CN107944133A - Perimeter antenna array Sparse methods based on multi-target quantum spider group's mechanism of Evolution - Google Patents
Perimeter antenna array Sparse methods based on multi-target quantum spider group's mechanism of Evolution Download PDFInfo
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Abstract
The present invention provides a kind of perimeter antenna array Sparse methods based on multi-target quantum spider group's mechanism of Evolution, establish perimeter antenna array sparse model, appropriate systematic parameter is set, and initializes quantum position of the every spider in solution space and { 0,1 } coding site in population.Design multiple target fitness function.The weight of every spider in population is calculated, the gender of spider is divided according to weight.According to initial population, initial elite disaggregation is generated.Concentrated from elite solution and choose globally optimal solution and suboptimal solution.Then the quantum position of female spider and male spider is updated respectively, and { 0,1 } coding site is converted into by way of measurement according to quantum position.Update elite disaggregation, and in Population Regeneration all spiders weight.Finally judge whether to reach maximum iteration, if reaching maximum iteration, export elite disaggregation；Otherwise iteration is returned.The present invention solves high-dimensional discrete multi-objective problem as the sparse structure of multiple target perimeter antenna array.
Description
Technical field
The present invention relates to a kind of perimeter antenna array Sparse methods based on multi-target quantum spider group's mechanism of Evolution, belong to
Intelligent array antenna technical field.
Background technology
Recently as the fast development of science and technology, requirement of the every field to antenna technology is also increasingly increased.In order to enable
Antenna meets demand caused by fast-developing science and technology, and antenna technology has quick emergence and development, many new antennas
Come into being, including aerial array.Aerial array is to put various antenna elements by certain arrangement mode, makes it
Radiation field it is vector superposed, meet the high-gain in practical application and high directivity requirement to obtain global radiation field.It is huge
The outstanding effect that shows of aerial array so that aerial array becomes essential part in some engineerings.
In some radars and satellite antenna system, aerial array is made of thousands of or even up to ten thousand antenna elements, is used
Amplitude-phase weighting method come after improving the directionality of aerial array, the feeding network of aerial array will become it is sufficiently complex so that
It is difficult to realize.Complicated system equipment, the failure rate and maintenance difficulty that can also cause system increase, the cost so not only put into
It can greatly increase, while the requirement of higher is proposed to the abilities of computer system processor data.
In many practical engineering applications, narrow scanning beam is only required to aerial array, and it is not excessive to gain
Requirement, such as the interference array day in the satellite earth antenna of environment resistant interference, high frequency ground radar antenna and radio astronomy
Line etc..And aerial array main beam width is related with bore full-size, gain is related with irradiation aperture area, so at this
The sparse antenna array of high directivity can be constructed using the sparse method of array in a little Practical Projects.Antenna after sparse
Array reduces the complexity of system equipment, thus also reduces the failure rate of system, reduces construction, maintenance cost, at the same time
The speed of service of system is accelerated, improves practicality.Can be so that directional diagram appearance be non-but the periodicity of antenna element is thinning
Often high secondary lobe, it is sparse after antenna array pattern effect compared with will become far short of what is expected when being abound with.Due to sparse antenna array
There are very big relation in the secondary lobe of directional diagram and the placement position of antenna element, it is therefore desirable to which element position in thinned array is carried out
Optimize to reduce its secondary lobe.So the effect approached when being abound with of how being tried one's best with sparse rear less antenna element, reaches institute's phase
The purpose of prestige simultaneously meets constraints, just becomes the antenna array scheme field key issue to be solved, while is also in the modern times
A key issue in the smart antenna field that the communications field plays a significant role.Therefore the present invention is based on quantum coding and institute
Multiple target spider group's mechanism of Evolution of proposition, proposes that the perimeter antenna array based on multi-target quantum spider group's mechanism of Evolution is sparse
Method.This method can be obtained in the case of difference is covered with rate, the opposite sidelobe level of maximum of sparse CDAA circularly disposed antenna array.Place well
The multiple target Solve problems of { 0,1 } coding have been managed, distribution diversity well can be obtained.Multiple target amount proposed by the invention
Sub- spider group rings battle array Sparse methods can effectively solve the problem of the sparse convergence rate of perimeter antenna array and convergence precision, solve
Multiple target ring battle array this sparse higher-dimension multiple target dispersed problem.Designed multi-target quantum spider group's evolution method is to solve
The new method of discrete multi-objective problem, did not meet relevant report in existing literature, more not discrete multi-target quantum spider
Spider group's mechanism of Evolution is applied to the report of the sparse this engineering roadblock of round battle array.
The content of the invention
The purpose of the invention is to provide a kind of perimeter antenna array based on multi-target quantum spider group's mechanism of Evolution
Sparse methods, improve the spider group's mechanism of Evolution for being only used for solving continuous optimization problems at present, it is proposed that more mesh
The advantages of marking spider group's mechanism of Evolution, and organically combining with quantum coding method, merged both, designing new can solve
Multi-target quantum spider group's mechanism of Evolution (Multi-objective Quantum Spider Swarm of dispersed problem
Optimization, MQSSO), successfully solve perimeter antenna array multiple target and solve problem, the Noninferior Solution Set finally obtained has
Distribution diversity well.
The object of the present invention is achieved like this：Step 1：Establish planar loop antennas array sparse model；
Step 2：Systematic parameter is set, and initialize in spider population quantum position of the every spider in solution space and
{ 0,1 } coding site；
Step 3：Multiple target fitness function is designed, calculates the object function vector of spider { 0,1 } coding site；
Step 4：Its weight is calculated according to spider object function vector, spider gender is divided according to weight；
Step 5：According to initial population, initial elite disaggregation is generated；
Step 6：Concentrated from elite solution and choose globally optimal solution and suboptimal solution；
Step 7：The quantum position of female spider and male spider is updated respectively, and measurement is passed through according to quantum position
Mode is converted into { 0,1 } coding site；
Step 8：The object function vector of { 0,1 } coding site after renewal is calculated, and is updated in elite disaggregation and population
The weight of all spiders；
Step 9：Judge whether to reach maximum iteration, if reaching maximum iteration, export elite disaggregation；
Otherwise iterations adds 1 and return to step six.
Present invention additionally comprises some such architectural features：
1. step 1 is specifically：
Known one in xoy planes, uniform single circle ring array that the center of circle is coordinate origin, radius is a, n-th of array element
The anglec of rotation between the line and x-axis of coordinate origin isPosition coordinates isCoordinate is former
The distance of point to far field observation station is r, and the distance of n-th of array element to the observation station is Rn, then the far region radiation field of the array element
Qiang Wei：
Wherein：C is constant, and j is imaginary unit, and k=2 π a/ λ are wave number, and λ is wavelength,Encouraged for array element, its
Middle InTo encourage amplitude, αnFor excitation phase；
Amplitude is done into approximate processingPhase isBy position coordinatesIn band applying aspect, have：
It is approximate and obtain the total intensity expression formula of uniformly single ring array and be that far field is carried out to the radiation field intensity expression formula：
In formula：Array factor isWave beam is in maximum direction side
ToMeet relationThen haveAnd substitute into battle array because
It can be obtained in sonArray element equidistant arrangement to
Determine on a circumference of radius, array element spacing is taken as 0.5 λ, and array element azimuth isAnd array element excitation constant amplitude is same
Phase, thus constitutes a uniformly single ring array；
Donut battle array is made of multiple single ring array with phase concentric different radii, it is assumed that one has M circle
The donut battle array of ring, its each annular radii is radially incremented by successively, NmRepresent the array element number on m-th of annulus, m-th
The azimuth size of n-th of array element on annulus isExcitation amplitude is Imn, excitation phase αmn, then by the side of single ring array
The pattern function that can derive donut battle array to figure function is：
The array element azimuth position of uniform donut battle arrayDonut radius ρmWith array number NmCalculation formula is distinguished
For：ρm=M Δs ρ and Nm=2 π ρm/ (λ/2), wherein, Δ ρ is the spacing of adjacent rings；
Sparse planar loop antennas array is on the basis of uniform donut array, selects uniformly normalization excitation width
Spend ImnArray element flag bit is used as 0 or 1, represents the position bay by sparse or there are two kinds of different states.
