom i.e. tri-directions of x, y and z.This model FEM (finite element) model as shown in Figure 1.

Optimality Criteria chooses the three dimension mode confidence criterion 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, ω is the weight coefficient (priority that regulation TMAC and R optimizes Sequentially), g (R) is redundancy function.TMAC formula is:In formula: F_i,jTo be laid by sensing station The i-th row jth column element in the Fisher information battle array of corresponding node.TMAC_i,j∈ [0,1], TMAC_i,jFor the i-th row in TMAC Jth column element.

By mass matrix and the stiffness matrix of model, model is carried out model analysis and can obtain Mode Shape matrix, Can be carried out the calculating of three dimension mode confidence criterion, and come object function optimizing by the method for the present invention.Parameter choose by The term of reference be given according to Columba livia group's algorithm is chosen, and the pigeon quantity of Columba livia group is N=60, scope of soaring [down, up] be [- 1,1], lifting height ri takes 0.1, neighbor scope M=5, maximum flying speed V_max=1, scope of going back to the nest [-rg, rg] be [-5, 5], flat number of times F equal with number of turns is flown₁=F₂=5, locally flight coefficient c₁=1 and overall situation flight coefficient c₂=1.Algorithm End condition is loop iteration 200 times.The node installation position of experimental result is as shown in Figure 2.The feelings that sensor node is adjacent Condition is less, lays more uniform, visual preferable.So the vibration information recorded is the most.Fig. 3 is according to the node laid By 5 z direction, rank formation fitted figure of cubic spline interpolation matching.Fitting effect is preferable.

Claims (1)

1. the discrete Columba livia group's algorithm for monitoring structural health conditions sensors location, it is characterised in that following steps:

(1) encode and initialize

(x c) represents that pigeon is individual, the feasible solution of respective sensor installation position to utilize ordered pair；Wherein, x is the position of pigeon Vector, c is binary vector, for representing the riding position of sensor；Coding and initialization procedure are as follows:

Step 1: using all nodes of containing in the structural modal vibration shape as the position candidate of transducer arrangements, it is assumed that wait to lay and pass Numbered 1～the integer of sum of sensor；

Step 2: with i-th pigeon in Columba livia group, i=1,2 ..., N, N are pigeon quantity in Columba livia group, and its homographic solution is X_i=X (x_i,c_i)={ (x_i,1,c_i,1),(x_i,2,c_i,2),…,(x_i,sum,c_i,sum), position vector x_iIt is from interval [x_down,x_upBetween] The real number array randomly generated, X_iIt is every pigeon current location；The representation in components of each of which dimension is:

x_i,j=rand × (x_up-x_down)+x_down (1)

In formula: rand is the random number in [0,1]；Y_i=Y (y_i,c_i)={ (y_i,1,c_i,1),(y_i,2,c_i,2),…,(y_i,sum, c_i,sum) it is the current optimal location of every pigeon i；P_b=P (p_b,c_b)={ (p_b,1,c_b,1),(p_b,2,c_b,2),…,(p_b,sum, c_b,sum) it is the current optimal location of Columba livia group；P_w=P (p_w,c_w)={ (p_w,1,c_w,1),(p_w,2,c_w,2),…,(p_w,sum,c_w,sum) it is The current worst position of Columba livia group；

c_i,jFor x_i,jThe binary coding vector changed by sig function and obtain:

$c_{i,j}=sig\left(x_{i,j}\right)=\frac{1}{1+e^{-x_{i,j}}}---\left(2\right)$

Method based on probabilistic method decision threshold ε is used to improve the initialized generation efficiency of Columba livia group；With Columba livia group individuality p_iJth dimension Component p_i,j, s_i,jThe probability of=1 is sp/sum so that s_i,jThe probability of=0 is 1-sp/sum so that Columba livia group's individuality initializes full Foot coding requirement；Set x_w, work as x_i,j∈[x_down,-x_w] time, s_i,j=0, and x_i,jProbability in this interval is 1-sp/sum； Work as x_i,j∈(-x_w,x_up] time, s_i,j=1, and x_i,jProbability in this interval is sp/sum；So x_wValue be:

x_w=(sp/num) × (x_up-x_down)-x_up (3)

I.e. pass through x_wBy interval [x_down,x_up] split, therefore the value of ε is

Step 3: Columba livia group's sensitivity initializes

Need to initialize the sensitivity coefficient α of every pigeon when Columba livia group being introduced_i, α_iRandomly generate from [0,1]；

