CN102722751A - 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

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

Technical field

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

Background technology

Oneself becomes one of gordian technique of modern opportunity of combat realization over-the-horizon air action fire control system collaborative Multi-target Attacking air combat decision, and its research has great importance.Collaborative Multi-target Attacking air combat decision is meant that independent or many aircraft of aircraft attack aerial a plurality of enemy's discrete target simultaneously.When enemy's number of vehicles more for a long time, we also need set out many aircraft simultaneously it is tackled, attacks, thereby forms Cooperative Air Combat.The key of collaborative Multi-target Attacking air combat decision is to distribute target according to our number of vehicles and situation for each friendly side's aircraft, and assessment of air battle situation and threat analysis are the bases of Target Assignment.Therefore, the assessment of air battle situation, threat analysis, collaborative Target Assignment have constituted the core content of collaborative Multi-target Attacking air combat decision together, and collaborative Target Assignment then is a wherein most important part.

The threat analysis of collaborative Multi-target Attacking air combat decision mainly is according to some basic experimental formulas at present, calculates the threat factor between the aircraft; The method of collaborative Target Assignment mainly contains methods such as ant crowd, neural network, population, but these method ubiquity inefficiencies, shortcoming such as can not restrain.Genetic algorithm is to be proposed and found in late 1960s by the John Holland of U.S. Michigan university, uses organic sphere evolutionism and genetic thought, has simulated the breeding that takes place in natural selection and the 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; Intersect and make a variation and pursue generation generation excellent individual, finally search more excellent individuality.But shortcomings such as genetic algorithm is absorbed in local convergence easily when the Multi-target Attacking air combat decision is worked in coordination with in solution, the evolution late convergence is slow, and precision is relatively poor.Quantum genetic optimization method (QGA) is proposed in 2000 by K.H.Han etc. the earliest, and this method is expressed the state vector of quantum and introduced genetic coding, utilizes the quantum revolving door to realize the adjustment of chromogene, and its notion is simple, realize easily, the hunting zone is big.But its binary coding mode has certain limitation when solving practical problems.In addition,, also has blind search, shortcoming such as speed of convergence is slow, and precision is relatively poor as a kind of random optimization method.

Summary of the invention

To the problem that exists in the prior art; The present invention proposes the heuristic quantum genetic method that a kind of air battle multiple goal is distributed; Purpose is the easy local convergence of genetic method for the collaborative Target Assignment that solves collaborative Multi-target Attacking air combat decision; Shortcomings such as the evolution late convergence is slow, and precision is relatively poor are out of shape conversion with the threat experimental formula of collaborative Multi-target Attacking air combat decision problem; Make it our weapon allocative decision (each the bar chromosome in the heuristic here quantum genetic algorithm is represented a solution) is carried out the quantum bit coding, and propose a kind of according to priority allocation value vector PAV _{ZN * 1}Heuristic quantum chromosome modification method at last through the quantum chromosomal variation, is accelerated the quantum bit corresponding state to global optimum's derotation, improves search efficiency.

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

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

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

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

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

Wherein subscript i representes our aircraft B _i(i=1,2 ..., M), wherein M representes the total quantity of our aircraft, subscript j representes enemy's aircraft R _j(j=1,2 ..., N), N representes the total quantity of enemy's aircraft, th _IjRepresent our aircraft B _iTo enemy's aircraft R _jThe threat 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 ₂Be non-negative weight coefficient, and satisfy 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 _BThe maximum tracking range of representing our aircraft radars;

We is aircraft B _iTo enemy's aircraft R _jAngle threaten the factor

Be specially:

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

ε wherein _IjExpression enemy aircraft R _jWith respect to we aircraft B _iOff-axis angle, λ ₁With λ ₂Be 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,

Expression enemy aircraft R _jSpeed;

Enemy's aircraft R in like manner _jTo we aircraft B _iThe threat 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 representes enemy's aircraft R _j, subscript i representes our aircraft B _i, th _JiExpression enemy aircraft R _jTo we aircraft B _iThe threat factor,

Expression enemy aircraft R _jTo we aircraft B _iDistance threaten the factor,

Expression enemy aircraft R _jTo we aircraft B _iAngle threaten the factor,

Expression enemy aircraft R _jTo we aircraft B _iSpeed threaten the factor, ω ₃With ω ₄Be non-negative weight coefficient, and satisfy ω ₃+ ω ₄=1;

