CN102722751B - Heuristic quantum genetic method of multi-target distribution in air war - Google Patents

Abstract

The invention provides a heuristic quantum genetic method of multi-target distribution in an air war and belongs to the technical field of computer simulation and method optimization. The heuristic quantum genetic method comprises the following steps: obtaining the current battlefield situation from a command control center; obtaining threat factors among aircrafts between us and the enemy of the current battlefield; obtaining all of attack distribution values of each weapon of the aircrafts of ourselves and establishing a priority attack distribution value vector; carrying out quantum bit encoding and initializing all quantum chromosomes in a population; filtering the quantum chromosomes; and correcting the quantum chromosomes according to the priority attack distribution value vector. According to the heuristic quantum genetic method, a threat empirical formula of collaborative multi-target attack air war decision problem is subjected to deformation conversion, a distribution scheme of the weapons of us is subjected to quantum bit encoding, and the representation range of feasible solution is enlarged. The priority attack distribution value vector PAVZN*1 is provided and designed according to all of the attack distribution values of each weapon, thus the quantum chromosomes are corrected in a heuristic mode according to the PAVZN*1, and the convergence velocity is accelerated.

Description

A kind of heuristic quantum genetic method that air battle multiple goal is distributed

Technical field

The present invention relates to a kind of heuristic quantum genetic method that air battle multiple goal is distributed, belong to Computer Simulation and method optimisation technique field.

Background technology

Oneself becomes Air Combat Decision-Making for Cooperative Multiple Target Attack modern opportunity of combat and realizes one of gordian technique of over-the-horizon air action fire control system, and its research has great importance.Air Combat Decision-Making for Cooperative Multiple Target Attack refers to that independent or many aircraft of aircraft attack aerial multiple enemy's discrete target simultaneously.In the time that enemy's number of vehicles is more, we also needs to set out many aircraft simultaneously it is tackled, is attacked, thereby forms Cooperative Air Combat.The key of Air Combat Decision-Making for Cooperative Multiple Target Attack is to be that each friend side aircraft distributes target according to our number of vehicles and situation, and air combat situation assessment and threat analysis are the bases of Target Assignment.Therefore, air combat situation assessment, threat analysis, collaborative Target Assignment have formed the core content of Air Combat Decision-Making for Cooperative Multiple Target Attack together, and collaborative Target Assignment is a most important part wherein.

The threat analysis of Air Combat Decision-Making for Cooperative Multiple Target Attack is mainly the experimental formula basic according to some at present, calculates the threat factor between aircraft; The method of collaborative Target Assignment mainly contains the methods such as ant group, neural network, population, but these method ubiquity inefficiencies, the shortcoming such as can not restrain.Genetic algorithm is proposed and found in late 1960s by the John Holland of Michigan university of the U.S., use Biologic evolution opinion and genetic thought, simulate the breeding occurring in natural selection and genetic process, mating and variation phenomenon, according to the survival of the fittest, the natural law of the survival of the fittest, utilizes genetic operator to select, crossover and mutation produces excellent individual by generation, finally searches preferably individual.But the shortcomings such as genetic algorithm is easily absorbed in local convergence in the time solving Air Combat Decision-Making for Cooperative Multiple Target Attack, and later stage of evolution speed of convergence is slow, and precision is poor.Quantum genetic optimization method (QGA) is proposed in 2000 by K.H.Han etc. the earliest, the method is expressed that the state vector of quantum introduce genetic coding, utilize Quantum rotating gate to realize the adjustment of chromogene, its concept is simple, easily realize, hunting zone is large.But its binary coding mode has certain limitation in the time of solving practical problems.In addition, as a kind of random optimization method, also there is blind search, the shortcoming such as speed of convergence is slow, and precision is poor.

Summary of the invention

For problems of the prior art, the present invention proposes a kind of heuristic quantum genetic method that air battle multiple goal is distributed, object is the easy local convergence of the genetic method of the collaborative Target Assignment in order to solve Air Combat Decision-Making for Cooperative Multiple Target Attack, later stage of evolution speed of convergence is slow, the shortcomings such as precision is poor, the threat experimental formula of Air Combat Decision-Making for Cooperative Multiple Target Attack problem is out of shape to conversion, make it our weapon allocative decision (the every item chromosome in heuristic quantum genetic algorithm represents a solution) carry out quantum bit coding here, and propose a kind of according to priority allocation value vector PAV _{zN × 1}heuristic quantum chromosomes modification method, last throughput daughter chromosome variation, accelerates quantum bit corresponding state to global optimum's derotation, improves search efficiency.

The present invention proposes a kind of heuristic quantum genetic method that air battle multiple goal is distributed, and comprises following step:

Step 1: obtain current situation of battlefield from command and control center:

Step 2: obtain the current battlefield threat factor between aircraft between ourselves and the enemy by experimental formula.

We to the threat factor experimental formula of enemy's aircraft is at aircraft:

${\mathrm{th}}_{\mathrm{ij}}={\mathrm{\ω}}_1{\mathrm{th}}_{\mathrm{ij}}^{D_{\mathrm{ij}}}{\mathrm{th}}_{\mathrm{ij}}^{{\mathrm{\ϵ}}_{\mathrm{ij}}}+{\mathrm{\ω}}_2{\mathrm{th}}_{\mathrm{ij}}^{V_{\mathrm{Bi}}}---\left(1\right)$

Wherein subscript i represents our aircraft B _i(i=1,2 ..., M), wherein M represents the total quantity of our aircraft, subscript j represents enemy's aircraft R _j(j=1,2 ..., N), N represents the total quantity of enemy's aircraft, th _ijrepresent our aircraft B _ito enemy's aircraft R _jthreat factor, represent our aircraft B _ito enemy's aircraft R _jdistance threaten the factor, represent our aircraft B _ito enemy's aircraft R _jangle threaten the factor, represent our aircraft B _ito enemy's aircraft R _jspeed threaten the factor, wherein ω ₁with ω ₂for non-negative weight coefficient, and meet ω ₁+ ω ₂=1;

We is aircraft B _ito enemy's aircraft R _jdistance threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ij}}^{D_{\mathrm{ij}}}=\left\{\begin{array}{cc}1.0& D_{\mathrm{ij}}\&le;{\mathrm{Ra}}_B\\ 1-\frac{D_{\mathrm{ij}}-{\mathrm{Ra}}_B}{{\mathrm{Tr}}_B-{\mathrm{Ra}}_B}& {\mathrm{Ra}}_B<D_{\mathrm{ij}}\&le;{\mathrm{Tr}}_B\\ 0.0& D_{\mathrm{ij}}>{\mathrm{Tr}}_B\end{array}\right.---\left(2\right)$

Wherein: D _ijrepresent our aircraft B _ito enemy's aircraft R _jdistance, Ra _brepresent our aircraft B _ithe average effective operating distance of entrained weapon, Tr _brepresent the maximum tracking range of our aircraft radars;

We is aircraft B _ito enemy's aircraft R _jangle threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ij}}^{{\mathrm{\&epsiv;}}_{\mathrm{ij}}}=e^{-{\mathrm{\&lambda;}}_1{({\mathrm{\&pi;\&epsiv;}}_{\mathrm{ij}}/180)}^{{\mathrm{\&lambda;}}_2}}---\left(3\right)$

Wherein ε _ijrepresent enemy's aircraft R _jwith respect to we aircraft B _ioff-axis angle, λ ₁with λ ₂for constant λ ₁with λ ₂generally, between 0 to 10, there is not the relation of mutual restriction in value;

We is aircraft B _ito enemy's aircraft R _jspeed threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ij}}^{V_{\mathrm{Bi}}}=\left\{\begin{array}{cc}1.0& V_{R_j}<0.5V_{B_i}\\ 1.5-V_{R_j}/V_{B_i}& 0.5V_{B_i}<V_{R_j}\&le;1.4V_{B_i}\\ 0.1& V_{R_j}>1.4V_{B_i}\end{array}\right.---\left(4\right)$

Wherein represent our aircraft B _ispeed, represent enemy's aircraft R _jspeed;

In like manner enemy's aircraft R _jto we aircraft B _ithreat experimental formula be:

${\mathrm{th}}_{\mathrm{ij}}={\mathrm{\&omega;}}_3{\mathrm{th}}_{\mathrm{ji}}^{D_{\mathrm{ji}}}{\mathrm{th}}_{\mathrm{ji}}^{{\mathrm{\&epsiv;}}_{\mathrm{ji}}}+{\mathrm{\&omega;}}_4{\mathrm{th}}_{\mathrm{ji}}^{V_{\mathrm{Rj}}}---\left(5\right)$