2. step 2 is specifically：
The systematic parameter includes the scale of population, the ratio of female spider and male spider, the iteration of colony's evolution time
Number and the size for following the factor, it is known that the quantity of spider individual is H in population scale, that is, population, and the quantity of female spider is Hf,
The quantity of male spider is Hm, and have：Hf+Hm=H, wherein,Represent downward rounding letter
Number, rdIt is one [0,1] interior uniform random number or female spider proportion is directly determined as fixed value 70%,
Spider quantum bit marked as i is set toAndQ=1,2 ..., Q；Q is solution
The dimension in space；{ 0,1 } coding site corresponding with the spider quantum position marked as i isAndOnly get 0 or 1；I represents the numbering of spider individual in population, i=1,2 ..., H, and t represents iterations.
3. step 3 is specifically：
The multiple target fitness function, including two be respectively intended to evaluation population in i-th spider { 0,1 } coding siteIn the good and bad object function of two aspectsWithThen constitute and can determine whether the excellent of potential solution in solution space
Bad target function value vector
Wherein： To be determined by mark bit vector Λ
Pattern function, thenRepresent the maximum opposite sidelobe level of directional diagram that i-th spider solves in the t times iteration, reflection
The quality of outgoing direction figure radiance；
Sum represents to seek { 0,1 } coding siteIn 1 number；ThenRepresent i-th
The sparse rate of ring battle array that spider solves in the t times iteration, reflects the quality of the sparse effect of ring battle array.
4. step 4 is specifically：
The weight of i-th spider individual is：
In formula：Represent the weight of i-th of spider during the t times iteration,WithRepresent respectively during the t times iteration i-th
Two target function values of spider,WithThe object function of all spiders during the t times iteration is represented respectivelyIn most
Big value and minimum value,WithThe object function of all spiders during the t times iteration is represented respectivelyIn maximum and most
Small value.
5. step 5 is specifically：
Then time initial elite disaggregation is generated by initial population, first spider individual acquiescence is first put into elite disaggregation,
Remaining all spiders are gone through, the dominance relation between each spider individual and the existing spider individual of elite solution concentration is judged, uses
Represent t for when elite disaggregation outside spider individual, c travels through these individual numberings, usesRepresent t for when elite disaggregation in
Elite solution, b travel through elite solution numbering, useRepresent to dominate and judge operator, represent left side solution and dominate the right solution, then have：IfI.e.DominateThen willConcentrate and reject from elite solution, and willContinue to concentrate next elite with elite solution
Solution judges dominance relation；IfI.e.DominateThe then spider individual outside the elite disaggregationIt is not eligible for adding
To elite disaggregation；IfWithDo not dominate mutually, then retain the elite solution that elite solution is concentratedAnd retain the outer spider of elite disaggregation
Spider individualInto the qualification of elite solution.
6. step 6 is specifically：
Selection globally optimal solution and suboptimal solution are concentrated from elite solution, selection is carried out based on crowding distance：
Concentrated in elite solution, the distance between two elite solutions i and j are defined as the object function vector of the two elite solutionsWithBetween Euclidean distanceThen elite solution i it is crowded away from
FromIt is defined as：T for when, the distance between elite solution i to the elite solution nearest apart from it；
The elite solution that elite solution is concentrated is sorted by crowding distance, and be located at t for when, elite solution concentrate elite solution
Number is v (t), if elite solution number v (t)=1 that elite solution is concentrated, which is globally optimal solution, by global optimum
Solution is based on mutation probability pmIt is suboptimal solution into the solution after row variation；If elite solution 2≤v of number (t)≤3, select it is crowded away from
It is globally optimal solution and suboptimal solution from best and next best elite solution；If elite solution number v (t) >=4, three it is crowded away from
Globally optimal solution is used as from random selection one in maximum elite solution, avoids being absorbed in local optimum, and from remaining elite solution
In be based on crowding distance, suboptimal solution is gone out using roulette selection policy selection, the probability that each elite solution is chosen as suboptimal solution isRepresent the probability that elite solution concentrates i-th of elite solution to be selected to.
7. step 7 is specifically：
Female spider has two kinds of behaviors：The globally optimal solution concentrated to elite solution learns and learns to suboptimal solution, is based on
Both behaviors and in view of the weight of female spider, then the quantum Vector Rotation angle more new formula of female spider is：
In formula：I takes the label all over all female spiders,It is quantum vector of i-th spider in the t+1 times iteration
The anglec of rotation；It is the Studying factors that female spider learns in the t times iteration to suboptimal solution,For female the t times iteration of spider
When to globally optimal solution learn Studying factors；WithT respectively for when concentrate from elite solution the globally optimal solution of selection
And suboptimal solution；T for when i-th of spider weight.In Population Regeneration during the quantum position of male spider, still using mould
Analog quantity sub-vector revolving door mode of operation；
Male spider can not only learn to globally optimal solution and suboptimal solution, also suffer from the influence of female spider in population,
Based on these three factors and consider the weight of male spider, then the quantum Vector Rotation angle more new formula of male spider is：
In formula：I takes the label all over all male spiders,Be in population a random female spider in the t times iteration
{ 0,1 } coding site；It is the Studying factors that male spider learns in the t times iteration to suboptimal solution,For male spider
The Studying factors learnt during the t times iteration to globally optimal solution,It is the factor of influence that male spider is influenced by female spider, table
Show the size that male spider is influenced be subject to female spider；
Using the sub- position of analog quantity sub-vector rotation door operation renewal amount, update mode is：
In formula：Same i only takes the label all over spider,It is i-th spider in the quantum position of the t+1 times iteration,All it is 1 Q dimensional vectors for all latitude coordinates,Represent that each correspondence position element is mutually multiplied respectively in vector
To " vector multiplication " of new vectorial correspondence position element, sqrt [] represents that each position element extracts square root to obtain respectively in vector
" the vectorial evolution " of new vector, abs [] represent that each position element takes absolute value to obtain " the vector of new vector respectively in vector
Absolute value "；
Quantum bit after renewal is set to1≤i≤H, the variable of each dimension is in [0,1] section
{ 0,1 } coding site can be just converted into by way of measurementThe mode of the measurement is：
In formula：It is random number, 1≤q≤Q, the i.e. variable each dimension in quantum position and one [0,1]
Random number in section compares, and the position coordinates less than or equal to random number is arranged to 1, and the position coordinates more than random number is arranged to
0。
8. step 8 is specifically：
By spider { 0,1 } coding site of a new generationCalculate its object function vectorSentence
Disconnected every spider individual and elite solution concentrate the dominance relation between existing spider individual, then update elite solution set spider weight
Amount；If the spider individual for treating newly to add when concentrating all elite solutions to judge dominance relation with elite solution, be dominant or
Do not dominated, then the spider individual of elite disaggregation to be added is added to elite solution concentrates, and rejects elite solution and concentrate by this
The elite solution that the spider individual newly added is dominated；If the spider individual that elite solution is concentrated has reached on the capacity of elite disaggregation
B is limited, then the spider individual of crowding distance minimum is rejected, then by formulaUpdate spider
Spider weight.