Enemy's aircraft R _jTo we aircraft B _iDistance threaten the factor

Be specially:

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

D wherein _JiExpression enemy aircraft R _jTo we aircraft B _iDistance, Ra _RExpression enemy aircraft R _jThe average effective operating distance of entrained weapon, Tr _RThe maximum tracking range of expression enemy aircraft radars; Enemy's aircraft R _jTo we aircraft B _iAngle threaten the factor

Be specially:

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

ε wherein _JiRepresent our aircraft B _iWith respect to enemy's aircraft R _jOff-axis angle, λ ₃With λ ₄Be 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 Expression enemy aircraft R _jSpeed,

Represent our aircraft B _iSpeed;

Step 3: all of each weapon of obtaining all our aircraft according to the apportioning cost experimental formula are attacked apportioning costs, make up the preferential apportioning cost vector of attacking:

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

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

Th wherein _IjRepresent our aircraft B _iTo enemy's aircraft R _jThe threat factor,

Expression enemy 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) the aircraft B at this end of institute _iThe integral body of all enemy's aircraft is attacked 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 ₁The attack apportioning cost, AV ₁₂Represent that our carrying arms is numbered 1 aircraft attack enemy aircraft R ₂The attack apportioning cost, AV _1NRepresent that our carrying arms is numbered 1 aircraft attack enemy aircraft R _NThe attack apportioning cost, AV ₂₁Represent that our carrying arms is numbered 2 aircraft attack enemy aircraft R ₁The attack apportioning cost, AV _ZNRepresent that our carrying arms is numbered the aircraft attack enemy aircraft R of Z _NThe attack apportioning cost.The whole apportioning cost vector AV that attacks _{ZN * 1}=[AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _ZN] in comprised our each weapon attack apportioning cost to each aircraft of enemy, comprise ZN altogether and attack apportioning cost;

Integral body is attacked apportioning cost vector AV _{ZN * 1}Middle ZN AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _ZNAttack apportioning cost and arrange, obtain priority allocation value vector PAV according to order from big to small _{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 the quantum chromosomes in quantum bit coding and the initialization population, wherein population scale is designated as NUM; Be chromosomal number in the population, the greatest iteration step number is designated as MAX, in i our weapon allocative decision; With our weapon r (r ∈ 1,2 ... Z) enemy's aircraft of being attacked carries out quantum bit coding, and the gene segment length of each weapon equals the number N of enemy's aircraft, and therefore our gene position of each weapon r correspondence is encoded in i chromosome $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{RN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{RN}}}\end{array}],$ I ∈ 1,2 ... NUM, wherein

Represent that we weapon r does not attack enemy's aircraft R in i the chromosome ₁The quantum bit probability amplitude, wherein

Represent that we weapon r attacks enemy's aircraft R in i the chromosome ₁The quantum bit probability amplitude,

Represent that we weapon r does not attack enemy's aircraft R in i the chromosome ₂Probability amplitude, wherein Represent that we weapon r attacks enemy's aircraft R in i the chromosome ₂The quantum bit probability amplitude,

Represent that we weapon r does not attack enemy's aircraft R in i the chromosome _NThe quantum bit probability amplitude, wherein

Represent that we weapon r attacks enemy's aircraft R in i the chromosome _NThe quantum bit probability amplitude, in a chromosome of our 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 corresponding gene position coding of we weapon r $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{RN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{RN}}}\end{array}],i\&Element;\mathrm{1,2},...\mathrm{NUM},$ Therefore include ZN gene position in the whole chromosome.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 fully according to each gene position coding after, from 1 to ZN serial number, the chromosome after then 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; In i chromosome of

expression the 1st, the 2nd ... (r-1) N+j ... ZN gene position do not attacked the quantum bit probability amplitude of enemy's aircraft,

in i chromosome of expression 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 the 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

thus make in every chromosome our each weapon attacking enemy aircraft identical with the probability of not attacking enemy's aircraft.