Wherein subscript j represents enemy's aircraft R _j, subscript i represents our aircraft B _i, th _jirepresent enemy's aircraft R _jto we aircraft B _ithreat factor, represent enemy's aircraft R _jto we aircraft B _idistance threaten the factor, represent enemy's aircraft R _jto we aircraft B _iangle threaten the factor, represent enemy's aircraft R _jto we aircraft B _ispeed threaten the factor, ω ₃with ω ₄for non-negative weight coefficient, and meet ω ₃+ ω ₄=1;

Enemy's aircraft R _jto we aircraft B _idistance threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ji}}^{D_{\mathrm{ji}}}=\left\{\begin{array}{cc}1.0& D_{\mathrm{ji}}\&le;{\mathrm{Ra}}_R\\ 1-\frac{D_{\mathrm{ji}}-{\mathrm{Ra}}_R}{{\mathrm{Tr}}_R-{\mathrm{Ra}}_R}& {\mathrm{Ra}}_R<D_{\mathrm{ji}}\&le;{\mathrm{Tr}}_R\\ 0.0& D_{\mathrm{ji}}>{\mathrm{Tr}}_R\end{array}\right.---\left(6\right)$

Wherein D _jirepresent enemy's aircraft R _jto we aircraft B _idistance, Ra _rrepresent enemy's aircraft R _jthe average effective operating distance of entrained weapon, Tr _rrepresent the maximum tracking range of enemy's aircraft radars; Enemy's aircraft R _jto we aircraft B _iangle threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ji}}^{{\mathrm{\&epsiv;}}_{\mathrm{ji}}}=e^{-{\mathrm{\&lambda;}}_3{({\mathrm{\&pi;\&epsiv;}}_{\mathrm{ji}}/180)}^{{\mathrm{\&lambda;}}_4}}---\left(7\right)$

Wherein ε _jirepresent our aircraft B _iwith respect to enemy's aircraft R _joff-axis angle, λ ₃with λ ₄for constant; Enemy's aircraft R _jto we aircraft B _ispeed threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ji}}^{V_{\mathrm{Rj}}}=\left\{\begin{array}{cc}1.0& V_{B_i}<0.5V_{R_j}\\ 1.5-V_{B_i}/V_{R_j}& 0.5V_{R_j}<V_{B_i}\&le;1.4V_{R_j}\\ 0.1& V_{B_i}>1.4V_{R_j}\end{array}\right.---\left(8\right)$

Wherein represent enemy's aircraft R _jspeed, represent our aircraft B _ispeed;

Step 3: obtain all attack apportioning costs of each weapon of all our aircraft according to apportioning cost experimental formula, build the preferential apportioning cost vector of attacking:

We is aircraft B _i(i=1,2 ..., M) and to enemy's aircraft R _j(j=1,2 ..., N) apportioning cost experimental formula be:

${\mathrm{AV}}_{\mathrm{ij}}={\mathrm{th}}_{\mathrm{ij}}\&CenterDot;\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{th}}_{\mathrm{ji}}---\left(9\right)$

Wherein th _ijrepresent our aircraft B _ito enemy's aircraft R _jthreat factor, represent enemy's aircraft R _jto we aircraft B _ithreat, AV _ijrepresent our aircraft B _iattack enemy's aircraft R _jattack apportioning cost;

According to apportioning cost experimental formula (9) calculate our all weapon r (r=1,2 ..., Z) and the aircraft B at this end of institute _ithe entirety of all enemy's aircraft is attacked to apportioning cost vector AV _{zN × 1}for

AV _ZN×1＝[AV ₁₁,AV ₁₂,…,AV _1N,AV ₂₁,…,AV _ZN]，

Wherein Z is the total quantity of the entrained weapon of our all aircraft, AV ₁₁represent that our carrying arms is numbered 1 aircraft attack enemy aircraft R ₁attack apportioning cost, AV ₁₂represent that our carrying arms is numbered 1 aircraft attack enemy aircraft R ₂attack apportioning cost, AV _1Nrepresent that our carrying arms is numbered 1 aircraft attack enemy aircraft R _nattack apportioning cost, AV ₂₁represent that our carrying arms is numbered 2 aircraft attack enemy aircraft R ₁attack apportioning cost, AV _zNrepresent that our carrying arms is numbered the aircraft attack enemy aircraft R of Z _nattack apportioning cost.Entirety is attacked apportioning cost vector AV _{zN × 1}=[AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _zN] in comprised the attack apportioning cost of our each weapon to each aircraft of enemy, comprise altogether ZN attack apportioning cost;

Entirety is attacked to apportioning cost vector AV _{zN × 1}a middle ZN AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _zNattack apportioning cost and arrange according to order from big to small, obtain priority allocation value vector PAV _{zN × 1}, vectorial dimension is ZN × 1;

Step 4: set population scale, greatest iteration step number and variation probability P _mto our weapon allocative decision, carry out all quantum chromosomes in quantum bit coding initialization population, wherein population scale is designated as NUM, for chromosomal number in population, greatest iteration step number is designated as MAX, in i our weapon allocative decision, by we weapon r (r ∈ 1,2 ..., Z) and enemy's aircraft of attacking carries out quantum bit coding, the gene segment length of each weapon equals the number N of enemy's aircraft, and therefore in i chromosome, gene position corresponding to we each weapon r is encoded to $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{rN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{rN}}}\end{array}],$ I ∈ 1,2 ... NUM, wherein represent that in i chromosome, we weapon r does not attack enemy's aircraft R ₁quantum bit probability amplitude, wherein represent that in i chromosome, we weapon r attacks enemy's aircraft R ₁quantum bit probability amplitude, represent that in i chromosome, we weapon r does not attack enemy's aircraft R ₂probability amplitude, wherein represent that in i chromosome, we weapon r attacks enemy's aircraft R ₂quantum bit probability amplitude, represent that in i chromosome, we weapon r does not attack enemy's aircraft R _nquantum bit probability amplitude, wherein represent that in i chromosome, we weapon r attacks enemy's aircraft R _nquantum bit probability amplitude, in the item chromosome of our a weapon allocative decision, comprise the gene section of our Z all weapons, therefore a chromosome total length is ZN, being encoded to an of whole chromosome of i our all weapons $g_i=\left[g_{i_1}\right|g_{i_2}|...|g_{i_r}|...|g_{i_Z}],i\&Element;\mathrm{1,2},...\mathrm{NUM},$ Comprise z gene section, wherein r gene section is encoded to the gene position coding that we weapon r is corresponding $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{rN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{rN}}}\end{array}],i\&Element;\mathrm{1,2},...\mathrm{NUM},$ Therefore in whole chromosome, include ZN gene position.Right $g_i=\left[g_{i_1}\right|g_{i_2}|...|g_{i_r}|...|g_{i_Z}],i\&Element;\mathrm{1,2},...\mathrm{NUM}$ In each gene position launch completely according to each gene position coding after, from 1 to ZN serial number, the chromosome after renumbeing is:

$g_i=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{(r-1)\&CenterDot;N+j}}\\ {\mathrm{\&beta;}}_{i_{(r-1)\&CenterDot;N+j}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}]=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}]---\left(10\right);$

Wherein i ∈ 1,2 ... NUM, r ∈ 1,2 ..., Z, j ∈ 1,2 ..., N, k=(r-1) N+j and k ∈ 1,2 ..., ZN; represent in i chromosome the 1st, the 2nd ... (r-1) N+j ... ZN gene position do not attacked the quantum bit probability amplitude of enemy's aircraft, represent in i chromosome the 1st, the 2nd ... (r-1) N+j ... ZN gene position attacked the quantum bit probability amplitude of enemy's aircraft;

Each gene position of whole chromosome to our all weapons in population is carried out initialization, makes all gene position $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|,$ $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{(r-1)\&CenterDot;N+j}}\\ {\mathrm{\&beta;}}_{i_{(r-1)\&CenterDot;N+j}}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{N\&CenterDot;Z}}\\ {\mathrm{\&beta;}}_{i_{N\&CenterDot;Z}}\end{array}\right|$ All be initialized as same numerical value thereby make in every chromosome our each weapon attacking enemy aircraft identical with the probability of not attacking enemy's aircraft.

