CN103336885A - Method for solving weapon-target assignment problem based on differential evolution algorithm - Google Patents
Method for solving weapon-target assignment problem based on differential evolution algorithm Download PDFInfo
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Abstract
The invention relates to a method for solving a weapon-target assignment problem based on a differential evolution algorithm, and belongs to the field of computer simulation and method optimization. According to the method, based on the traditional weapon-target assignment problem, a sensor is added to detect a target; factors such as detection transfer time of the sensor, target number capable of being detected simultaneously, interconnection constraint between the sensor and a weapon, and reserved observing time of the weapon are taken into consideration; a larger feasible solution space is determined first, an intercept point is set for the special target according to the weapon-sensor interconnection constraint; the solution space is constrained and reduced; the reduced solution space is subjected to code reconstruction; and an optimal solution is found with the differential evolution algorithm by taking a position of each ammunition of the weapon in an assignable interval of the weapon as an optimization variable. The method is more approximate to the actual weapon-target assignment problem, reduces the optimization complexity, improves the optimization efficiency, reduces the space occupied by the solution space, and is more convenient and flexible to operate.
Description
Technical field
The invention belongs to Computer Simulation and method and optimize the field, relate to a kind of method that solves weapon-target assignment problem based on differential evolution algorithm.
Background technology
Weapon-target assignment problem is an important topic in the operation decision-making, be exactly how reasonably to distribute our troops to meet enemy troops head-on, to reach best fighting effect, belong to NP(Non-deterministic Polynomial, the uncertain problems of polynomial expression complexity) complete problem does not still have effective determinacy method for solving at present.The fundamental purpose of its research is, fast and effeciently solve the assignment problem of extensive weapon-target, to improve the automatization level of battlefield commander's control, namely at a plurality of threat targets, defence can distribute the defence resource timely and effectively, eliminate unfriendly target effectively and threaten, make the loss minimum of defence side.Generally speaking troops' resource that weapon-target assignment problem relates to only limits to weapon and target, and as the sensor of surveying resource not at the row of troops' resource.
From the development of five sixties of 20th century so far, the solution of weapon-target assignment problem has experienced the improvement from the traditional algorithm to the intelligent optimization algorithm.The eighties mainly was limited to traditional algorithm in the past, and as implicit enumeration method, dynamic programming etc., these algorithms are comparatively simple, but comparatively loaded down with trivial details when realizing, when especially destination number increased, speed of convergence was just very slow.Since the eighties, some optimize algorithm, as artificial neural network, chaos and heuristic search algorithm etc., provide new thinking and means for solving challenge.
Differential evolution algorithm is based on the optimization algorithm of swarm intelligence theory, it can by in the colony between individuality cooperation and competition realize finding the solution optimization problem.Be compared to evolution algorithm, differential evolution algorithm has kept the global search strategy based on population, adopts real coding, operates and man-to-man competition surviving policy based on the simple editing of difference, has reduced the complicacy of genetic manipulation.Differential evolution algorithm has the individual optimum solution of memory and the shared characteristics of middle group's internal information, its essence is a kind of greedy genetic algorithm with blessing thought based on real coding, this algorithm is simple and easy to use, robustness is good, ability of searching optimum is strong, differential evolution algorithm has multiple strategy to select simultaneously, can adjust hunting zone and speed of convergence as required.
Summary of the invention
The objective of the invention is, sensor is listed among troops' resource to be allocated, proposed weapon-target assignment problem of tallying with the actual situation more, and a kind of method that solves weapon-target assignment problem based on differential evolution algorithm is provided.
The present invention is based on the method for differential evolution algorithm solution weapon-target assignment problem, with the sensor resource adding weapon-target assignment problem of defend equipment, solution specifically comprises following step:
Step 1: the input variable and the initializing variable that obtain weapon-target assignment problem.
Input variable comprises: target number N, weapon number M, sensor number G, the priority of resource allocation S of each target
i, i=1,2 ..., N; The ammunition quantity B initial or every kind of current weapon has
j, j=1,2 ..., M; The destination number O initial or each current sensor can be surveyed simultaneously
k, k=1,2 ..., G; The belligerent matrix of target-weapon, comprising information has: but but but the weapon of weapon sequence number, target sequence number and corresponding commit time section section launch time intercept point correspondence thereof and target distance from; The detectable matrix of target-sensor, comprising information has: sensor sequence number, target sequence number and corresponding detectable time period, the target in the detectable time period and the distance between sensor thereof; The interconnection constraint of weapon and sensor comprises related weapon and sensor information, related temporal information.