Compared with prior art, the beneficial effects of the invention are as follows：The present invention is only capable of solving for existing spider group's mechanism of Evolution
Certainly continuous optimization problems, it is impossible to solved applied to dispersed problems such as sparse antenna arrays, and multiple-objection optimization can not be solved and asked
The shortcomings that topic, it is proposed that quantum coding method is dilute with the discrete multiple target ring battle array of solution that multiple target spider group's mechanism of Evolution is combined
The multi-target quantum spider group's mechanism of Evolution for the problem of dredging.The ring battle array Sparse methods can obtain high-precision multiple target disaggregation at the same time,
The shortcomings that conventional method is easily trapped into local extremum is overcome, and the distribution preferable elite disaggregation of diversity, capsule can be provided
Include the optimum optimization scheme in the case of various sparse rates.(1) present invention the mode of operation of analog quantity sub-vector revolving door with it is more
Target spider group's mechanism of Evolution combines, and the spider group's mechanism of Evolution that may only handle continuous problem is applied in plane annular day
The sparse field of linear array, successfully solves this sparse high-dimensional multiple target dispersed problem of ring battle array and solves problem, perfect spider
Group's mechanism of Evolution is theoretical, expands its scope of application.(2) compared with the field conventional method, multi-target quantum spider group rings
Battle array Sparse methods can obtain the distribution more preferable elite solution of diversity, contain a series of optimal solutions, meet for two
Various demands during a entirely different, optimization aim for mutually limiting to a certain extent, can solve various feelings during practical application
Condition.
The simulation results show this method outstanding global optimizing performance of the present invention, can be given at for two completely
The good Pareto forward position of diversity during the different, optimization aim that mutually limits to a certain extent.A series of optimal solutions can be with
Meet the actual demand under different situations, illustrate having for the ring battle array Sparse methods based on multi-target quantum spider group's mechanism of Evolution
Effect property.
Brief description of the drawings
Fig. 1 is the perimeter antenna array Sparse methods flow chart based on multi-target quantum spider group's mechanism of Evolution.
Fig. 2 is the sparse structure illustraton of model of perimeter antenna array in three-dimensional cartesian coordinate system.
Fig. 3 is the perimeter antenna array sparse result based on multi-target quantum spider group's mechanism of Evolution.
Embodiment
The present invention is described in further detail with embodiment below in conjunction with the accompanying drawings.
With reference to Fig. 1 to Fig. 3, the present invention includes the following steps：
Step 1：For ring battle array Sparse Problems to be solved, perimeter antenna array sparse model is established.
Step 2：Appropriate systematic parameter is set, and initializes quantum bit of the every spider in solution space in spider population
Put and { 0,1 } coding site.
Step 3：For the sparse multiple target Solve problems of ring battle array to be solved, multiple target fitness function is designed, is calculated
The object function vector of spider { 0,1 } coding site.
Step 4：Its weight is calculated according to spider object function vector, spider gender is divided according to weight.
Step 5：According to initial population, initial elite disaggregation is generated.
Step 6：Concentrated from elite solution and choose globally optimal solution and suboptimal solution.
Step 7：The quantum position of female spider and male spider, and the side that measurement is passed through according to quantum position are updated respectively
Formula is converted into { 0,1 } coding site.
Step 8：The object function vector of { 0,1 } coding site after renewal is calculated, and is updated in elite disaggregation and population
The weight of all spiders.
Step 9：Judge whether to reach maximum iteration, if reaching maximum iteration, export elite disaggregation；It is no
Then iterations adds 1 and return to step 6.
In step 1, when establishing planar loop antennas array, it should be noted that the scale of array, the radius of ring battle array, the orientation of array element
Angular spacing, the disposing way of array element etc..For one in xoy planes, the center of circle is coordinate origin, and radius is the uniform Dan Yuan of a
Ring array, the anglec of rotation between the line and x-axis of n-th of array element and coordinate origin areIts position coordinates isThe distance of false coordinate origin to far field observation station is r, n-th of array element to the observation
The distance of point is Rn, then the far region radiation field of the array element be by force：
Wherein C is constant, and j is imaginary unit, and k=2 π a/ λ are wave number, and λ is wavelength,Encouraged for array element, its
Middle InTo encourage amplitude, αnFor excitation phase.For the far region radiation field strongly expressed formula, amplitude therein can do approximate processingPhase isBy position coordinatesBand
In applying aspect, have
It is approximate and obtain the total intensity expression formula of uniformly single ring array and be that far field can be then carried out to the radiation field intensity expression formula：
Array factor in formula isWave beam is directed toward in maximum
DirectionMeet relationThen haveAnd substitute into battle array
It can be obtained in the factorArray element equidistant arrangement exists
On one circumference of given radius, array element spacing is taken as 0.5 λ, and array element azimuth isAnd array element encourages constant amplitude
Same phase, thus constitutes a uniformly single ring array., can be according to uniform list when the annular radii of uniform single ring array determines
Obtain its array element number in annulus array element interval.
Donut battle array is made of multiple single ring array with phase concentric different radii.Assuming that one has M circle
The donut battle array of ring, its each annular radii is radially incremented by successively, NmRepresent the array element number on m-th of annulus, m-th
The azimuth size of n-th of array element on annulus isExcitation amplitude is Imn, excitation phase αmn, then by single ring array
Pattern function can derive that the pattern function of donut battle array is as follows：
Since uniform donut battle array needs to meet array element equidistantly distributed and adjacent rings spacing phase on each annulus
Same requirement, then the array element azimuth position of uniform donut battle arrayDonut radius ρmWith array number NmCalculate public
Formula is respectively：ρm=M Δs ρ and Nm=2 π ρm/(λ/2).Wherein, Δ ρ is the spacing of adjacent rings.Circular array
It is exactly on the basis of the uniform donut array of above-mentioned foundation to arrange sparse, selects uniformly normalization excitation amplitude ImnMake for 0 or 1
For array element flag bit, the position bay is represented by sparse or there are two kinds of different states.
The systematic parameter for needing to set in step 2 includes the ratio of the scale of population, female spider and male spider, colony
The iterations of evolution and follow size of the factor etc..Population scale is represented with H, i.e., the quantity of spider individual in population.Female
Population can balance when spider accounts for about 70%, so can pass through formulaTo calculate female spider
Quantity, H in formulafRepresent the quantity of female spider,Represent downward bracket function, rdIt is [0,1] interior uniform random number；
Female spider proportion directly can also be determined as fixed value 70%.Use HmRepresent the quantity of male spider, then Hf+Hm=
H.Sparse bay number is actually needed, determines the dimension of solution space, if Q is the dimension of solution space, in iterative process
All spiders are all moved in a Q ties up solution space into row position in population, find elite solution.So the spider marked as i can be set
Spider quantum bit is set toAndQ=1,2 ..., Q；{ 0,1 } corresponding with the quantum position
Coding site can be set toAndOnly get 0 or 1；I represents spider individual in population
Numbering, i=1,2 ..., H, t represent iterations.Quantum position is represented during spider finds elite solution in solution space
Position before measurement, and { 0,1 } coding site is transformed by quantum position by way of measurement, represents array element mark in ring battle array
The vectorial Λ that will position is formed, decides the shape of sparse ring battle array directional diagram, so representing the potential solution in solution space.In population
The initial quantum position of all spidersWith initial { 0,1 } coding site
Determined by random manner, and if as some special circumstances, need or cannot have in some specific positions
If antenna element, then need to force to represent the mark position 1 of the specific antenna element position in { 0,1 } coding site or put
0.Such as holding array aperture is needed in Thinning Process, the array element on some positions in the outmost turns of ring battle array cannot be dilute
Dredge, then need the flag bit of these positions to force to put 1；Or since orographic factor, some specific location of ring battle array can not be placed
Antenna, then need the tick lables position to force to set to 0.