Step 5: quantum chromosome is filtered (the method is called observation in quantum calculation), confirm the value of each gene position in the 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 value, produces the random number between 0 to 1 immediately, if random number less than

Value after k gene position filtered is 1, otherwise is taken as 0, the chromosome g after then 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),

Be the chromosome g after filtering _i' the k position gene position value, k is NZ the k in the gene position;

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

According to the preferential attack apportioning cost vector PAV that obtains in the step 3 _{ZN * 1}, the chromosome g after will filtering successively _i', i ∈ 1,2 ... The attack apportioning cost AV that NUM calculates according to formula (9) _IjLittle and

Gene location be 0, makes chromosome satisfy our weapon and only attack enemy's aircraft, and each enemy's aircraft distributes 2 weapons to attack at most;

If the whole chromosome g after filtering _i' in

Number less than the total number Z of our weapon, according to preferential attack apportioning cost vector PAV _{ZN * 1}Whole chromosome g after will filtering successively _i' middle attack apportioning cost AV _IjBig and

Gene location be 1;

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

Threaten in the experimental formula for the quantum bit coding that filters after stain colour solid gene position in the step 4 is corresponded to, the threaten degree objective function carried out 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 representes the threaten degree objective function, and 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}N gene position of j+ (r-1) of representing 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 can know k=(r-1) N+j by the corresponding relation in the formula (10), then represent us to be numbered the weapon attacking enemy aircraft R of r _jIf we the weapon that is numbered r does not attack enemy's aircraft R 0 expression _j

Calculate the chromosome g ' after the i bar filters in the population _iThe threaten degree target function value E that process formula (12) obtains _i, wherein i ∈ 1,2 ..., NUM as chromosomal current the separating of i bar, in individual current the separating of the first generation, finds out the current E of separating of all chromosomes _iIn minimum value as the historical optimum solution of population, be designated as E _b, the chromosome g ' after the corresponding filtration _iFor filtering chromosome, the optimum of population is designated as g _b', corresponding unfiltered chromosome g _iOptimum chromosome g for population _b

If not the first generation is individual, this generation every chromosomal current separating with historical optimum solution compare, if i the chromosomal current E that separates _iLess than historical optimum solution E _b, i.e. E _i＜E _b, then with this chromosomal current E that separates _iValue give E _b, i.e. E _b=E _i, filter chromosome g with i _i' give optimum to filter chromosome g _b', i.e. g _b'=g _i', with i chromosome g _iGive optimum chromosome g _b, g _b=g _i

Step 8: all chromosomes in the population are carried out 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 the prochromosome gene position, α ' _k, β ' _kFor filtering postrotational quantum bit probability amplitude in the after stain colour solid gene position, θ _kExpression quantum rotation angle, inquiry quantum rotation angle θ _kTable is rotated θ in the quantum rotation door to every chromosome _kQuestion blank as shown in table 1:

Table 1: θ in the quantum rotation door _kQuestion blank

F in the above-mentioned table (x) is a target function value, here for enemy's aircraft behind our weapon attacking that obtains according to the threat experimental formula (12) after the conversion in the step 7 to the threaten degree functional value of our aircraft; S (α _kβ _k) be θ _kSymbol; b _kAnd x _kBe respectively that the optimum that obtains in the step 7 filters chromosome g _b' to carry out the filtration chromosome g that the quantum door rotates with current _i' (i ∈ 1,2 ..., k NUM) (k ∈ 1,2 ..., the ZN) value of individual gene position; After the rotation of quantum door, 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 the variation probability P _m, all chromosomes in the population are carried out mutation operation;

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

The gene position comparison procedure is: the chromosome g after will filtering _i' filter chromosome g ' with optimum _bCarry out corresponding gene for relatively, with g ' _bIn gene position be 1 and g _i' middle gene position is that 0 gene position is taken out, if g _i' in k (k ∈ 1,2 ..., ZN) individual gene position is removed, and the chromosome g of corresponding filtered _iThe probability amplitude of k gene position satisfy

Then with g _iIn two probability amplitudes of k gene position

With

Exchange the g after the 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

then probability amplitude do not exchange;

If P＜P _m, chromosome g then _iSkip mutation process;

Step 10: judge whether iterations reaches greatest iteration step number MAX,, return step 5, continue circulation if do not reach; If iterations reaches MAX, withdraw from circulation;

Step 11: after the process step 10 withdraws from circulation, the resulting optimum chromosome g ' that filters _bBe the air battle multiple goal allocative decision that obtains.