Step 5: quantum chromosomes is filtered to (the method is called observation in quantum calculation), determine the value of each gene position in chromosome;

To chromosome $g_i=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}],$ I ∈ 1,2 ... NUM filters, and with random chance, each gene position of chromosome is carried out to value, produces immediately the random number between 0 to 1, if random number is less than value after k gene position filtered is 1, otherwise is taken as 0, the chromosome g after filtering _i' be:

$g_i^{\&prime;}=\left[{G_i}_1\right|{G_i}_2|...|{G_i}_{N-Z}],i\&Element;\mathrm{1,2},...\mathrm{NUM}---\left(11\right)$

Wherein or 0 (k ∈ 1,2 ..., NZ), for the chromosome g after filtering _ithe ' the k position gene position value, k is NZ the k in gene position;

Step 6: according to preferential attack apportioning cost vector corrected quantum chromosomes.

According to the preferential attack apportioning cost vector PAV obtaining in step 3 _{zN × 1}, successively by the chromosome g after filtering _i', i ∈ 1,2 ... the attack apportioning cost AV that NUM calculates according to formula (9) _ijlittle and gene location be 0, makes chromosome meet our weapon and only attack enemy's aircraft, and each enemy's aircraft distributes at most 2 weapons to attack;

If the whole chromosome g after filtering _i' in number be less than the total number Z of our weapon, according to preferential attack apportioning cost vector PAV _{zN × 1}successively by the whole chromosome g after filtering _i' middle attack apportioning cost AV _ijlarge and gene location be 1;

Step 7: obtain through the threaten degree of enemy's aircraft to our aircraft after our weapon attacking according to the threat experimental formula after conversion, and find out historical optimum solution;

For the quantum bit coding that filters after stain colour solid gene position in step 4 is corresponded to and threatened in experimental formula, threaten degree objective function is carried out to following conversion:

$E=\min \underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\{{\mathrm{th}}_{\mathrm{ji}}\&CenterDot;[\underset{r=1}{\overset{Z}{\mathrm{\&Pi;}}}{(1-{\mathrm{th}}_{\mathrm{rj}})}^{X_{\mathrm{rj}}}\left]\right\}$

$=\min \underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\{{\mathrm{th}}_{\mathrm{ji}}\&CenterDot;[\underset{r=1}{\overset{Z}{\mathrm{\&Pi;}}}{(1-{\mathrm{th}}_{\mathrm{rj}})}^{X_{\mathrm{rj}}}\left]\right\}$

$=\min \underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\{{\mathrm{th}}_{\mathrm{ji}}\&CenterDot;[\underset{r=1}{\overset{Z}{\mathrm{\&Pi;}}}{(1-{\mathrm{th}}_{\mathrm{rj}})}^{G_{j+(r-1)\&CenterDot;N}}\left]\right\}---\left(12\right)$

Wherein: E represents threaten degree objective function, N is the total number of enemy's aircraft, and M is the total number of our aircraft, and Z is the total number of our weapon, G _{j+ (r-1) N}represent N gene position of j+ (r-1) of we the chromosome g' after filtering, j ∈ 1,2 ..., N, r ∈ 1,2 ..., ZN; If gene position G _k=1 (k ∈ 1 ... 2, Z, 1, and by the known k=of corresponding relation (r-1) N+j in formula (10), represent that we is numbered the weapon attacking enemy aircraft R of r _jif 0 represents that the weapon that we is numbered r do not attack enemy's aircraft R _j;

Calculate the chromosome g ' after i article of filtration in population _ithe threaten degree target function value E obtaining through formula (12) _i, wherein i ∈ 1,2 ..., NUM, as i article of chromosomal current solution, in the current solution of first generation individuality, finds out the current solution of all chromosome E _iin minimum value as the historical optimum solution of population, be designated as E _b, the chromosome g ' after corresponding filtration _ifor filtering chromosome, the optimum of population is designated as g _b', corresponding unfiltered chromosome g _ifor the optimum chromosome g of population _b;

If not first generation individuality, this generation every chromosomal current solution and historical optimum solution compare, if i chromosomal current solution E _ibe less than historical optimum solution E _b, i.e. E _i< E _b, by this chromosomal current solution E _ivalue give E _b, i.e. E _b=E _i, filter chromosome g by i _i' give optimum to filter chromosome g _b', i.e. g _b'=g _i', by i chromosome g _igive optimum chromosome g _b, g _b=g _i;

Step 8: all chromosomes in population are carried out to the rotation of quantum door.

$\left[\begin{array}{c}{\mathrm{\&alpha;}}_k^{,}\\ {\mathrm{\&beta;}}_k^{,}\end{array}]=[\begin{array}{cc}\cos {\mathrm{\&theta;}}_k& -\sin {\mathrm{\&theta;}}_k\\ \sin {\mathrm{\&theta;}}_k& \cos {\mathrm{\&theta;}}_k\end{array}\left]\right[\begin{array}{c}{\mathrm{\&alpha;}}_k\\ {\mathrm{\&beta;}}_k\end{array}\right]---\left(13\right)$

With reference to experimental formula (13), wherein α _k, β _kfor filtering the chromosomal quantum bit probability amplitude that will be rotated in prochromosome gene position, α ' _k, β ' _kfor filtering postrotational quantum bit probability amplitude in after stain colour solid gene position, θ _krepresent quantum rotation angle, inquiry quantum rotation angle θ _ktable, is rotated θ in Quantum rotating gate to every chromosome _kquestion blank as shown in table 1:

Table 1: θ in Quantum rotating gate _kquestion blank

F in above-mentioned table (x) is target function value, is here the threaten degree functional value of enemy's aircraft to our aircraft after our weapon attacking obtaining according to the threat experimental formula (12) after conversion in step 7; S (α _kβ _k) be θ _ksymbol; b _kand x _krespectively that the optimum obtaining in step 7 filters chromosome g _b' and the current filtration chromosome g that will carry out the rotation of quantum door _i' (i ∈ 1,2 ..., NUM) k (k ∈ 1,2 ..., ZN) and the value of individual gene position; Through after quantum door rotation, the probability amplitude of k gene position of postrotational chromosome by $\left|\begin{array}{c}{\mathrm{\&alpha;}}_k\\ {\mathrm{\&beta;}}_k\end{array}\right|$ Become $\left|\begin{array}{c}{\mathrm{\&alpha;}}_k^{,}\\ {\mathrm{\&beta;}}_k^{,}\end{array}\right|;$

Step 9: filter chromosome g ' according to optimum _bwith variation probability P _m, all chromosomes in population are carried out to mutation operation;

To the chromosome g in population _i(i ∈ 1,2 ..., NUM) and carry out mutation operation, produce first at random a random number P, if P>=P _m, the chromogene bit comparison after filtering;

Gene position comparison procedure is: by the chromosome g after filtering _i' filter chromosome g ' with optimum _bcarry out corresponding gene for relatively, by g ' _bmiddle gene position is 1 and g _i' gene position that middle gene position is 0 is taken out, if g _i' in k (k ∈ 1,2 ..., ZN) and individual gene position is removed, and the chromosome g of corresponding filtered _ik gene position probability amplitude meet by g _iin two probability amplitudes of k gene position with exchange the g after exchange _iin k gene position by $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}\right|$ Become $\left|\begin{array}{c}{\mathrm{\&beta;}}_{i_k}\\ {\mathrm{\&alpha;}}_{i_k}\end{array}\right|,$ G _iby $g_i=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}\right|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}]$ Become $g_i=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...|\begin{array}{c}{\mathrm{\&beta;}}_{i_k}\\ {\mathrm{\&alpha;}}_{i_k}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}];$ If probability amplitude does not exchange;

If P < is P _m, chromosome g _iskip mutation process;

Step 10: judge whether iterations reaches greatest iteration step number MAX, if do not reach, returns to step 5, continue circulation; If iterations reaches MAX, exit circulation;

Step 11: after step 10 exits circulation, the optimum obtaining filters chromosome g ' _bfor the air battle multiple goal allocative decision obtaining.

The invention has the advantages that:

(1) the present invention proposes a kind of heuristic quantum genetic method that air battle multiple goal is distributed, the threat experimental formula of Air Combat Decision-Making for Cooperative Multiple Target Attack problem is out of shape to conversion, our weapon allocative decision is carried out to quantum bit coding, expanded the expression scope of feasible solution;

(2) the present invention proposes a kind of heuristic quantum genetic method that air battle multiple goal is distributed, and according to all attack apportioning costs of each weapon, proposes and design preferential attack apportioning cost vector PAV _{zN × 1}, make chromosome according to PAV _{zN × 1}didactic correction daughter chromosome, convergence speedup speed;

(3) the present invention proposes a kind of heuristic quantum genetic method that air battle multiple goal is distributed, and proposes the Mutation Strategy of the probability amplitude exchange of quantum chromosomes, has accelerated quantum bit corresponding state to global optimum's derotation, improves search efficiency;

(4) the present invention proposes a kind of heuristic quantum genetic method that air battle multiple goal is distributed, and quantum genetic algorithm is applied in air battle multiple goal assignment problem, uses intelligent method to obtain a good air battle multiple goal allocative decision.