Multiple target fitness function, including two object functions are designed in step 3WithIt is respectively intended to comment
I-th spider { 0,1 } coding site in valency populationIn the quality of two aspects, target function value vector is then formedIt can determine whether the quality of potential solution in solution space.For aerial array Sparse Problems, the shape of directional diagram
Whether the energy that an antenna array radiation can be embodied is concentrated, i.e., whether sufficiently narrow main lobe width is, and secondary lobe is
It is sufficiently low, whether null depth sufficiently large etc., and { 0,1 } coding site of i-th spiderIt can be mapped as sparse ring battle array mark
Will bit vector Λ, so as to determine the shape of sparse ring battle array directional diagram.So for i-th spider { 0,1 } coding of rational evaluation
PositionQuality in terms of maximum opposite sidelobe level, should be first by its { 0,1 } coding siteIt is mapped as sparse ring battle array mark
Bit vector Λ, the pattern function determined by mark bit vector ΛLeave for first fitness function of structure.It is the ring battle array pattern function represented with logarithmic form, whereinIt is ring battle array direction
Maximum in figure function absolute value.The major lobe of directional diagram is among directional diagram, then sets S as directional diagram secondary lobe region, as go
Fall the remainder of the directional diagram of main lobe, main lobe refers to main lobe top to the part between main lobe zero energy width.Then maximum phase
Sidelobe level can be expressed asWherein max () is maximizing function.So object functionIt is designed as：Represent the maximum opposite secondary lobe of directional diagram that i-th spider solves in the t times iteration
Level, reflects the quality of directional diagram radiance, is maximum optimization problem；Object functionIt is designed as：In formula, sum represents to seek { 0,1 } coding siteIn 1 number, i.e., not by it is sparse fall antenna array
The number of member, the object function are to represent the sparse rate of ring battle array that i-th spider solves in the t times iteration, reflect that ring battle array is sparse
The quality of effect, is maximum optimization problem.
Step 4 is first by the target function value vector of i-th spider individualCalculate its weightSo
Its gender is divided according to weight afterwards.In population, the different spider of gender has different behavior patterns.Weight calculation formula
For：In formulaRepresent the weight of i-th of spider during the t times iteration,WithTable respectively
Two target function values of i-th of spider when showing the t times iteration,WithThe mesh of all spiders during the t times iteration is represented respectively
Scalar functionsIn maximum and minimum value,WithThe object function of all spiders during the t times iteration is represented respectivelyIn maximum and minimum value.According to weight by heavier preceding HfSpider is divided into female spider, is left lighter in weight
HmOnly it is divided into male spider.
In step 5, initial elite disaggregation is generated by initial population, first spider individual acquiescence is first put into elite solution
Collection, then travels through remaining all spiders, judges the domination between each spider individual and the existing spider individual of elite solution concentration
Relation.WithRepresent t for when elite disaggregation outside spider individual, c travels through these individual numberings, usesRepresent t for when
Elite solution in elite disaggregation, b travel through the numbering of elite solution, useRepresent to dominate and judge operator, represent left side solution and dominate the right
Solution, then have：IfI.e.DominateThen willConcentrate and reject from elite solution, and willContinue and elite disaggregation
In next elite solution judge dominance relation；IfI.e.DominateThe then spider individual outside the elite disaggregation
It is not eligible for being added to elite disaggregation；IfWithDo not dominate mutually, then retain the elite solution that elite solution is concentratedAnd retain
The outer spider individual of elite disaggregationInto the qualification of elite solution.Only have the spider individual outside elite disaggregation to be concentrated with elite solution
When all elite solutions judge dominance relation, it is dominant or is not dominated, just the spider individual can be added to elite solution
Concentrate, and elite solution concentrates the elite solution dominated by spider individual to be removed, all essences that final elite solution is concentrated
English solution is in identical dominance hierarchy.
Step 6 concentrates selection globally optimal solution and suboptimal solution from elite solution, and selection is carried out based on crowding distance.In elite solution
Concentrate, the distance between two elite solutions i and j are defined as the object function vector of the two elite solutionsWith
Between Euclidean distanceThe then crowding distance of elite solution iIt is defined as：
T for when, the distance between elite solution i to the elite solution nearest apart from it.The elite solution that elite solution is concentrated is by crowding distance
Sequence, and be located at t for when, elite solution concentrate elite solution number be v (t).If the elite solution number v that elite solution is concentrated
(t)=1, then the elite solution is globally optimal solution, and globally optimal solution is based on mutation probability pmIt is suboptimum into the solution after row variation
Solution；If elite solution 2≤v of number (t)≤3, select crowding distance preferably and next best elite solution is globally optimal solution and secondary
Excellent solution；If elite solution number v (t) >=4, one is randomly choosed in the elite solution of three crowding distance maximums as global
Optimal solution, avoids being absorbed in local optimum, and crowding distance is based on from remaining elite solution, using roulette selection policy selection
Go out suboptimal solution, the probability that each elite solution is chosen as suboptimal solution isIn formula,Represent that elite solution is concentrated i-th
The probability that elite solution is selected to.
Step 7 completes the renewal of spider position in population.In Population Regeneration during the quantum position of female spider, simulation is employed
Quantum Vector Rotation door operation mode, so first having to structure quantum Vector Rotation angle more new formula.Female spider has two kinds of rows
For：The globally optimal solution concentrated to elite solution learns and learns to suboptimal solution, based on both behaviors and in view of female spider
Weight, then the quantum Vector Rotation angle more new formula of female spider be：
In formula, i takes the label all over all female spiders, i.e. i=1,2 ..., Hf,It is amount of i-th spider in the t+1 times iteration
The sub-vector anglec of rotation；It is the Studying factors that female spider learns in the t times iteration to suboptimal solution,For female spider t
The Studying factors learnt during secondary iteration to globally optimal solution；WithT respectively for when concentrate from elite solution the overall situation of selection
Optimal solution and suboptimal solution；T for when i-th of spider weight.In Population Regeneration during the quantum position of male spider, still
Using analog quantity sub-vector revolving door mode of operation.Male spider can not only learn to globally optimal solution and suboptimal solution, can also be by
The influence of female spider into population, based on these three factors and in view of the quantum of the weight of male spider, then male spider
Vector Rotation angle more new formula is：
In formula, i takes the label all over all male spiders, i.e. i=Hf+1,Hf+ 2 ..., H,It is random one female spider in population
{ 0,1 } coding site of spider in the t times iteration；It is male spider learns in the t times iteration to suboptimal solution
Practise the factor,For male the t times iteration of spider when to globally optimal solution learn Studying factors,Male spider by
The factor of influence that female spider influences, represents the size that male spider is influenced be subject to female spider.Update in population and owned
After spider quantum Vector Rotation angle, using the sub- position of analog quantity sub-vector rotation door operation renewal amount, update mode is：In formula, same i only takes the label all over spider,It is i-th
Spider in the quantum position of the t+1 times iteration,All it is 1 Q dimensional vectors for all latitude coordinates,Represent to
Each correspondence position element is multiplied to obtain respectively " vector multiplication " of new vectorial correspondence position element in amount, sqrt [] represent to
Each position element extracts square root to obtain " the vectorial evolution " of new vector respectively in amount, and abs [] represents each position element in vector
Take absolute value to obtain " absolute value of a vector " of new vector respectively.