The invention has the advantages that:

(1) the present invention proposes the heuristic quantum genetic method that a kind of air battle multiple goal is distributed; The threat experimental formula of collaborative Multi-target Attacking air combat decision problem is out of shape conversion; Our weapon allocative decision is carried out the quantum bit coding, enlarged the expression scope of feasible solution;

(2) the present invention proposes the heuristic quantum genetic method that a kind of 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 is accelerated speed of convergence;

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

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

Description of 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 a quantum door rotation diagram.

Embodiment

To combine accompanying drawing that the present invention is done further detailed description below:

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

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

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

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

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

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

Wherein subscript i representes our aircraft B _i(i=1,2 ..., M), wherein M representes the total quantity of our aircraft, subscript j representes enemy's aircraft R _j(j=1,2 ..., N), N representes the total quantity th of enemy's aircraft _IjRepresent our aircraft B _iTo enemy's aircraft R _jThe threat 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 ₂Be non-negative weight coefficient, and satisfy ω ₁+ ω ₂=1;

We is aircraft B _iTo enemy's aircraft R _jDistance threaten the factor

Be specially:

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

D wherein _IjRepresent our aircraft B _iTo enemy's aircraft R _jDistance, Ra _BRepresent our aircraft B _iThe average effective operating distance of entrained weapon, Tr _BThe maximum tracking range of representing our aircraft radars;

We is aircraft B _iTo enemy's aircraft R _jAngle threaten the factor

Be specially:

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

ε wherein _IjExpression enemy aircraft R _jWith respect to we aircraft B _iOff-axis angle, λ ₁With λ ₂Be 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,

Expression enemy aircraft R _jSpeed;

In like manner, enemy's aircraft R _jTo we aircraft B _iThe threat 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 representes enemy's aircraft R _j, subscript i representes our aircraft B _i, th _JiExpression enemy aircraft R _jTo we aircraft B _iThe threat factor,

Expression enemy aircraft R _jTo we aircraft B _iDistance threaten the factor,

Expression enemy aircraft R _jTo we aircraft B _iAngle threaten the factor,

Expression enemy aircraft R _jTo we aircraft B _iSpeed threaten the factor, ω ₃With ω ₄Be non-negative weight coefficient, and satisfy ω ₃+ ω ₄=1;

Enemy's aircraft R _jTo we aircraft B _iDistance threaten the factor Be specially:

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

D wherein _JiExpression enemy aircraft R _jTo we aircraft B _iDistance, Ra _RExpression enemy aircraft R _jThe average effective operating distance of entrained weapon, Tr _RThe maximum tracking range of expression enemy aircraft radars;

Enemy's aircraft R _jTo we aircraft B _iAngle threaten the factor

Be specially:

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

ε wherein _JiRepresent our aircraft B _iWith respect to enemy's aircraft R _jOff-axis angle, λ ₃With λ ₄Be constant, λ ₃With λ ₄Value generally between 0 to 10, do not have 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

Expression enemy aircraft R _jSpeed,

Represent our aircraft B _iSpeed;

Step 3: all of each weapon of obtaining all our aircraft according to the apportioning cost experimental formula are attacked apportioning costs, make up the preferential apportioning cost vector of attacking.

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

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

Th wherein _IjRepresent our aircraft B _iTo enemy's aircraft R _jThe threat factor, Expression enemy 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) the aircraft B at this end of institute _iThe integral body of all enemy's aircraft is attacked 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 ₁The attack apportioning cost, AV ₁₂Represent that our carrying arms is numbered 1 aircraft attack enemy aircraft R ₂The attack apportioning cost, AV _1NRepresent that our carrying arms is numbered 1 aircraft attack enemy aircraft R _NThe attack apportioning cost, AV ₂₁Represent that our carrying arms is numbered 2 aircraft attack enemy aircraft R ₁The attack apportioning cost, AV _ZNRepresent that our carrying arms is numbered the aircraft attack enemy aircraft R of Z _NThe attack apportioning cost.The whole apportioning cost vector AV that attacks _{ZN * 1}=[AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _ZN] in comprised our each weapon attack apportioning cost to each aircraft of enemy, comprise ZN altogether and attack apportioning cost.

Integral body is attacked apportioning cost vector AV _{ZN * 1}Middle ZN AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _ZNAttack apportioning cost and arrange, obtain priority allocation value vector PAV according to order from big to small _{ZN * 1}, vectorial dimension is ZN * 1.