Brief description of the drawings

The process flow diagram of the heuristic quantum genetic method that a kind of air battle multiple goal that Fig. 1 the present invention proposes is distributed;

Fig. 2 is quantum door rotation diagram.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail:

The present invention proposes a kind of heuristic quantum genetic method that air battle multiple goal is distributed, and flow process as shown in Figure 1, comprises following step:

Step 1: obtain current situation of battlefield from command and control center.

Obtain current situation of battlefield from command and control center, current situation of battlefield comprises the average effective operating distance of the position of the entrained weapon quantity of quantity, our every aircraft of our aircraft and enemy's aircraft, all aircraft in current battlefield and attitude, both sides at war's aircraft speed and the maximum tracking range of radar, the entrained weapon of both sides' aircraft;

Step 2: obtain the current battlefield threat factor between aircraft between ourselves and the enemy by experimental formula.

We to the threat factor experimental formula of enemy's aircraft is at aircraft:

${\mathrm{th}}_{\mathrm{ij}}={\mathrm{\&omega;}}_1{\mathrm{th}}_{\mathrm{ij}}^{D_{\mathrm{ij}}}{\mathrm{th}}_{\mathrm{ij}}^{{\mathrm{\&epsiv;}}_{\mathrm{ij}}}+{\mathrm{\&omega;}}_2{\mathrm{th}}_{\mathrm{ij}}^{V_{\mathrm{Bi}}}---\left(1\right)$

Wherein subscript i represents our aircraft B _i(i=1,2 ..., M), wherein M represents the total quantity of our aircraft, subscript j represents enemy's aircraft R _j(j=1,2 ..., N), N represents the total quantity th of enemy's aircraft _ijrepresent our aircraft B _ito enemy's aircraft R _jthreat factor, represent our aircraft B _ito enemy's aircraft R _jdistance threaten the factor, represent our aircraft B _ito enemy's aircraft R _jangle threaten the factor, represent our aircraft B _ito enemy's aircraft R _jspeed threaten the factor, ω ₁with ω ₂for non-negative weight coefficient, and meet ω ₁+ ω ₂=1;

We is aircraft B _ito enemy's aircraft R _jdistance threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ij}}^{D_{\mathrm{ij}}}=\left\{\begin{array}{cc}1.0& D_{\mathrm{ij}}\&le;{\mathrm{Ra}}_B\\ 1-\frac{D_{\mathrm{ij}}-{\mathrm{Ra}}_B}{{\mathrm{Tr}}_B-{\mathrm{Ra}}_B}& {\mathrm{Ra}}_B<D_{\mathrm{ij}}\&le;{\mathrm{Tr}}_B\\ 0.0& D_{\mathrm{ij}}>{\mathrm{Tr}}_B\end{array}\right.---\left(2\right)$

Wherein D _ijrepresent our aircraft B _ito enemy's aircraft R _jdistance, Ra _brepresent our aircraft B _ithe average effective operating distance of entrained weapon, Tr _brepresent the maximum tracking range of our aircraft radars;

We is aircraft B _ito enemy's aircraft R _jangle threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ij}}^{{\mathrm{\&epsiv;}}_{\mathrm{ij}}}=e^{-{\mathrm{\&lambda;}}_1{({\mathrm{\&pi;\&epsiv;}}_{\mathrm{ij}}/180)}^{{\mathrm{\&lambda;}}_2}}---\left(3\right)$

Wherein ε _ijrepresent enemy's aircraft R _jwith respect to we aircraft B _ioff-axis angle, λ ₁with λ ₂for constant λ ₁with λ ₂generally, between 0 to 10, there is not the relation of mutual restriction in value.

We is aircraft B _ito enemy's aircraft R _jspeed threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ij}}^{V_{\mathrm{Bi}}}=\left\{\begin{array}{cc}1.0& V_{R_j}<0.5V_{B_i}\\ 1.5-V_{R_j}/V_{B_i}& 0.5V_{B_i}<V_{R_j}\&le;1.4V_{B_i}\\ 0.1& V_{R_j}>1.4V_{B_i}\end{array}\right.---\left(4\right)$

Wherein represent our aircraft B _ispeed, represent enemy's aircraft R _jspeed;

In like manner, enemy's aircraft R _jto we aircraft B _ithreat experimental formula be:

${\mathrm{th}}_{\mathrm{ji}}={\mathrm{\&omega;}}_3{\mathrm{th}}_{\mathrm{ji}}^{D_{\mathrm{ji}}}{\mathrm{th}}_{\mathrm{ji}}^{{\mathrm{\&epsiv;}}_{\mathrm{ji}}}+{\mathrm{\&omega;}}_4{\mathrm{th}}_{\mathrm{ji}}^{V_{\mathrm{Rj}}}---\left(5\right)$

Wherein subscript j represents enemy's aircraft R _j, subscript i represents our aircraft B _i, th _jirepresent enemy's aircraft R _jto we aircraft B _ithreat factor, represent enemy's aircraft R _jto we aircraft B _idistance threaten the factor, represent enemy's aircraft R _jto we aircraft B _iangle threaten the factor, represent enemy's aircraft R _jto we aircraft B _ispeed threaten the factor, ω ₃with ω ₄for non-negative weight coefficient, and meet ω ₃+ ω ₄=1;

Enemy's aircraft R _jto we aircraft B _idistance threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ji}}^{D_{\mathrm{ji}}}=\left\{\begin{array}{cc}1.0& D_{\mathrm{ji}}\&le;{\mathrm{Ra}}_R\\ 1-\frac{D_{\mathrm{ji}}-{\mathrm{Ra}}_R}{{\mathrm{Tr}}_R-{\mathrm{Ra}}_R}& {\mathrm{Ra}}_R<D_{\mathrm{ji}}\&le;{\mathrm{Tr}}_R\\ 0.0& D_{\mathrm{ji}}>{\mathrm{Tr}}_R\end{array}\right.---\left(6\right)$

Wherein D _jirepresent enemy's aircraft R _jto we aircraft B _idistance, Ra _rrepresent enemy's aircraft R _jthe average effective operating distance of entrained weapon, Tr _rrepresent the maximum tracking range of enemy's aircraft radars;

Enemy's aircraft R _jto we aircraft B _iangle threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ji}}^{{\mathrm{\&epsiv;}}_{\mathrm{ji}}}=e^{-{\mathrm{\&lambda;}}_3{({\mathrm{\&pi;\&epsiv;}}_{\mathrm{ji}}/180)}^{{\mathrm{\&lambda;}}_4}}---\left(7\right)$

Wherein ε _jirepresent our aircraft B _iwith respect to enemy's aircraft R _joff-axis angle, λ ₃with λ ₄for constant, λ ₃with λ ₄value generally between 0 to 10, there is not the relation of mutual restriction.

Enemy's aircraft R _jto we aircraft B _ispeed threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ji}}^{V_{\mathrm{Rj}}}=\left\{\begin{array}{cc}1.0& V_{B_i}<0.5V_{R_j}\\ 1.5-V_{B_i}/V_{R_j}& 0.5V_{R_j}<V_{B_i}\&le;1.4V_{R_j}\\ 0.1& V_{B_i}>1.4V_{R_j}\end{array}\right.---\left(8\right)$

Wherein represent enemy's aircraft R _jspeed, represent our aircraft B _ispeed;

Step 3: obtain all attack apportioning costs of each weapon of all our aircraft according to apportioning cost experimental formula, build the preferential apportioning cost vector of attacking.