Quantum bit after renewal is set to1≤i≤H, the variable of each dimension is in [0,1] section
{ 0,1 } coding site can be just converted into by way of measurementThe mode of measurement is：In formulaIt is random number, 1≤q≤Q, i.e., random in the variable and [0, a 1] section of each dimension in quantum position
Number compares, and the position coordinates less than or equal to random number is arranged to 1, and the position coordinates more than random number is arranged to 0.
Step 8 updates elite disaggregation and spider weight.By spider { 0,1 } coding site of a new generationCalculate its target
Functional vectorJudge that every spider individual and elite solution concentrate the domination between existing spider individual to close
System, then updates elite solution set spider weight.Update mode and step 5 are identical, i.e., if the spider individual for treating newly to add exists
When judging dominance relation with all elite solutions of elite solution concentration, it is dominant or is not dominated, then by elite disaggregation to be added
Spider individual be added to elite solution concentration, and reject elite solution and concentrate by the elite that is dominated of spider individual of the new addition
Solution.If the spider individual that elite solution is concentrated has reached the maximum size B of elite disaggregation, the spider of crowding distance minimum is rejected
Individual.Then by formulaUpdate spider weight.
Step 9 judges whether to reach maximum iteration, if reaching maximum iteration, exports elite disaggregation, its
In include a series of optimal sparse solutions of ring battle array.If being not reaching to maximum iteration, iterations adds 1, i.e. t
=t+1, and return to step 6, into new round iteration.
The specific embodiment of the present invention is provided below in conjunction with the accompanying drawings：
Step 1：Establish planar loop antennas array.For one in xoy planes, the center of circle is coordinate origin, radius a
Uniform single circle ring array, the anglec of rotation between the line and x-axis of n-th of array element and coordinate origin isIts position coordinates isThe distance of false coordinate origin to far field observation station is r, n-th of array element to the observation
The distance of point is Rn, then the far region radiation field of the array element be by force：
Wherein C is constant, and j is imaginary unit, and k=2 π a/ λ are wave number, and λ is wavelength,Encouraged for array element, its
Middle InTo encourage amplitude, αnFor excitation phase.For the far region radiation field strongly expressed formula, amplitude therein can do approximate processingPhase isBy position coordinatesBring into
In phase, have
It is approximate and obtain the total intensity expression formula of uniformly single ring array and be that far field can be then carried out to the radiation field intensity expression formula：
Array factor in formula isWave beam is directed toward in maximum
DirectionMeet relationThen haveAnd substitute into battle array
It can be obtained in the factorArray element equidistant arrangement exists
On one circumference of given radius, array element spacing is taken as 0.5 λ, and array element azimuth isAnd array element encourages constant amplitude
Same phase, thus constitutes a uniformly single ring array., can be according to uniform list when the annular radii of uniform single ring array determines
Obtain its array element number in annulus array element interval.
Donut battle array is made of multiple single ring array with phase concentric different radii.Assuming that one has M circle
The donut battle array of ring, its each annular radii is radially incremented by successively, NmRepresent the array element number on m-th of annulus, m-th
The azimuth size of n-th of array element on annulus isExcitation amplitude is Imn, excitation phase αmn, then by the side of single ring array
It can derive that the pattern function of donut battle array is as follows to figure function：
Since uniform donut battle array needs to meet array element equidistantly distributed and adjacent rings spacing phase on each annulus
Same requirement, then the array element azimuth position of uniform donut battle arrayDonut radius ρmWith array number NmCalculate public
Formula is respectively：ρm=M Δs ρ and Nm=2 π ρm/(λ/2).Wherein, Δ ρ is the spacing of adjacent rings.Circular array
It is exactly on the basis of the uniform donut array of above-mentioned foundation to arrange sparse, selects uniformly normalization excitation amplitude ImnMake for 0 or 1
For array element flag bit, the position bay is represented by sparse or there are two kinds of different states.
Step 2：Systematic parameter is set.Population scale is represented with H, i.e., the quantity of spider individual in population.Female spider accounts for
Population can balance when about 70%, so can pass through formulaTo calculate the number of female spider
Measure, H in formulafRepresent the quantity of female spider,Represent downward bracket function, rdIt is [0,1] interior uniform random number；Also may be used
Female spider proportion directly is determined as fixed value 70%.Use HmRepresent the quantity of male spider, then Hf+Hm=H.It is real
Border needs sparse bay number, determines the dimension of solution space, if Q is the dimension of solution space, population in iterative process
In all spiders all moved in Q ties up solution space into row position, find elite solution.So the spider amount marked as i can be set
Sub- position isAndQ=1,2 ..., Q；{ 0,1 } corresponding with the quantum position encodes
Position can be set toAndOnly get 0 or 1；I represents the volume of spider individual in population
Number, i=1,2 ..., H, t represent iterations.Quantum position represents during spider finds elite solution in solution space and surveys
Position before amount, and { 0,1 } coding site is transformed by quantum position by way of measurement, represents array element mark in ring battle array
The vectorial Λ that position is formed, decides the shape of sparse ring battle array directional diagram, so representing the potential solution in solution space.Institute in population
There is the initial quantum position of spiderWith initial { 0,1 } coding site
Determined by random manner, and if as some special circumstances, needed in some specific positions or there cannot be day
If line unit, then need to force to represent the mark position 1 of the specific antenna element position in { 0,1 } coding site or set to 0.
Such as holding array aperture is needed in Thinning Process, the array element on some positions in the outmost turns of ring battle array cannot be sparse,
The flag bit of these positions is then needed to force to put 1；Or since orographic factor, some specific location of ring battle array can not place day
Line, then need the tick lables position to force to set to 0.
Step 3：Design multiple target fitness function.Including two object functionsWithIt is respectively intended to evaluate
I-th spider { 0,1 } coding site in populationIn the quality of two aspects, target function value vector is then formedIt can determine whether the quality of potential solution in solution space.For aerial array Sparse Problems, the shape of directional diagram
Whether the energy that an antenna array radiation can be embodied is concentrated, i.e., whether sufficiently narrow main lobe width is, and secondary lobe is
It is sufficiently low, whether null depth sufficiently large etc., and { 0,1 } coding site of i-th spiderIt can be mapped as sparse ring battle array mark
Will bit vector Λ, so as to determine the shape of sparse ring battle array directional diagram.So for i-th spider { 0,1 } coding of rational evaluation
PositionQuality in terms of maximum opposite sidelobe level, should be first by its { 0,1 } coding siteIt is mapped as sparse ring battle array mark
Bit vector Λ, the pattern function determined by mark bit vector ΛLeave for first fitness function of structure.It is the ring battle array pattern function represented with logarithmic form, whereinIt is ring battle array direction
Maximum in figure function absolute value.The major lobe of directional diagram is among directional diagram, then sets S as directional diagram secondary lobe region, as go
Fall the remainder of the directional diagram of main lobe, main lobe refers to main lobe top to the part between main lobe zero energy width.Then maximum phase
Sidelobe level can be expressed asWherein max () is maximizing function.So object functionIt is designed as：Represent the maximum opposite secondary lobe of directional diagram that i-th spider solves in the t times iteration
Level, reflects the quality of directional diagram radiance, is maximum optimization problem；Object functionIt is designed as：In formula, sum represents to seek { 0,1 } coding siteIn 1 number, i.e., not by it is sparse fall antenna array
The number of member, the object function are to represent the sparse rate of ring battle array that i-th spider solves in the t times iteration, reflect that ring battle array is sparse
The quality of effect, is maximum optimization problem.