Step 4: Columba livia group velocity initializes

Vector V_i=(v_i,1,v_i,2,…,v_i,j,…v_i,sum) it is the flight speed of pigeon i, [-V_max,V_max] it is the model of flight speed Enclose, v_ijTherefrom randomly generating, its expression formula is:

v_i,j=δ V_max (4)

In formula: δ is the random number in [-1,1]；

(2) take off

(1) soar

Columba livia group is when taking off, and the height pedaling ground is different；According to this characteristic, homogenization initial value, definition [down, up] is The interval of soaring of Columba livia group；

Step 1: set Δ X_i=(Δ x_i,1,Δx_i,2,…,Δx_i,j,…,Δx_i,sum) it is the height of arch of pigeon i, Δ X_iIn every One-dimensional component randomly generates from the scope of soaring, its expression formula:

Δx_i,j=κ (up-down)+down (5)

In formula: κ is the random number in [0,1]；

Step 2: update the current location X (x of every pigeon_i,c_i), its expression formula

X(x_i,c_i)=Y (y_i,c_i)+α_i*ΔX_i (6)

If X is (x_i,c_i) it is better than current optimal location Y (y_i,c_i), then by current location X (x_i,c_i) it is assigned to current optimal location Y (y_i, c_i), i.e. Y (y_i,c_i)=X (x_i,c_i), if X_iIt is better than Columba livia group current optimal location P (p_b,c_b), then make P (p_b,c_b)=X (x_i,c_i)；

In step 2, at Y (y_i,c_i)+α_i*ΔX_iTime, due to Y (y_i,c_i)={ (y_i,1,c_i,1),(y_i,2,c_i,2),…,(y_i,sum, c_i,sum), Δ X_i=(Δ x_i,1,Δx_i,2,…,Δx_i,j,…,Δx_i,sum), it practice, when being specifically added, be the most one-dimensional point Amount y_i,j+α_i*Δx_i,jIt is added, and component c new after being added_Newi,jIt is still new component y_i,jChanged by sig function and obtain The binary coding vector arrived, runs into the addition of phase position vector when subtracting each other situation, all first individually to position in subsequent step Vector is added and subtracted, and calculates binary vector c by the position vector of each dimension_Newi,j；But calculating every one-dimensional component y_i,j+α_i*Δx_i,jTime, the new component obtained may produce beyond interval [x_down,x_up] situation, it is stipulated that if beyond upper limit x_up, Then value is x_up；If less than lower limit x_down, then value is x_down；At flight course with during going back to the nest, if running into analogue, All adopt and process in the same way；

For improving degree of accuracy and the speed of the convergence of algorithm later stage；Soar interval [down, up] along with Columba livia group current optimal location P (p_b,c_b) change and change, its degree of accuracy and P (p_b,c_bMaximum in) is identical；P(p_b,c_b)={ (p_b,1,c_b,1),(p_b,2, c_b,2),…,(p_b,sum,c_b,sum), work as p_b,1,p_b,2,…,p_b,sumIn the degree of accuracy of maximum when being 0.1, soar interval holding Identical degree of accuracy:

$\left\{\begin{array}{c}{\mathrm{up}}_{new}=up*0.1\\ {\mathrm{down}}_{new}=down*0.1\end{array}\right.---\left(7\right)$

(2) rise

Columba livia group has uphill process after soaring, and makes Columba livia group towards more excellent direction flight；Simulate this characteristic, with pseudo-gradient method, seek Look for the direction of optimal solution, referred to as ascent direction f '_{I, j}(X(x_i,c_i))；

Step 1: by formula (8), randomly generates vector Δ C_i=(Δ c_i,1,Δc_i,2,…,Δc_i,j,…,Δc_i,sum)

In formula: ri is lifting height；

Step 2: calculate the pigeon i ascent direction f ' at every dimension j_i,j(X_i), its expression formula:

$\begin{array}{ccc}{f}_{i,j}^{\&prime;}\left(X\right(x_i,c_i\left)\right)=\frac{f\left(X\right(x_i,c_i)+{\mathrm{\&Delta;C}}_i)-f\left(X\right(x_i,c_i)-{\mathrm{\&Delta;C}}_i)}{2{\mathrm{\&Delta;c}}_{i,j}},& i=1,2,...,N,& j=1,2,...,sum\end{array}---\left(9\right)$

Step 3: update the current location X (x of every pigeon_i,c_i), its expression formula:

x_i,j=y_i,j+ri*sign(f′_i,j(X(x_i,c_i))) (10)