We is aircraft B _i(i=1,2 ..., M) and to enemy's aircraft R _j(j=1,2 ..., N) apportioning cost experimental formula be:

${\mathrm{AV}}_{\mathrm{ij}}={\mathrm{th}}_{\mathrm{ij}}\&CenterDot;\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{th}}_{\mathrm{ji}}---\left(9\right)$

Wherein th _ijrepresent our aircraft B _ito enemy's aircraft R _jthreat factor, represent enemy's aircraft R _jto we aircraft B _ithreat, AV _ijrepresent our aircraft B _iattack enemy's aircraft R _jattack apportioning cost;

According to apportioning cost experimental formula (9) calculate our all weapon r (r=1,2 ..., Z) and the aircraft B at this end of institute _ithe entirety of all enemy's aircraft is attacked to apportioning cost vector AV _{zN × 1}for

AV _ZN×1＝[AV ₁₁,AV ₁₂,…,AV _1N,AV ₂₁,…,AV _ZN]，

Wherein Z is the total quantity of the entrained weapon of our all aircraft, AV ₁₁represent that our carrying arms is numbered 1 aircraft attack enemy aircraft R ₁attack apportioning cost, AV ₁₂represent that our carrying arms is numbered 1 aircraft attack enemy aircraft R ₂attack apportioning cost, AV _1Nrepresent that our carrying arms is numbered 1 aircraft attack enemy aircraft R _nattack apportioning cost, AV ₂₁represent that our carrying arms is numbered 2 aircraft attack enemy aircraft R ₁attack apportioning cost, AV _zNrepresent that our carrying arms is numbered the aircraft attack enemy aircraft R of Z _nattack apportioning cost.Entirety is attacked apportioning cost vector AV _{zN × 1}=[AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _zN] in comprised the attack apportioning cost of our each weapon to each aircraft of enemy, comprise altogether ZN attack apportioning cost.

Entirety is attacked to apportioning cost vector AV _{zN × 1}a middle ZN AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _zNattack apportioning cost and arrange according to order from big to small, obtain priority allocation value vector PAV _{zN × 1}, vectorial dimension is ZN × 1.

Step 4: set population scale, greatest iteration step number and variation probability P _m, to our weapon allocative decision, carry out all quantum chromosomes in quantum bit coding initialization population.Wherein, population scale is designated as NUM, it is chromosomal number in population, greatest iteration step number is designated as MAX, be the maximum cycle of step 5 to step 9, our weapon allocative decision refers to the concrete distribution method of our all weapon attacking enemy aircraft, and our each weapon that comprises entirety in our a weapon allocative decision is once attacked all independent subscheme in distribution at certain.In the present invention, adopt item chromosome to represent a kind of our weapon allocative decision.

In i our weapon allocative decision (being in i chromosome of population), by we weapon r (r ∈ 1,2, Z) enemy's aircraft of attacking carries out quantum bit coding, the gene segment length of each weapon equals the number N of enemy's aircraft, and therefore in i chromosome, gene position corresponding to we each weapon r is encoded to $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{rN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{rN}}}\end{array}],i\&Element;\mathrm{1,2},...\mathrm{NUM},$ Wherein α _irepresent that in i chromosome, we weapon r does not attack enemy's aircraft R ₁quantum bit probability amplitude, wherein represent that in i chromosome, we weapon r attacks enemy's aircraft R ₁quantum bit probability amplitude, represent that in i chromosome, we weapon r does not attack enemy's aircraft R ₂probability amplitude, wherein represent that in i chromosome, we weapon r attacks enemy's aircraft R ₂quantum bit probability amplitude, represent that in i chromosome, we weapon r does not attack enemy's aircraft R _nquantum bit probability amplitude, wherein represent that in i chromosome, we weapon r attacks enemy's aircraft R _nquantum bit probability amplitude.The gene section that comprises our Z all weapons in the item chromosome of our a weapon allocative decision, therefore a chromosome total length is ZN, being encoded to an of whole chromosome of i our all weapons $g_i=\left[g_{i_1}\right|g_{i_2}|...|g_{i_r}|...|g_{i_Z}],i\&Element;\mathrm{1,2},...\mathrm{NUM},$ Comprise z gene section, wherein r gene section is encoded to the gene position coding that we weapon r is corresponding $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{rN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{rN}}}\end{array}],i\&Element;\mathrm{1,2},...\mathrm{NUM},$ Therefore in whole chromosome, include ZN gene position.Right $g_i=\left[g_{i_1}\right|g_{i_2}|...|g_{i_r}|...|g_{i_Z}],i\&Element;\mathrm{1,2},...\mathrm{NUM}$ In each gene position launch completely according to each gene position coding after, from 1 to ZN serial number, the chromosome after renumbeing is:

$g_i=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{(r-1)\&CenterDot;N+j}}\\ {\mathrm{\&beta;}}_{i_{(r-1)\&CenterDot;N+j}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}]=[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}]---\left(10\right);$

Wherein i ∈ 1,2 ... NUM, r ∈ 1,2 ..., Z, j ∈ 1,2 ..., N, k=(r-1) N+j and k ∈ 1,2 ..., ZN; represent in i chromosome the 1st, the 2nd ... (r-1) N+j ... ZN gene position do not attacked the quantum bit probability amplitude of enemy's aircraft, represent in i chromosome the 1st, the 2nd ... (r-1) N+j ... ZN gene position attacked the quantum bit probability amplitude of enemy's aircraft;

Each gene position of whole chromosome to our all weapons in population is carried out initialization, makes all gene position $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|,$ $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{(r-1)\&CenterDot;N+j}}\\ {\mathrm{\&beta;}}_{i_{(r-1)\&CenterDot;N+j}}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{N\&CenterDot;Z}}\\ {\mathrm{\&beta;}}_{i_{N\&CenterDot;Z}}\end{array}\right|$ All be initialized as same numerical value thereby make in every chromosome our each weapon attacking enemy aircraft identical with the probability of not attacking enemy's aircraft.

Step 5: quantum chromosomes is filtered to (being called " observation " in quantum calculation), determine the value of each gene position in chromosome.

To chromosome $g_i=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}],i\&Element;\mathrm{1,2},...\mathrm{NUM}$ Filter, with random chance, each gene position of chromosome is carried out to value, for example: to first gene position $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|$ Filter, produce immediately the random number between 0 to 1, if random number is less than value after k gene position filtered is 1, otherwise is taken as 0, the chromosome g after filtering _i' be:

$g_i^{\&prime;}=\left[{G_i}_1\right|{G_i}_2|...|{G_i}_{N-Z}],i\&Element;\mathrm{1,2},...\mathrm{NUM}---\left(11\right)$

Wherein or 0 (k ∈ 1,2 ..., NZ), for the chromosome g after filtering _ithe ' the k position gene position value, k is NZ the k in gene position.

Step 6: according to preferential attack apportioning cost vector corrected quantum chromosomes.

According to the preferential attack apportioning cost vector PAV obtaining in step 3 _{zN × 1}, successively by the chromosome g after filtering _i', i ∈ 1,2 ... the attack apportioning cost AV that NUM calculates according to formula (9) _ijlittle and gene location be 0, makes chromosome meet our weapon and only attack enemy's aircraft, and each enemy's aircraft distributes at most 2 weapons to attack;

If the whole chromosome g after filtering _i' in number be less than the total number Z of our weapon, according to preferential attack apportioning cost vector PAV _{zN × 1}successively by the whole chromosome g after filtering _i' middle attack apportioning cost AV _ijlarge and gene location be 1.

Step 7: obtain through the threaten degree of enemy's aircraft to our aircraft after our weapon attacking according to the threat experimental formula after conversion, and find out historical optimum solution.

For the quantum bit coding that filters after stain colour solid gene position in step 4 is corresponded to and threatened in experimental formula, threaten degree objective function is carried out to following conversion:

$E=\min \underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\{{\mathrm{th}}_{\mathrm{ji}}\&CenterDot;[\underset{r=1}{\overset{Z}{\mathrm{\&Pi;}}}{(1-{\mathrm{th}}_{\mathrm{rj}})}^{X_{\mathrm{rj}}}\left]\right\}$

$=\min \underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\{{\mathrm{th}}_{\mathrm{ji}}\&CenterDot;[\underset{r=1}{\overset{Z}{\mathrm{\&Pi;}}}{(1-{\mathrm{th}}_{\mathrm{rj}})}^{X_{\mathrm{rj}}}\left]\right\}$

$=\min \underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j-1}{\overset{N}{\mathrm{\&Sigma;}}}\{{\mathrm{th}}_{\mathrm{ji}}\&CenterDot;[\underset{r=1}{\overset{Z}{\mathrm{\&Pi;}}}{(1-{\mathrm{th}}_{\mathrm{rj}})}^{G_{j+(r-1)\&CenterDot;N}}\left]\right\}---\left(12\right)$

Wherein: E represents threaten degree objective function, N is the total number of enemy's aircraft, and M is the total number of our aircraft, and Z is the total number of our weapon, G _{j+ (r-1) N}represent N gene position of j+ (r-1) of we the chromosome g' after filtering, j ∈ 1,2 ..., N, r ∈ 1,2 ..., ZN; If gene position G _k=1 (k ∈ 1 ... 2, Z, 1, and by the known k=of corresponding relation (r-1) N+j in formula (10), represent that we is numbered the weapon attacking enemy aircraft R of r _jif 0 represents that the weapon that we is numbered r do not attack enemy's aircraft R _j.