Step 4：First by the target function value vector of i-th spider individualCalculate its weightSo
Its gender is divided according to weight afterwards.Weight calculation formula is：In formulaRepresent the t times
The weight of i-th of spider during iteration,WithThe fitness value 1 and 2 of i-th of spider during the t times iteration is represented respectively,WithMaximum and minimum value in all spider fitness values 1 during the t times iteration are represented respectively,WithT is represented respectively
Maximum and minimum value during secondary iteration in all spider fitness values 2.According to weight by heavier preceding HfSpider is divided into
Female spider, is left the H of lighter in weightmOnly it is divided into male spider.
Step 5：Initial elite disaggregation is generated by initial population.Detailed process is first to put first spider individual acquiescence
Enter elite disaggregation, then travel through remaining all spiders, judge that each spider individual and elite solution concentrate existing spider individual
Between dominance relation.WithRepresent t for when elite disaggregation outside spider individual, c travels through these individual numberings, usesTable
Show t for when elite disaggregation in elite solution, b travel through elite solution numbering, useRepresent to dominate and judge operator, represent left side solution
The right solution is dominated, then is had：IfI.e.DominateThen willConcentrate and reject from elite solution, and willContinue with
Elite solution concentrates next elite solution to judge dominance relation；IfI.e.DominateThe then spider outside the elite disaggregation
Spider individualIt is not eligible for being added to elite disaggregation；IfWithDo not dominate mutually, then retain the elite solution that elite solution is concentratedAnd retain the outer spider individual of elite disaggregationInto the qualification of elite solution.I.e. only have elite disaggregation outside spider individual with
When all elite solutions of elite solution concentration judge dominance relation, it is dominant or is not dominated, spider individual can be just added
Enter to elite solution and concentrate, and elite solution concentrates the elite solution dominated by spider individual to be removed, final elite disaggregation
In all elite solutions be in identical dominance hierarchy.
Step 6：Elite solution concentrates selection globally optimal solution and suboptimal solution.Selection is carried out based on crowding distance, in elite solution
Concentrate, the distance between two elite solutions i and j are defined as the object function vector of the two elite solutionsWith
Between Euclidean distanceThe then crowding distance of elite solution iIt is defined as：
T for when, the distance between elite solution i to the elite solution nearest apart from it.The elite solution that elite solution is concentrated is by crowding distance
Sequence, and be located at t for when, elite solution concentrate elite solution number be v (t).If the elite solution number v that elite solution is concentrated
(t)=1, then the elite solution is globally optimal solution, and globally optimal solution is based on mutation probability pmIt is suboptimum into the solution after row variation
Solution；If elite solution 2≤v of number (t)≤3, select crowding distance preferably and next best elite solution is globally optimal solution and secondary
Excellent solution；If elite solution number v (t) >=4, one is randomly choosed in the elite solution of three crowding distance maximums as global
Optimal solution, avoids being absorbed in local optimum, and crowding distance is based on from remaining elite solution, using roulette selection policy selection
Go out suboptimal solution, the probability that each elite solution is chosen as suboptimal solution isIn formula,Represent that elite solution is concentrated i-th
The probability that elite solution is selected to.
Step 7：Complete the renewal of spider position in population.In Population Regeneration during the quantum position of female spider, use
Analog quantity sub-vector revolving door mode of operation, so first having to structure quantum Vector Rotation angle more new formula.Female spider
Spider has two kinds of behaviors：Learn to the globally optimal solution study concentrated of elite solution and the suboptimal solution concentrated to elite solution, base
In both behaviors and consider the weight of female spider, then the quantum Vector Rotation angle more new formula of female spider is：In formula, i takes the label all over all female spiders, i.e. i=1,
2,…,Hf,It is quantum Vector Rotation angle of i-th spider in the t+1 times iteration；It is female spider at the t times
The Studying factors learnt during iteration to suboptimal solution,To learn during female the t times iteration of spider to what globally optimal solution learnt
The factor；WithT respectively for when concentrate from elite solution the globally optimal solution and suboptimal solution of selection；T for when i-th
The weight of a spider.In Population Regeneration during the quantum position of male spider, door operation is still rotated using analog quantity sub-vector
Mode.Male spider can not only learn to globally optimal solution and suboptimal solution, also suffer from the influence of female spider in population, be based on
These three factors and in view of the weight of male spider, then the quantum Vector Rotation angle more new formula of male spider is：In formula, i is taken all over all male spiders
Label, i.e. i=Hf+1,Hf+ 2 ..., H,It is that random one female spider in the t times iteration { 0,1 } encodes in population
Position；It is the Studying factors that male spider learns in the t times iteration to suboptimal solution,For male the t times iteration of spider when
The Studying factors learnt to globally optimal solution,It is the factor of influence that male spider is influenced by female spider, represents male spider
The size influenced be subject to female spider.Update in population after all spider quantum Vector Rotation angles, using simulation quantum arrow
The sub- position of amount rotation door operation renewal amount, update mode are：
In formula, same i only takes the label all over spider,It is i-th spider in the quantum position of the t+1 times iteration,For
All latitude coordinates are all 1 Q dimensional vectors,Represent that each correspondence position element is multiplied to obtain respectively new vectorial corresponding in vector
" vector multiplication " of position element, sqrt [] represent that each position element extracts square root to obtain " the vector of new vector respectively in vector
Evolution ", abs [] represent that each position element takes absolute value to obtain " absolute value of a vector " of new vector respectively in vector.
Quantum bit after renewal is set to1≤i≤H, the variable of each dimension is in [0,1] section
{ 0,1 } coding site can be just converted into by way of measurementThe mode of measurement is：In formulaIt is uniform random number, 1≤q≤Q, i.e., in the variable and [0, a 1] section of each dimension in quantum position
Random number compares, and the position coordinates less than or equal to random number is arranged to 1, and the position coordinates more than random number is arranged to 0.
Step 8：Update elite disaggregation and spider weight.By spider { 0,1 } coding site of a new generationCalculate its mesh
Offer of tender number vectorJudge the domination between every spider individual and the existing spider individual of elite solution concentration
Relation, then updates elite solution set spider weight.Update mode and step 5 are identical, i.e., if treating the spider individual newly added
When concentrating all elite solutions to judge dominance relation with elite solution, it is dominant or is not dominated, then by elite solution to be added
The spider individual of collection is added to elite solution concentration, and rejects elite solution and concentrate the essence dominated by the spider individual of the new addition
Ying Xie.If the spider individual that elite solution is concentrated has reached the maximum size B of elite disaggregation, the spider of crowding distance minimum is rejected
Spider individual.Then by formulaUpdate spider weight.
Step 9：Judge whether to reach maximum iteration, if reaching maximum iteration, export elite disaggregation, its
In include a series of optimal sparse solutions of ring battle array.If being not reaching to maximum iteration, iterations adds 1, i.e. t
=t+1, and return to step 6, into new round iteration.
Beneficial effects of the present invention are further illustrated below by emulation experiment：
During the sparse structure of perimeter antenna array, emulation is carried out for the donut array of six circles to size and has been tested
Card.Six circle dimension Q=129, innermost circle annular radii is 0.5 λ, and λ is wavelength, and the semidiameter between often enclosing is 0.5 λ.From it is interior to
Antenna number on outer each annulus is followed successively by 6,12,18,25,31,37, and specifying information is given in the table below：
The quantity of spider in population is set as H=200, female spider Hf=140, male spider Hm=60.Elite solution
Integrate maximum size as B=100.Mutation probability is pm=0.01.Female spider is when updating the quantum anglec of rotation, to globally optimal solution
The factor that follows with suboptimal solution is respectivelyWithG is maximum iteration in formula.