Step 4: set population scale, greatest iteration step number and variation probability P _m,, carry out all the quantum chromosomes in quantum bit coding and the initialization population to our weapon allocative decision.Wherein, Population scale is designated as NUM; Be chromosomal number in the population, the greatest iteration step number is designated as MAX, and promptly step 5 is to the maximum cycle of step 9; Our weapon allocative decision is meant the concrete distribution method of our all weapon attacking enemy aircraft, comprises our whole each weapon in our the weapon allocative decision and once attacks all the independent subschemes in the distribution at certain.Adopt a kind of our weapon allocative decision of chromosome representative among the present invention.

In i our weapon allocative decision (being in i chromosome of population); With we weapon r (r ∈ 1; 2 ..., enemy's aircraft of Z) being attacked carries out the quantum bit coding; Therefore the gene segment length of each weapon equals the number N of enemy's aircraft, and our gene position of each weapon r correspondence is encoded in i chromosome $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{rN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{rN}}}\end{array}],i\&Element;\mathrm{1,2},...\mathrm{NUM},$ α wherein _iRepresent that we weapon r does not attack enemy's aircraft R in i the chromosome ₁The quantum bit probability amplitude, wherein

Represent that we weapon r attacks enemy's aircraft R in i the chromosome ₁The quantum bit probability amplitude, Represent that we weapon r does not attack enemy's aircraft R in i the chromosome ₂Probability amplitude, wherein

Represent that we weapon r attacks enemy's aircraft R in i the chromosome ₂The quantum bit probability amplitude, Represent that we weapon r does not attack enemy's aircraft R in i the chromosome _NThe quantum bit probability amplitude, wherein

Represent that we weapon r attacks enemy's aircraft R in i the chromosome _NThe quantum bit probability amplitude.The gene section that in a chromosome of our weapon allocative decision, comprises 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 corresponding gene position coding of we weapon r $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{RN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{RN}}}\end{array}],i\&Element;\mathrm{1,2},...\mathrm{NUM},$ Therefore include ZN gene position in the whole chromosome.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 fully according to each gene position coding after, from 1 to ZN serial number, the chromosome after then 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; In i chromosome of

expression the 1st, the 2nd ... (r-1) N+j ... ZN gene position do not attacked the quantum bit probability amplitude of enemy's aircraft,

in i chromosome of expression 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 the 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 thus make in every chromosome our each weapon attacking enemy aircraft identical with the probability of not attacking enemy's aircraft.

Step 5: quantum chromosome is filtered (in quantum calculation, being called " observation "), confirm the value of each gene position in the 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, each gene position of chromosome is carried out value, for example: first gene position with random chance $\left|\begin{array}{c}{\mathrm{\&alpha;}}_{i_1}\\ {\mathrm{\&beta;}}_{i_1}\end{array}\right|$ Filter, produce the random number between 0 to 1 immediately, if random number less than

Value after k gene position filtered is 1, otherwise is taken as 0, the chromosome g after then 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),

Be the chromosome g after filtering _i' the k position gene position value, k is NZ the k in the gene position.

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

According to the preferential attack apportioning cost vector PAV that obtains in the step 3 _{ZN * 1}, the chromosome g after will filtering successively _i', i ∈ 1,2 ... The attack apportioning cost AV that NUM calculates according to formula (9) _IjLittle and

Gene location be 0, makes chromosome satisfy our weapon and only attack enemy's aircraft, and each enemy's aircraft distributes 2 weapons to attack at most;

If the whole chromosome g after filtering _i' in

Number less than the total number Z of our weapon, according to preferential attack apportioning cost vector PAV _{ZN * 1}Whole chromosome g after will filtering successively _i' middle attack apportioning cost AV _IjBig and Gene location be 1.