Calculate the chromosome g ' after i article of filtration in population _ithe threaten degree target function value E obtaining through formula (12) _i(wherein i ∈ 1,2 ..., NUM), as i article of chromosomal current solution, in the current solution (the threaten degree target function value calculating according to formula (12) for the first time) of first generation individuality, find out the current solution of all chromosome E _iin minimum value be designated as E as the historical optimum solution (abbreviation optimum solution) of population _b, the chromosome g ' after corresponding filtration _ifor filtering chromosome, the optimum of population is designated as g _b', corresponding unfiltered chromosome g _ifor the optimum chromosome g of population _b.

If not first generation individuality (not being to carry out iteration through step 5 to nine for the first time), this generation every chromosomal current solution compare with historical optimum solution, if i individual chromosomal current solution E _ibe less than historical optimum solution E _b, i.e. E _i< E _b, by this chromosomal current solution E _ivalue give E _b, i.e. E _b=E _i, filter chromosome g by i _i' give optimum to filter chromosome g _b', i.e. g _b'=g _i', by i chromosome g _igive optimum chromosome g _b, i.e. g _b=g _i.So will obtain historical optimum solution E through step 7 at every turn _b, the optimum chromosome g that filters _b' and optimum chromosome g _b.

Step 8: all chromosomes in population are carried out to the rotation of quantum door.

$\left[\begin{array}{c}{\mathrm{\&alpha;}}_k^{,}\\ {\mathrm{\&beta;}}_k^{,}\end{array}\right]=\left[\begin{array}{cc}\cos {\mathrm{\&theta;}}_k& -\sin {\mathrm{\&theta;}}_k\\ \sin {\mathrm{\&theta;}}_k& \cos {\mathrm{\&theta;}}_k\end{array}\right]\left[\begin{array}{c}{\mathrm{\&alpha;}}_k\\ {\mathrm{\&beta;}}_k\end{array}\right]---\left(13\right)$

With reference to experimental formula (13), wherein α _k, β _kfor filtering the chromosomal quantum bit probability amplitude that will be rotated in prochromosome gene position, α ' _k, β ' _kfor filtering postrotational quantum bit probability amplitude in after stain colour solid gene position, θ _krepresent quantum rotation angle.Inquiry quantum rotation angle θ _ktable, is rotated θ in Quantum rotating gate to every chromosome _kquestion blank as shown in table 1 under:

Table 1: θ in Quantum rotating gate _kquestion blank

F in above-mentioned table (x) is target function value, is the threaten degree functional value of enemy's aircraft to our aircraft after our weapon attacking obtaining according to the threat experimental formula (12) after conversion in step 7; S (α _kβ _k) be θ _ksymbol; b _kand x _kbe respectively k in the optimum chromosome that obtains in step 7 and the current chromosome solution that will carry out the rotation of quantum door (k ∈ 1,2 ..., ZN) and the value of individual gene position.Quantum door rotation diagram as shown in Figure 2, through after quantum door rotation, the probability amplitude of k gene position of postrotational chromosome by $\left|\begin{array}{c}{\mathrm{\&alpha;}}_k\\ {\mathrm{\&beta;}}_k\end{array}\right|$ Become $\left|\begin{array}{c}{\mathrm{\&alpha;}}_k^{,}\\ {\mathrm{\&beta;}}_k^{,}\end{array}\right|.$

Step 9: filter chromosome g ' according to optimum _bwith variation probability P _m, all chromosomes in population are carried out to mutation operation.

To the chromosome g in population _ii ∈ 1,2 ..., NUM carries out mutation operation.First produce at random a random number P, if P>=P _m, the chromogene bit comparison after filtering;

Gene position comparison procedure is: by the chromosome g after filtering _i' filter chromosome g ' with optimum _bcarry out corresponding gene for relatively, by g ' _bmiddle gene position is 1 and g _i' gene position that middle gene position is 0 is taken out, if g _i' in k (k ∈ 1,2 ..., ZN) and individual gene position is removed, and the chromosome g of corresponding filtered _ik gene position probability amplitude meet by g _iin two probability amplitudes of k gene position with exchange the g after exchange _iin k gene position by $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}\right|$ Become $\left|\begin{array}{c}{\mathrm{\&beta;}}_{i_k}\\ {\mathrm{\&alpha;}}_{i_k}\end{array}\right|,$ G _iby $g_i=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}]$ Become $g_i=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}|...|\begin{array}{c}{\mathrm{\&beta;}}_{i_k}\\ {\mathrm{\&alpha;}}_{i_k}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}];$ If probability amplitude does not exchange.

If P < is P _m, chromosome g _iskip mutation process.

Step 10: judge whether iterations reaches greatest iteration step number MAX, if do not reach, returns to step 5, continue circulation; If iterations reaches MAX, exit circulation.

Step 11: after step 10 exits circulation, the optimum obtaining filters chromosome g ' _bfor the air battle multiple goal allocative decision obtaining.

Claims (1)

1. the heuristic quantum genetic method that air battle multiple goal is distributed, is characterized in that: comprise following step:

Step 1: obtain current situation of battlefield from command and control center:

Step 2: obtain the current battlefield threat factor between aircraft between ourselves and the enemy by experimental formula;

We to the threat factor experimental formula of enemy's aircraft is at aircraft:

${\mathrm{th}}_{\mathrm{ij}}={\mathrm{\&omega;}}_1{\mathrm{th}}_{\mathrm{ij}}^{D_{\mathrm{ij}}}{\mathrm{th}}_{\mathrm{ij}}^{{\mathrm{\&epsiv;}}_{\mathrm{ij}}}+{\mathrm{\&omega;}}_2{\mathrm{th}}_{\mathrm{ij}}^{V_{\mathrm{Bi}}}---\left(1\right)$

Wherein subscript i represents our aircraft B _i(i=1,2 ..., M), wherein M represents the total quantity of our aircraft, subscript j represents enemy's aircraft R _j(j=1,2 ..., N), N represents the total quantity of enemy's aircraft, th _ijrepresent our aircraft B _ito enemy's aircraft R _jthreat factor, represent our aircraft B _ito enemy's aircraft R _jdistance threaten the factor, represent our aircraft B _ito enemy's aircraft R _jangle threaten the factor, represent our aircraft B _ito enemy's aircraft R _jspeed threaten the factor, wherein ω ₁with ω ₂for non-negative weight coefficient, and meet ω ₁+ ω ₂=1;

We is aircraft B _ito enemy's aircraft R _jdistance threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ij}}^{D_{\mathrm{ij}}}=\{1-\begin{array}{cc}1.0& D_{\mathrm{ij}}\&le;{\mathrm{Ra}}_B\\ \frac{D_{\mathrm{ij}}-{\mathrm{Ra}}_B}{{\mathrm{Tr}}_B-{\mathrm{Ra}}_B}& {\mathrm{Ra}}_B<D_{\mathrm{ij}}\&le;{\mathrm{Tr}}_B\\ 0.0& D_{\mathrm{ij}}>{\mathrm{Tr}}_B\end{array}---\left(2\right)$

Wherein: D _ijrepresent our aircraft B _ito enemy's aircraft R _jdistance, Ra _brepresent our aircraft B _ithe average effective operating distance of entrained weapon, Tr _brepresent the maximum tracking range of our aircraft radars;

We is aircraft B _ito enemy's aircraft R _jangle threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ij}}^{{\mathrm{\&epsiv;}}_{\mathrm{ij}}}=e^{-{\mathrm{\&lambda;}}_1{({\mathrm{\&pi;\&epsiv;}}_{\mathrm{ij}}/180)}^{{\mathrm{\&lambda;}}_2}}---\left(3\right)$

Wherein ε _ijrepresent enemy's aircraft R _jwith respect to we aircraft B _ioff-axis angle, λ ₁with λ ₂for constant λ ₁with λ ₂generally, between 0 to 10, there is not the relation of mutual restriction in value;

We is aircraft B _ito enemy's aircraft R _jspeed threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ij}}^{V_{\mathrm{Bi}}}=\left\{\begin{array}{cc}1.0& V_{R_j}<0.5V_{B_i}\\ 1.5-V_{R_j}/V_{B_i}& 0.5V_{B_i}<V_{R_j}\&le;1.4V_{B_i}\\ 0.1& V_{R_j}>1.4V_{B_i}\end{array}\right.---\left(4\right)$

Wherein represent our aircraft B _ispeed, represent enemy's aircraft R _jspeed;

In like manner enemy's aircraft R _jto we aircraft B _ithreat experimental formula be:

${\mathrm{th}}_{\mathrm{ji}}={\mathrm{\&omega;}}_3{\mathrm{th}}_{\mathrm{ji}}^{D_{\mathrm{ji}}}{\mathrm{th}}_{\mathrm{ji}}^{{\mathrm{\&epsiv;}}_{\mathrm{ji}}}+{\mathrm{\&omega;}}_4{\mathrm{th}}_{\mathrm{ji}}^{V_{\mathrm{Rj}}}---\left(5\right)$

Wherein subscript j represents enemy's aircraft R _j, subscript i represents our aircraft B _i, th _jirepresent enemy's aircraft R _jto we aircraft B _ithreat factor, represent enemy's aircraft R _jto we aircraft B _idistance threaten the factor, represent enemy's aircraft R _jto we aircraft B _iangle threaten the factor, represent enemy's aircraft R _jto we aircraft B _ispeed threaten the factor, ω ₃with ω ₄for non-negative weight coefficient, and meet ω ₃+ ω ₄=1;

Enemy's aircraft R _jto we aircraft B _idistance threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ji}}^{D_{\mathrm{ji}}}=\{1-\begin{array}{cc}1.0& D_{\mathrm{ji}}\&le;{\mathrm{Ra}}_R\\ \frac{D_{\mathrm{ji}}-{\mathrm{Ra}}_R}{{\mathrm{Tr}}_R-{\mathrm{Ra}}_R}& {\mathrm{Ra}}_R<D_{\mathrm{ji}}\&le;{\mathrm{Tr}}_R\\ 0.0& D_{\mathrm{ji}}>{\mathrm{Tr}}_R\end{array}---\left(6\right)$

Wherein D _jirepresent enemy's aircraft R _jto we aircraft B _idistance, Ra _rrepresent enemy's aircraft R _jthe average effective operating distance of entrained weapon, Tr _rrepresent the maximum tracking range of enemy's aircraft radars;

Enemy's aircraft R _jto we aircraft B _iangle threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ji}}^{{\mathrm{\&epsiv;}}_{\mathrm{ji}}}=e^{-{\mathrm{\&lambda;}}_3{({\mathrm{\&pi;\&epsiv;}}_{\mathrm{ji}}/180)}^{{\mathrm{\&lambda;}}_4}}---\left(7\right)$

Wherein ε _jirepresent our aircraft B _iwith respect to enemy's aircraft R _joff-axis angle, λ ₃with λ ₄for constant;

Enemy's aircraft R _jto we aircraft B _ispeed threaten the factor be specially:

${\mathrm{th}}_{\mathrm{ji}}^{V_{\mathrm{Rj}}}=\left\{\begin{array}{cc}1.0& V_{B_i}<0.5V_{R_j}\\ 1.5-V_{B_i}/V_{R_j}& 0.5V_{R_j}<V_{B_i}\&le;1.4V_{R_j}\\ 0.1& V_{B_i}>1.4V_{R_j}\end{array}\right.---\left(8\right)$

Wherein represent enemy's aircraft R _jspeed, represent our aircraft B _ispeed;

Step 3: obtain all attack apportioning costs of each weapon of all our aircraft according to apportioning cost experimental formula, build the preferential apportioning cost vector of attacking:

We is aircraft B _i(i=1,2 ..., M) and to enemy's aircraft R _j(j=1,2 ..., N) apportioning cost experimental formula be:

${\mathrm{AV}}_{\mathrm{ij}}={\mathrm{th}}_{\mathrm{ij}}\&CenterDot;\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}{\mathrm{th}}_{\mathrm{ji}}---\left(9\right)$

Wherein th _ijrepresent our aircraft B _ito enemy's aircraft R _jthreat factor, represent enemy's aircraft R _jto we aircraft B _ithreat, AV _ijrepresent our aircraft B _iattack enemy's aircraft R _jattack apportioning cost;

According to apportioning cost experimental formula (9) calculate our all weapon r (r=1,2 ..., Z) and the aircraft B at this end of institute _ithe entirety of all enemy's aircraft is attacked to apportioning cost vector AV _{zN × 1}for

AV _ZN×1＝[AV ₁₁,AV ₁₂,…,AV _1N,AV ₂₁,…,AV _ZN]，

Wherein Z is the total quantity of the entrained weapon of our all aircraft, AV ₁₁represent that our carrying arms is numbered 1 aircraft attack enemy aircraft R ₁attack apportioning cost, AV ₁₂represent that our carrying arms is numbered 1 aircraft attack enemy aircraft R ₂attack apportioning cost, AV _1Nrepresent that our carrying arms is numbered 1 aircraft attack enemy aircraft R _nattack apportioning cost, AV ₂₁represent that our carrying arms is numbered 2 aircraft attack enemy aircraft R ₁attack apportioning cost, AV _zNrepresent that our carrying arms is numbered the aircraft attack enemy aircraft R of Z _nattack apportioning cost, entirety is attacked apportioning cost vector AV _{zN × 1}=[AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _zN] in comprised the attack apportioning cost of our each weapon to each aircraft of enemy, comprise altogether ZN attack apportioning cost;

Entirety is attacked to apportioning cost vector AV _{zN × 1}a middle ZN AV ₁₁, AV ₁₂,, AV _1N, AV ₂₁,, AV _zNattack apportioning cost and arrange according to order from big to small, obtain priority allocation value vector PAV _{zN × 1}, vectorial dimension is ZN × 1;

Step 4: set population scale, greatest iteration step number and variation probability P _mto our weapon allocative decision, carry out all quantum chromosomes in quantum bit coding initialization population, wherein population scale is designated as NUM, for chromosomal number in population, greatest iteration step number is designated as MAX, in i our weapon allocative decision, by we weapon r (r ∈ 1,2 ..., Z) and enemy's aircraft of attacking carries out quantum bit coding, the gene segment length of each weapon equals the number N of enemy's aircraft, and therefore in i chromosome, gene position corresponding to we each weapon r is encoded to $g_{i_r}=[\left.\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{r_{r1}}\end{array}\right|\left.\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{rN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{rN}}}\end{array}\right.],$ I ∈ 1,2 ... NUM, wherein represent that in i chromosome, we weapon r does not attack enemy's aircraft R ₁quantum bit probability amplitude, wherein represent that in i chromosome, we weapon r attacks enemy's aircraft R ₁quantum bit probability amplitude, represent that in i chromosome, we weapon r does not attack enemy's aircraft R ₂probability amplitude, wherein represent that in i chromosome, we weapon r attacks enemy's aircraft R ₂quantum bit probability amplitude, represent that in i chromosome, we weapon r does not attack enemy's aircraft R _nquantum bit probability amplitude, wherein represent that in i chromosome, we weapon r attacks enemy's aircraft R _nquantum bit probability amplitude, in the item chromosome of our a weapon allocative decision, comprise the gene section of our Z all weapons, therefore a chromosome total length is ZN, a whole chromosome of i our all weapons be encoded to gi=[gi ₁| gi ₂| ... | g _ir| ... | gi _z], i ∈ 1,2 ... NUM, comprises z gene section, and wherein r gene section is encoded to the gene position coding that we weapon r is corresponding $g_{i_r}=[\left.\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{r_{r1}}\end{array}\right|\left.\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{rN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{rN}}}\end{array}\right.],$ I ∈ 1,2 ... NUM, therefore includes ZN gene position in whole chromosome, right i ∈ 1,2 ... after each gene position in NUM is launched completely according to each gene position coding, from 1 to ZN serial number, the chromosome after renumbeing is:

$g_i=[\left.\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\left.\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{(r-1)\&CenterDot;N+j}}\\ {\mathrm{\&beta;}}_{i_{(r-1)\&CenterDot;N+j}}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}\right.]=[\left.\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|\left.\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}\right|...\left.\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}\right.]---\left(10\right)$

Wherein i ∈ 1,2 ... NUM, r ∈ 1,2 ..., Z, j ∈ 1,2 ..., N, k=(r-1) N+j and k ∈ 1,2 ..., ZN; represent in i chromosome the 1st, the 2nd ... (r-1) N+j ... ZN gene position do not attacked the quantum bit probability amplitude of enemy's aircraft, represent in i chromosome the 1st, the 2nd ... (r-1) N+j ... ZN gene position attacked the quantum bit probability amplitude of enemy's aircraft;

Each gene position of whole chromosome to our all weapons in population is carried out initialization, makes all gene position $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|,\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{(r-1)\&CenterDot;N+j}}\\ {\mathrm{\&beta;}}_{i_{(r-1)\&CenterDot;N+j}}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}\right|$ All be initialized as same numerical value thereby make in every chromosome our each weapon attacking enemy aircraft identical with the probability of not attacking enemy's aircraft;