In formula: sign (x) is sign function, as x > 0 time sign (x)=1；Sign (x)=0 as x=0；As x < sign when 0 (x)=-1；If X is (x_i,c_i) it is better than current optimal location Y (y_i,c_i), then by current location X (x_i,c_i) it is assigned to current optimal location Y(y_i,c_i), i.e. Y (y_i,c_i)=X (x_i,c_i), if X_iIt is better than Columba livia group current optimal location P (p_b,c_b), then make P (p_b,c_b)=X (x_i,c_i)；

Step 4: step 1 of recirculation is to step 3；

(3) flight

(1) flat fly and turn

The neighbor scope of definition pigeon i is M pigeon around M, the i.e. pigeon neighbours as self；Ave_iFor neighbours Columba livia group's Mean place；It is flat that to fly number of times be F₁；Variable r, span is [1, F₁], often put down and fly once to add 1；

Step 1: calculate mean place ave of pigeon i_i, its expression formula:

In formula (11), M is a very important parameter, and it affects the optimizing of local optimum；When the value of M is excessive Time, Ave_iValue level off to global optimum, affect convergence of algorithm speed；When the value of M is too small, algorithm is easily precocious to be received Hold back, affect the precision of algorithm；In this formulaIt it is downward bracket function；

Step 2: calculate flight speed V of pigeon i_i；Formula is as follows

V_i=w*V_i+c₁*(Ave_i-X(x_i,c_i)) (12)

The value of w is as follows:

$w=0.9-\frac{0.5}{M_c-1}*(cn-1)---\left(13\right)$

Can produce when calculated new velocity vector beyond interval [-V_max,V_max] situation, therefore specify, if beyond upper Limit V_max, then value is V_max；If less than lower limit-V_max, then value is-V_max；

Step 3: update the current location of every pigeon, its expression formula is as follows:

X^r+1(x_i,c_i)=X^r(x_i,c_i)+V_i (14)

Step 4: repeat step 1 to step 3, until it reaches put down and fly cycle-index F₁；

(2) turn

Step 1: definition number of turns is F₂；Calculate flight speed V of pigeon i_i；

V_i=c₂*(P(p_b,c_b)-Y(y_i,c_i)) (15)

In formula: c₂It it is the overall situation flight factor；

Step 2: update the current location of every pigeon, the same formula of its expression formula (14)；

If X^r+1(x_i,c_i) it is better than current optimal location Y (y_i,c_i), then make Y (y_i,c_i)=X^r+1(x_i,c_i), if X is (x_i,c_i) be better than Columba livia group current optimal location P (p_b,c_b), then make P (p_b,c_b)=X^r+1(x_i,c_i)；

Step 3: repeat step 1 to step 2, until it reaches turning cycle-index F₂；

(3) chase

Step 1: randomly generate integer-bit cp, as position alternative point between [n/2]～the n dimension of n-dimensional space vector:

Cp=[n/2]+[φ (n/2)] (16)

In formula: φ is the random number in [0,1]；

Step 2: by P_b=P (p_b,c_b)={ (p_b,1,c_b,1),(p_b,2,c_b,2),…,(p_b,cp,c_b,cp),…,(p_b,sum,c_b,sum)} In copy to P from the value of cp～sum_w=P (p_w,c_w)={ (p_w,1,c_w,1),(p_w,2,c_w,2),…,(p_w,cp,c_w,cp),…, (p_w,sum,c_w,sum) in cp～sum relevant position, if the worst position P of the colony after Geng Xining_wWorst position before being better than, then Retain and update, be not updated；Additionally, due to need to meet the number that sensor is laid, if so P after Geng Xining_w The number requirement that sensor is laid can not be met, be not updated；

(4) go back to the nest

Step 1: for pigeon i, randomly generates the coefficient r that goes back to the nest in [-rg, rg]_i；

Step 2: according to the current optimal location of every pigeon, it is judged that individual body position and the gap of other pigeon mean places；

${\mathrm{\&Delta;H}}_i=r_i*\left(\right(\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}Y\left(y_i,c_i\right)-Y\left(y_i,c_i\right))/(N-1)-Y(y_i,c_i\left)\right)---\left(17\right)$

Step 3: update the current location of pigeon i；

X(x_i,c_i)=Y (y_i,c_i)+ΔH_i (18)

If X is (x_i,c_i) it is better than current optimal location Y (y_i,c_i), then make Y (y_i,c_i)=X (x_i,c_i), if X is (x_i,c_i) it is better than Columba livia group Current optimal location P (p_b,c_b), then make P (p_b,c_b)=X (x_i,c_i)；

A complete algorithm flow is i.e.: encodes and initializes, take off, fly, four big processes of going back to the nest；Iterate this process, Until finding globally optimal solution or meeting end condition.