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

Threaten in the experimental formula for the quantum bit coding that filters after stain colour solid gene position in the step 4 is corresponded to, the threaten degree objective function carried out 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 representes the threaten degree objective function, and 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}N gene position of j+ (r-1) of representing 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 can know k=(r-1) N+j by the corresponding relation in the formula (10), then represent us to be numbered the weapon attacking enemy aircraft R of r _jIf we the weapon that is numbered r does not attack enemy's aircraft R 0 expression _j

Calculate the chromosome g ' after the i bar filters in the population _iThe threaten degree target function value E that process formula (12) obtains _i(wherein i ∈ 1,2 ..., NUM),, in individual current the separating of the first generation (the threaten degree target function value that promptly calculates according to formula (12) for the first time), find out the current E of separating of all chromosomes as chromosomal current the separating of i bar _iIn minimum value be designated as E as the historical optimum solution (abbreviation optimum solution) of population _b, the chromosome g ' after the corresponding filtration _iFor filtering chromosome, the optimum of population is designated as g _b', corresponding unfiltered chromosome g _iOptimum chromosome g for population _b

If not the first generation individual (promptly not being to carry out iteration through step 5 to nine for the first time), this generation every chromosomal current separating with historical optimum solution compare, if i the chromosomal current E that separates _iLess than historical optimum solution E _b, i.e. E _i＜E _b, then with this chromosomal current E that separates _iValue give E _b, i.e. E _b=E _i, filter chromosome g with i _i' give optimum to filter chromosome g _b', i.e. g _b'=g _i', with i chromosome g _iGive optimum chromosome g _b, i.e. g _b=g _iSo 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 the population are carried out 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 the prochromosome gene position, α ' _k, β ' _kFor filtering postrotational quantum bit probability amplitude in the after stain colour solid gene position, θ _kExpression quantum rotation angle.Inquiry quantum rotation angle θ _kTable is rotated θ in the quantum rotation door to every chromosome _kQuestion blank as shown in table 1 down:

Table 1: θ in the quantum rotation door _kQuestion blank

F in the above-mentioned table (x) is a target function value, in the step 7 according to enemy's aircraft behind our weapon attacking that obtains of threat experimental formula (12) after the conversion to the threaten degree functional value of our aircraft; S (α _kβ _k) be θ _kSymbol; b _kAnd x _kBe respectively k during the optimum chromosome that obtains in the step 7 and the current chromosome that will carry out the rotation of quantum door are separated (k ∈ 1,2 ..., the ZN) value of individual gene position.Quantum door rotation diagram is as shown in Figure 2, after the rotation of quantum door, 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 the variation probability P _m, all chromosomes in the population are carried out mutation operation.

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

The gene position comparison procedure is: the chromosome g after will filtering _i' filter chromosome g ' with optimum _bCarry out corresponding gene for relatively, with g ' _bIn gene position be 1 and g _i' middle gene position is that 0 gene position is taken out, if g _i' in k (k ∈ 1,2 ..., ZN) individual gene position is removed, and the chromosome g of corresponding filtered _iThe probability amplitude of k gene position satisfy Then with g _iIn two probability amplitudes of k gene position

With Exchange the g after the 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

then probability amplitude do not exchange.

If P＜P _m, chromosome g then _iSkip mutation process.

Step 10: judge whether iterations reaches greatest iteration step number MAX,, return step 5, continue circulation if do not reach; If iterations reaches MAX, withdraw from circulation.

Step 11: after the process step 10 withdraws from circulation, the resulting optimum chromosome g ' that filters _bBe the air battle multiple goal allocative decision that obtains.

Claims (1)

1. an air battle multiple goal heuristic quantum genetic method of distributing is characterized in that: comprise following step:

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

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

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

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

Wherein subscript i representes our aircraft B _i(i=1,2 ..., M), wherein M representes the total quantity of our aircraft, subscript j representes enemy's aircraft R _j(j=1,2 ..., N), N representes the total quantity of enemy's aircraft, th _IjRepresent our aircraft B _iTo enemy's aircraft R _jThe threat 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 ₂Be non-negative weight coefficient, and satisfy 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 _BThe average effective operating distance of representing the entrained weapon of we aircraft Bi, Tr _BThe maximum tracking range of representing our aircraft radars;

We is aircraft B _iTo enemy's aircraft R _jAngle threaten the factor

Be specially:

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

ε wherein _IjExpression enemy aircraft R _jWith respect to we aircraft B _iOff-axis angle, λ ₁With λ ₂Be 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,

Expression enemy aircraft R _jSpeed; Enemy's aircraft R in like manner _jTo we aircraft B _iThe threat 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 representes enemy's aircraft R _j, subscript i representes our aircraft B _i, th _JiExpression enemy aircraft R _jTo we aircraft B _iThe threat factor, Expression enemy aircraft R _jTo we aircraft B _jDistance threaten the factor, Expression enemy aircraft R _jTo we aircraft B _iAngle threaten the factor,