Step 5: quantum chromosomes is filtered, determine the value of each gene position in chromosome;

To chromosome $g_i=\left[\begin{array}{c}\begin{array}{c}{\text{\&alpha;}}_{i_1}\\ {\text{\&beta;}}_{i_1}\end{array}\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}\right|\text{...}\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}\right.\end{array}\right],$ I ∈ 1,2 ... NUM filters, and with random chance, each gene position of chromosome is carried out to value, produces immediately the random number between 0 to 1, if random number is less than value after k gene position filtered is 1, otherwise is taken as 0, the chromosome g ' after filtering _ifor:

$g_i^{\text{'}}=\left[G_{i_1}\right|G_{i_2}|...|G_{i_{N\&CenterDot;Z}}|i\&Element;\mathrm{1,2},...\mathrm{NUM}---\left(11\right)$

Wherein or 0 (k ∈ 1,2 ..., NZ), for the chromosome g ' after filtering _ik position gene position value, k is NZ the k in gene position;

Step 6: according to preferential attack apportioning cost vector corrected quantum chromosomes;

According to the preferential attack apportioning cost vector PAV obtaining in step 3 _{zN × 1}, successively by the chromosome g ' after filtering _i, i ∈ 1,2 ... the attack apportioning cost AV that NUM calculates according to formula (9) _ijlittle and gene location be 0, makes chromosome meet our weapon and only attack enemy's aircraft, and each enemy's aircraft distributes at most 2 weapons to attack;

If the whole chromosome g ' after filtering _iin number be less than the total number Z of our weapon, according to preferential attack apportioning cost vector PAV _{zN × 1}successively by the whole chromosome g ' after filtering _imiddle attack apportioning cost AV _ijlarge and gene location be 1;

Step 7: obtain through the threaten degree of enemy's aircraft to our aircraft after our weapon attacking according to the threat experimental formula after conversion, and find out historical optimum solution;

For the quantum bit coding that filters after stain colour solid gene position in step 4 is corresponded to and threatened in experimental formula, threaten degree objective function is carried out to following conversion:

$E=\min \underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\{{\mathrm{th}}_{\mathrm{ji}}\&CenterDot;[\underset{r=1}{\overset{Z}{\mathrm{\&Pi;}}}{(1-{\mathrm{th}}_{\mathrm{rj}})}^{X_{\mathrm{rj}}}\left]\right\}$

$\begin{array}{c}=\min \underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\{{\mathrm{th}}_{\mathrm{ji}}\&CenterDot;[\underset{r=1}{\overset{Z}{\mathrm{\&Pi;}}}{(1-{\mathrm{th}}_{\mathrm{rj}})}^{X_{\mathrm{rj}}}\left]\right\}\\ =\min \underset{i=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\{{\mathrm{th}}_{\mathrm{ji}}\&CenterDot;[\underset{r=1}{\overset{Z}{\mathrm{\&Pi;}}}{(1-{\mathrm{th}}_{\mathrm{rj}})}^{G_{j+(r-1)\&CenterDot;N}}\left]\right\}\end{array}---\left(12\right)$

Wherein: E represents threaten degree objective function, N is the total number of enemy's aircraft, and M is the total number of our aircraft, and Z is the total number of our weapon, G _{j+ (r-1) N}represent N gene position of j+ (r-1) of we the chromosome g' after filtering, j ∈ 1,2 ..., N, r ∈ 1,2 ..., ZN; If gene position

G _k=1 (k ∈ 1,2 ..., ZN), and by the known k=of corresponding relation (r-1) N+j in formula (10), represent that we is numbered the weapon attacking enemy aircraft R of r _jif 0 represents that the weapon that we is numbered r do not attack enemy's aircraft R _j;

Calculate the chromosome g' after i article of filtration in population _ithe threaten degree target function value E obtaining through formula (12) _i, wherein i ∈ 1,2 ..., NUM, as i article of chromosomal current solution, in the current solution of first generation individuality, finds out the current solution of all chromosome E _iin minimum value as the historical optimum solution of population, be designated as E _b, the chromosome g' after corresponding filtration _ifor filtering chromosome, the optimum of population is designated as g ' _b, corresponding unfiltered chromosome g _ifor the optimum chromosome g of population _b;

If not first generation individuality, this generation every chromosomal current solution and historical optimum solution compare, if i chromosomal current solution E _ibe less than historical optimum solution E _b, i.e. E _i< E _b, by this chromosomal current solution E _ivalue give E _b, i.e. E _b=E _i, filter chromosome g ' by i _igive the optimum chromosome g ' that filters _i, i.e. g ' _b=g ' _i, by i chromosome g _igive optimum chromosome g _b, g _b=g _i;

Step 8: all chromosomes in population are carried out to the rotation of quantum door;

$\left[\begin{array}{c}{\mathrm{\&alpha;}}_k^{\text{'}}\\ {\mathrm{\&beta;}}_k^{\text{'}}\end{array}\right]=\left[\begin{array}{cc}\cos {\mathrm{\&theta;}}_k& -\sin {\mathrm{\&theta;}}_k\\ \sin {\mathrm{\&theta;}}_k& \cos {\mathrm{\&theta;}}_k\end{array}\right]\left[\begin{array}{c}{\mathrm{\&alpha;}}_k\\ {\mathrm{\&beta;}}_k\end{array}\right]---\left(13\right)$

With reference to experimental formula (13), wherein α _k, β _kfor filtering the chromosomal quantum bit probability amplitude that will be rotated in prochromosome gene position, α ' _k, β ' _kfor filtering postrotational quantum bit probability amplitude in after stain colour solid gene position, θ _krepresent quantum rotation angle, inquiry quantum rotation angle θ _ktable, is rotated every chromosome, through after quantum door rotation, the probability amplitude of k gene position of postrotational chromosome by $\left|\begin{array}{c}{\mathrm{\&alpha;}}_k\\ {\mathrm{\&beta;}}_k\end{array}\right|$ Become $\left|\begin{array}{c}{\mathrm{\&alpha;}}_k^{\text{'}}\\ {\mathrm{\&beta;}}_k^{\text{'}}\end{array}\right|;$

Step 9: filter chromosome g' according to optimum _bwith variation probability P _m, all chromosomes in population are carried out to mutation operation;

To the chromosome g in population _i(i ∈ 1,2 ..., NUM) and carry out mutation operation, produce first at random a random number P, if P>=P _m, the chromogene bit comparison after filtering;

Gene position comparison procedure is: by the chromosome g ' after filtering _ifilter chromosome g ' with optimum _bcarry out corresponding gene for relatively, by g ' _bmiddle gene position is 1 and g ' _imiddle gene position is that 0 gene position is taken out, if g ' _iin k (k ∈ 1,2 ..., ZN) and individual gene position is removed, and the chromosome g of corresponding filtered _ik gene position probability amplitude meet by g _iin two probability amplitudes of k gene position with exchange the g after exchange _iin k gene position by $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}\right|$ Become $\left|\begin{array}{c}{\mathrm{\&beta;}}_{i_k}\\ {\mathrm{\&alpha;}}_{i_k}\end{array}\right|,$ G _iby $g_i=\left[\begin{array}{c}\begin{array}{c}{\text{\&alpha;}}_{i_1}\\ {\text{\&beta;}}_{i_1}\end{array}\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_k}\\ {\mathrm{\&beta;}}_{i_k}\end{array}\right|\text{...}\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}\right.\end{array}\right]$ Become $g_i=\left[\begin{array}{c}\begin{array}{c}{\text{\&alpha;}}_{i_1}\\ {\text{\&beta;}}_{i_1}\end{array}\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_2}\\ {\mathrm{\&beta;}}_{i_2}\end{array}\right|...\left|\begin{array}{c}{\mathrm{\&beta;}}_{i_k}\\ {\mathrm{\&alpha;}}_{i_k}\end{array}\right|\text{...}\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{Z\&CenterDot;N}}\\ {\mathrm{\&beta;}}_{i_{Z\&CenterDot;N}}\end{array}\right.\end{array}\right];$ If probability amplitude does not exchange;

If P < is P _m, chromosome g _iskip mutation process;

Step 10: judge whether iterations reaches greatest iteration step number MAX, if do not reach, returns to step 5, continue circulation; If iterations reaches MAX, exit circulation;

Step 11: after step 10 exits circulation, the optimum obtaining filters chromosome g' _bfor the air battle multiple goal allocative decision obtaining.