Male spider is respectively on the follow factor and the factor of influence influenced by female spider of globally optimal solution and suboptimal solutionWith
To sum up, the present invention provides the sparse structure of planar loop antennas array based on multi-target quantum spider group's mechanism of Evolution
Method, relate to the fields such as array antenna and intelligence computation, mainly provides and solves wireless communication system and radar communications system
The middle array Sparse methods that required optimal direction figure is obtained using finite antenna, the elite disaggregation obtained meet various
The optimization of the opposite sidelobe level of maximum in the case of different sparse rates.Obtained sparse antenna array is handled by the way that array is sparse
Structure, has the characteristics that antenna aperature is big, array element is few, reduces the complexity of system, thus also just reduce cost and
Failure rate, improves system processing speed, meets the high performance overall requirement of antenna array system multiple target.The master of this method
The step is wanted to be：First against ring battle array Sparse Problems to be solved, perimeter antenna array sparse model is established, sets and appropriate is
System parameter, and initialize quantum position of the every spider in solution space and { 0,1 } coding site in population.Secondly it is directed to and wants
The sparse multi-objective optimization question of ring battle array of solution, designs multiple target fitness function.Calculate the weight of every spider in population, root
According to the gender of weight division spider.Next according to initial population, initial elite disaggregation is generated.Concentrated from elite solution and choose the overall situation
Optimal solution and suboptimal solution.Then the quantum position of female spider and male spider is updated respectively, and survey is passed through according to quantum position
The mode of amount is converted into { 0,1 } coding site.Elite disaggregation, and Population Regeneration are updated according to { 0,1 } coding site after renewal
In all spiders weight.Finally judge whether to reach maximum iteration, if reaching maximum iteration, export elite
Disaggregation；Otherwise iteration is returned.It this method solve high-dimensional discrete more mesh as the sparse structure of multiple target perimeter antenna array
Mark problem.This method has the convergence precision of faster convergence rate and higher, can provide the distribution preferable elite of diversity
Disaggregation, significantly reduces the complexity and cost of antenna array system, has reached expected requirement.
Claims (9)
1. the perimeter antenna array Sparse methods based on multi-target quantum spider group's mechanism of Evolution, it is characterised in that：Step is as follows：
Step 1：Establish planar loop antennas array sparse model；
Step 2：Systematic parameter is set, and initializes quantum position of the every spider in solution space and { 0,1 } in spider population
Coding site；
Step 3：Multiple target fitness function is designed, calculates the object function vector of spider { 0,1 } coding site；
Step 4：Its weight is calculated according to spider object function vector, spider gender is divided according to weight；
Step 5：According to initial population, initial elite disaggregation is generated；
Step 6：Concentrated from elite solution and choose globally optimal solution and suboptimal solution；
Step 7：The quantum position of female spider and male spider is updated respectively, and according to quantum position by way of measurement
It is converted into { 0,1 } coding site；
Step 8：The object function vector of { 0,1 } coding site after renewal is calculated, and updates in elite disaggregation and population and owns
The weight of spider；
Step 9：Judge whether to reach maximum iteration, if reaching maximum iteration, export elite disaggregation；Otherwise
Iterations adds 1 and return to step six.
2. the perimeter antenna array Sparse methods according to claim 1 based on multi-target quantum spider group's mechanism of Evolution,
It is characterized in that：Step 1 is specifically：
Known one in xoy planes, uniform single circle ring array that the center of circle is coordinate origin, radius is a, n-th of array element and seat
Mark origin line and x-axis between the anglec of rotation bePosition coordinates isCoordinate origin
Distance to far field observation station is r, and the distance of n-th of array element to the observation station is Rn, then the far region radiation field of the array element is strong
For：
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Wherein：C is constant, and j is imaginary unit, and k=2 π a/ λ are wave number, and λ is wavelength,Encouraged for array element, wherein In
To encourage amplitude, αnFor excitation phase；
Amplitude is done into approximate processingPhase isBy position coordinatesIn band applying aspect, have：
It is approximate and obtain the total intensity expression formula of uniformly single ring array and be that far field is carried out to the radiation field intensity expression formula：
In formula：Array factor isWave beam is in maximum pointing directionMeet relationThen haveAnd substitute into array factor
In can obtainArray element equidistant arrangement is given
On one circumference of radius, array element spacing is taken as 0.5 λ, and array element azimuth isAnd array element excitation constant amplitude is same
Phase, thus constitutes a uniformly single ring array；
Donut battle array is made of multiple single ring array with phase concentric different radii, it is assumed that one has M annulus
Donut battle array, its each annular radii is radially incremented by successively, NmRepresent the array element number on m-th of annulus, m-th of annulus
On the azimuth size of n-th of array element beExcitation amplitude is Imn, excitation phase αmn, then by the direction of single ring array
Figure function can derive that the pattern function of donut battle array is：
The array element azimuth position of uniform donut battle arrayDonut radius ρmWith array number NmCalculation formula is respectively：ρm=M Δs ρ and Nm=2 π ρm/ (λ/2), wherein, Δ ρ is the spacing of adjacent rings；
Sparse planar loop antennas array is on the basis of uniform donut array, selects uniformly normalization excitation amplitude Imn
Array element flag bit is used as 0 or 1, represents the position bay by sparse or there are two kinds of different states.
3. the perimeter antenna array Sparse methods according to claim 2 based on multi-target quantum spider group's mechanism of Evolution,
It is characterized in that：Step 2 is specifically：
The scale of the systematic parameter including population, female spider and the male ratio of spider, the iterations of colony's evolution and
Follow the size of the factor, it is known that the quantity of spider individual is H in population scale, that is, population, and the quantity of female spider is Hf, male
The quantity of spider is Hm, and have：Hf+Hm=H, wherein,Represent downward bracket function,
rdIt is one [0,1] interior uniform random number or female spider proportion is directly determined as fixed value 70%,
Spider quantum bit marked as i is set toAndQ is empty for solution
Between dimension；{ 0,1 } coding site corresponding with the spider quantum position marked as i isAndOnly get 0 or 1；I represents the numbering of spider individual in population, i=1,2 ..., H, and t represents iterations.
4. the perimeter antenna array Sparse methods according to claim 3 based on multi-target quantum spider group's mechanism of Evolution,
It is characterized in that：Step 3 is specifically：
The multiple target fitness function, including two be respectively intended to evaluation population in i-th spider { 0,1 } coding site
The good and bad object function of two aspectsWithThen constitute and can determine whether the good and bad of potential solution in solution space
Target function value vector
Wherein： For the direction determined by mark bit vector Λ
Figure function, thenRepresent the maximum opposite sidelobe level of directional diagram that i-th spider solves in the t times iteration, the side of reflecting
To the quality of figure radiance；
Sum represents to seek { 0,1 } coding siteIn 1 number；ThenRepresent i-th spider
The sparse rate of ring battle array solved in the t times iteration, reflects the quality of the sparse effect of ring battle array.