Expression enemy aircraft R _jTo we aircraft B _iSpeed threaten the factor, ω ₃With ω ₄Be non-negative weight coefficient, and satisfy ω ₃+ ω ₄=1;

Enemy's aircraft R _jTo we aircraft B _iDistance threaten the factor Be specially:

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

D wherein _JiExpression enemy aircraft R _jTo we aircraft B _iDistance, Ra _RExpression enemy aircraft R _jThe average effective operating distance of entrained weapon, Tr _RThe maximum tracking range of expression enemy aircraft radars;

Enemy's aircraft R _jTo we aircraft B _iAngle threaten the factor

Be specially:

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

ε wherein _JiRepresent our aircraft B _iWith respect to enemy's aircraft R _jOff-axis angle, λ ₃With λ ₄Be 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

Expression enemy aircraft R _jSpeed,

Represent our aircraft B _iSpeed;

Step 3: all of each weapon of obtaining all our aircraft according to the apportioning cost experimental formula are attacked apportioning costs, make up the preferential apportioning cost vector of attacking:

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

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

Th wherein _IjRepresent our aircraft B _iTo enemy's aircraft R _jThe threat factor,

Expression enemy 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) the aircraft B at this end of institute _iThe integral body of all enemy's aircraft is attacked 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 ₁The attack apportioning cost, AV ₁₂Represent that our carrying arms is numbered 1 aircraft attack enemy aircraft R ₂The attack apportioning cost, AV _1NRepresent that our carrying arms is numbered 1 aircraft attack enemy aircraft R _NThe attack apportioning cost, AV ₂₁Represent that our carrying arms is numbered 2 aircraft attack enemy aircraft R ₁The attack apportioning cost, AV _ZNRepresent that our carrying arms is numbered the aircraft attack enemy aircraft R of Z _NThe attack apportioning cost, the whole apportioning cost vector AV that attacks _{ZN * 1}=[AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _ZN] in comprised our each weapon attack apportioning cost to each aircraft of enemy, comprise ZN altogether and attack apportioning cost;

Integral body is attacked apportioning cost vector AV _{ZN * 1}Middle ZN AV ₁₁, AV ₁₂..., AV _1N, AV ₂₁..., AV _ZNAttack apportioning cost and arrange, obtain priority allocation value vector PAV according to order from big to small _{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 the quantum chromosomes in quantum bit coding and the initialization population, wherein population scale is designated as NUM; Be chromosomal number in the population, the greatest iteration step number is designated as MAX, in i our weapon allocative decision; With our weapon r (r ∈ 1,2 ... Z) enemy's aircraft of being attacked carries out quantum bit coding, and the gene segment length of each weapon equals the number N of enemy's aircraft, and therefore our gene position of each weapon r correspondence is encoded in i chromosome $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{RN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{RN}}}\end{array}],$ I ∈ 1,2 ... NUM, wherein

Represent that we weapon r does not attack enemy's aircraft R in i the chromosome ₁The quantum bit probability amplitude, wherein

Represent that we weapon r attacks enemy's aircraft R in i the chromosome ₁The quantum bit probability amplitude,

Represent that we weapon r does not attack enemy's aircraft R in i the chromosome ₂Probability amplitude, wherein Represent that we weapon r attacks enemy's aircraft R in i the chromosome ₂The quantum bit probability amplitude,

Represent that we weapon r does not attack enemy's aircraft R in i the chromosome _NThe quantum bit probability amplitude, wherein

Represent that we weapon r attacks enemy's aircraft R in i the chromosome _NThe quantum bit probability amplitude, in a chromosome of our 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 corresponding gene position coding of we weapon r $g_{i_r}=\left[\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r1}}\\ {\mathrm{\&beta;}}_{i_{r1}}\end{array}\right|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{r2}}\\ {\mathrm{\&beta;}}_{i_{r2}}\end{array}|...|\begin{array}{c}{\mathrm{\&alpha;}}_{i_{\mathrm{RN}}}\\ {\mathrm{\&beta;}}_{i_{\mathrm{RN}}}\end{array}],i\&Element;\mathrm{1,2},...\mathrm{NUM},$ Therefore include ZN gene position in the whole chromosome, 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 fully according to each gene position coding after, from 1 to ZN serial number, the chromosome after then 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; In i chromosome of

expression the 1st, the 2nd ... (r-1) N+j ... ZN gene position do not attacked the quantum bit probability amplitude of enemy's aircraft, in i chromosome of

expression 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 the 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 thus make in every chromosome our each weapon attacking enemy aircraft identical with the probability of not attacking enemy's aircraft;

Step 5: quantum chromosome is filtered, confirm the value of each gene position in the 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 value, produces the random number between 0 to 1 immediately, if random number less than

Value after k gene position filtered is 1, otherwise is taken as 0, the chromosome g after then 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), Be the chromosome g after filtering _i' the k position gene position value, k is NZ the k in the gene position;

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

According to the preferential attack apportioning cost vector PAV that obtains in the step 3 _{ZN * 1}, the chromosome g after will filtering successively _i', i ∈ 1,2 ... The attack apportioning cost AV that NUM calculates according to formula (9) _IjLittle and

Gene location be 0, makes chromosome satisfy our weapon and only attack enemy's aircraft, and each enemy's aircraft distributes 2 weapons to attack at most;

If the whole chromosome g after filtering _i' in

Number less than the total number Z of our weapon, according to preferential attack apportioning cost vector PAV _{ZN * 1}Whole chromosome g after will filtering successively _i' middle attack apportioning cost AV _IjBig and

Gene location be 1;

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

Threaten in the experimental formula for the quantum bit coding that filters after stain colour solid gene position in the step 4 is corresponded to, the threaten degree objective function carried out 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 representes the threaten degree objective function, and 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}N gene position of j+ (r-1) of representing 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 can know k=(r-1) N+j by the corresponding relation in the formula (10), then represent us to be numbered the weapon attacking enemy aircraft R of r _jIf we the weapon that is numbered r does not attack enemy's aircraft R 0 expression _j

Calculate the chromosome g ' after the i bar filters in the population _iThe threaten degree target function value E that process formula (12) obtains _i, wherein i ∈ 1,2 ..., NUM as chromosomal current the separating of i bar, in individual current the separating of the first generation, finds out the current E of separating of all chromosomes _iIn minimum value as the historical optimum solution of population, be designated as E _b, the chromosome g ' after the corresponding filtration _iFor filtering chromosome, the optimum of population is designated as g _b', corresponding unfiltered chromosome g _iOptimum chromosome g for population _b

If not the first generation is individual, this generation every chromosomal current separating with historical optimum solution compare, if i the chromosomal current E that separates _iLess than historical optimum solution E _b, i.e. E _i＜E _b, then with this chromosomal current E that separates _iValue give E _b, i.e. E _b=E _i, filter chromosome g with i _i' give optimum to filter chromosome g _b', i.e. g _b'=g _i', with i chromosome g _iGive optimum chromosome g _b, g _b=g _i

Step 8: all chromosomes in the population are carried out 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 the prochromosome gene position, α ' _k, β ' _kFor filtering postrotational quantum bit probability amplitude in the after stain colour solid gene position, θ _kExpression quantum rotation angle, inquiry quantum rotation angle θ _kTable is rotated every chromosome, after the rotation of quantum door, 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 the variation probability P _m, all chromosomes in the population are carried out mutation operation;

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

The gene position comparison procedure is: the chromosome g after will filtering _i' filter chromosome g ' with optimum _bCarry out corresponding gene for relatively, with g ' _bIn gene position be 1 and g _i' middle gene position is that 0 gene position is taken out, if g _i' in k (k ∈ 1,2 ..., ZN) individual gene position is removed, and the chromosome g of corresponding filtered _iThe probability amplitude of k gene position satisfy

Then with g _iIn two probability amplitudes of k gene position

With Exchange the g after the 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

then probability amplitude do not exchange;

If P＜P _m, chromosome g then _iSkip mutation process;

Step 10: judge whether iterations reaches greatest iteration step number MAX,, return step 5, continue circulation if do not reach; If iterations reaches MAX, withdraw from circulation;

Step 11: after the process step 10 withdraws from circulation, the resulting optimum chromosome g ' that filters _bBe the air battle multiple goal allocative decision that obtains.

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