5. the perimeter antenna array Sparse methods according to claim 4 based on multi-target quantum spider group's mechanism of Evolution,
It is characterized in that：Step 4 is specifically：
The weight of i-th spider individual is：
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In formula：Represent the weight of i-th of spider during the t times iteration,WithI-th of spider during the t times iteration is represented respectively
Two target function values,WithThe object function of all spiders during the t times iteration is represented respectivelyIn maximum
And minimum value,WithThe object function of all spiders during the t times iteration is represented respectivelyIn maximum and minimum
Value.
6. the perimeter antenna array Sparse methods according to claim 5 based on multi-target quantum spider group's mechanism of Evolution,
It is characterized in that：Step 5 is specifically：
Initial elite disaggregation is generated by initial population, first spider individual acquiescence is first put into elite disaggregation, then traversal is surplus
Under all spiders, judge that each spider individual and elite solution concentrate the dominance relation between existing spider individual, useRepresent
T for when elite disaggregation outside spider individual, c travels through these individual numberings, usesRepresent t for when elite disaggregation in essence
Ying Xie, b travel through the numbering of elite solution, represent that domination judges operator with ＜, represent left side solution and dominate the right solution, then have：IfI.e.DominateThen willConcentrate and reject from elite solution, and willContinue to concentrate next elite with elite solution
Solution judges dominance relation；IfI.e.DominateThe then spider individual outside the elite disaggregationIt is not eligible for adding
To elite disaggregation；IfWithDo not dominate mutually, then retain the elite solution that elite solution is concentratedAnd retain the outer spider of elite disaggregation
Spider individualInto the qualification of elite solution.
7. the perimeter antenna array Sparse methods according to claim 6 based on multi-target quantum spider group's mechanism of Evolution,
It is characterized in that：Step 6 is specifically：
Selection globally optimal solution and suboptimal solution are concentrated from elite solution, selection is carried out based on crowding distance：
Concentrated in elite solution, the distance between two elite solutions i and j are defined as the object function vector of the two elite solutionsWithBetween Euclidean distanceThen elite solution i it is crowded away from
FromIt is defined as：T for when, the distance between elite solution i to the elite solution nearest apart from it；
The elite solution that elite solution is concentrated is sorted by crowding distance, and be located at t for when, elite solution concentrate elite solution number be
V (t), if elite solution number v (t)=1 that elite solution is concentrated, which is globally optimal solution, by globally optimal solution base
In mutation probability pmIt is suboptimal solution into the solution after row variation；If elite solution 2≤v of number (t)≤3, crowding distance is selected most
Good and next best elite solution is globally optimal solution and suboptimal solution；If elite solution number v (t) >=4, in three crowding distances most
One is randomly choosed in big elite solution and is used as globally optimal solution, avoids being absorbed in local optimum, and the base from remaining elite solution
In crowding distance, suboptimal solution is gone out using roulette selection policy selection, the probability that each elite solution is chosen as suboptimal solution is Represent the probability that elite solution concentrates i-th of elite solution to be selected to.
8. the perimeter antenna array Sparse methods according to claim 7 based on multi-target quantum spider group's mechanism of Evolution,
It is characterized in that：Step 7 is specifically：
Female spider has two kinds of behaviors：The globally optimal solution study concentrated to elite solution and learn to suboptimal solution, based on this two
Kind of behavior and in view of the weight of female spider, then the quantum Vector Rotation angle more new formula of female spider is：
<mrow>
<msubsup>
<mi>U</mi>
<mi>i</mi>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>w</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<msubsup>
<mi>E</mi>
<mi>f</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>P</mi>
<mi>p</mi>
<mi>t</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>Z</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>w</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<msubsup>
<mi>L</mi>
<mi>f</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>P</mi>
<mi>g</mi>
<mi>t</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>Z</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
In formula：I takes the label all over all female spiders,It is quantum Vector Rotation of i-th spider in the t+1 times iteration
Angle；It is the Studying factors that female spider learns in the t times iteration to suboptimal solution,For female the t times iteration of spider when to
The Studying factors of globally optimal solution study；WithT respectively for when from elite solution concentrate selection globally optimal solution and time
Excellent solution；T for when i-th of spider weight, in Population Regeneration during the quantum position of male spider, still using analog quantity
Sub-vector revolving door mode of operation；
Male spider can not only learn to globally optimal solution and suboptimal solution, also suffer from the influence of female spider in population, be based on
These three factors and in view of the weight of male spider, then the quantum Vector Rotation angle more new formula of male spider is：
<mrow>
<msubsup>
<mi>U</mi>
<mi>i</mi>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>w</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<msubsup>
<mi>E</mi>
<mi>m</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>P</mi>
<mi>p</mi>
<mi>t</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>Z</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>w</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<msubsup>
<mi>L</mi>
<mi>m</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>P</mi>
<mi>g</mi>
<mi>t</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>Z</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msubsup>
<mi>w</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<msubsup>
<mi>K</mi>
<mi>m</mi>
<mi>t</mi>
</msubsup>
<mo>&times;</mo>
<mrow>
<mo>(</mo>
<msubsup>
<mi>Z</mi>
<mi>r</mi>
<mi>t</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>Z</mi>
<mi>i</mi>
<mi>t</mi>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
In formula：I takes the label all over all male spiders,Be in population a random female spider in the t times iteration 0,
1 } coding site；It is the Studying factors that male spider learns in the t times iteration to suboptimal solution,For male spider the t times
The Studying factors learnt during iteration to globally optimal solution,It is the factor of influence that male spider is influenced by female spider, represents male
The size that property spider is influenced be subject to female spider；
Using the sub- position of analog quantity sub-vector rotation door operation renewal amount, update mode is：
In formula：Same i only takes the label all over spider, Vi t+1It is i-th spider in the quantum position of the t+1 times iteration,All it is 1 Q dimensional vectors for all latitude coordinates, ◇ represents that each correspondence position element is mutually multiplied respectively in vector
To " vector multiplication " of new vectorial correspondence position element, sqrt [] represents that each position element extracts square root to obtain respectively in vector
" the vectorial evolution " of new vector, abs [] represent that each position element takes absolute value to obtain " the vector of new vector respectively in vector
Absolute value "；
Quantum bit after renewal is set to Vi t+1, 1≤i≤H, the variable of each dimension is in [0,1] sectionPass through
The mode of measurement can just be converted into { 0,1 } coding siteThe mode of the measurement is：
<mrow>
<msubsup>
<mi>Z</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>q</mi>
</mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msubsup>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>q</mi>
</mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>&le;</mo>
<msubsup>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>q</mi>
</mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msubsup>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>q</mi>
</mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>></mo>
<msubsup>
<mi>r</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>q</mi>
</mrow>
<mrow>
<mi>t</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
In formula：It is random number, 1≤q≤Q, the i.e. variable each dimension in quantum position and [0, a 1] section
Interior random number compares, and the position coordinates less than or equal to random number is arranged to 1, and the position coordinates more than random number is arranged to 0.
9. the perimeter antenna array Sparse methods according to claim 8 based on multi-target quantum spider group's mechanism of Evolution,
It is characterized in that：Step 8 is specifically：
By spider { 0,1 } coding site of a new generationCalculate its object function vectorJudge every
Spider individual and elite solution concentrate the dominance relation between existing spider individual, then update elite solution set spider weight；
If the spider individual for treating newly to add when concentrating all elite solutions to judge dominance relation with elite solution, be dominant or not by
Dominate, then the spider individual of elite disaggregation to be added is added to elite solution concentrates, and rejects elite solution and concentrate and newly added by this
The elite solution that the spider individual entered is dominated；If the spider individual that elite solution is concentrated has reached the maximum size B of elite disaggregation,
The spider individual of crowding distance minimum is then rejected, then by formulaUpdate spider weight
Amount.
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