Initializing variable comprises: the property value C of each target
Ni, the property value C of each weapon
Mj, the property value C of each sensor
Gk, j weapon M
jTo i target N
iThe estimated value P of kill probability
Ij, detection T transfer time of each sensor
d_ G
k, wherein, i=1,2 ..., N, j=1,2 ..., M, k=1,2 ..., G; Reserve T observing time
dGiven kill probability value P
GivenGiven priority of resource allocation is not worth S
Given
Step 2: determine the feasible solution space, comprise step 2.1～step 2.3.
Step 2.1: that determines target can be by the weapon attacking time shaft, specifically: find out N from the belligerent matrix of target-weapon
iCan be by weapon M
jSection MT effective time that attacks
Ij, with MT
IjSplice in chronological order, form target N
iCan be by the time shaft MT of weapon attacking
i, time shaft MT
iOn each time period canned data have: but but target, weapon attack time section zero-time attack time section concluding time; Wherein, i=1,2 ..., N, j=1,2 ..., M.
Step 2.2: that determines target can be by sensor detection time axle, specifically: find out N from the detectable matrix of sensor-target
iCan be by sensor G
kSection GT effective time that surveys
Ik, with GT
IkSplice according to time sequencing, form target N
iBe detected time shaft GT
i, time shaft GT
iOn each time period canned data have: target, sensor, detectable time period zero-time, detectable concluding time time period; Wherein, i=1,2 ..., N, k=1,2 ..., G.
Step 2.3: determine the be blocked time shaft of target, specifically: with target N
iCan be by weapon attacking time shaft MT
iWith can be by sensor detection time axle GT
iPut in order according to time sequencing, will have overlapping part to merge on the time shaft, obtain target N
iBe blocked time shaft T
iThe N of a N target correspondence time shaft has constituted initial solution space A
1
Use the mode of binary digit coding to record attacked weapon and the detectable sensor information of each target in each time period.The coding binary figure place of record weapon information is identical with the number of weapon in each time period, from right to left, each represents the weapon that the weapon sequence number is serial number, every value is 1 or 0, the corresponding weapon of 1 expression can be attacked target in this time period, and the corresponding weapon of 0 expression can not be attacked target in this time period.The coding binary figure place of record sensor information is identical with number of sensors in each time period, from right to left, each representative sensor sequence number is the sensor of serial number, every value is 1 or 0,1 expression respective sensor can be surveyed target in this time period, and 0 expression respective sensor can not be surveyed target in this time period.
Step 3: dwindle the initial solution space, comprise step 3.1 and step 3.2.
Step 3.1: dwindle solution space according to weapon-sensor interconnection constraint.Reject the weapon attacking information of the interconnection constraint of not satisfying weapon-sensor, will can not be rejected the solution space A that obtains dwindling by the time period of any weapon attacking in the solution space then
2
Will be in the solution space can not be rejected by the time period of any weapon attacking, specifically: to the target N of interconnection constraint that weapon-sensor is arranged
i, at the interconnection constraint of every weapon-sensor, carry out following operation:
If weapon M
jWith sensor G
kThere is interconnection constraint, traversal target N
iBe blocked time shaft T
iOn all time periods, to can be by weapon M
jCertain time period of attacking, judge whether satisfy sensor G in this time period
kRequirement, if do not satisfy, then at time shaft T
iOn should the time period in weapon M
jTo target N
iThe information of attacking is rejected, if satisfy, order is got the next time period, if can be by weapon M in this time period
jAttack and satisfy sensor G again
kRequirement, then continue to take off a time period, up to can not be by M
jAttack or do not satisfy sensor G
kRequirement; At this moment, judge that all can be by weapon M
jAttack and satisfy sensor G again
kThe time period T of requirement
I.x1～T
I.x2, whether cover weapon M
jWith sensor G
kSection correlation time, if not, then at time shaft T
iGo up time period T
I.x1～T
I.x2Interior weapon M
jTo target N
iThe information of attacking is rejected.
Step 3.2: dwindle solution space for specific objective arranges the intercept point constraint.The traversal target is priority of resource allocation S
iMore than or equal to given priority level value S
GivenTarget, an intercept point is set at least; After having traveled through all targets, the more state of modern weapons and sensor, and surplus resources; Then, will distributing the time period of intercept point to reject from solution space, be that the attack information of zero weapon is rejected in solution space with the residue ammunition; To can not be rejected the solution space A that obtains dwindling by the time period of any weapon attacking in the solution space at last
3
If target N
iPriority of resource allocation be not worth S
i〉=S
Given, the operation of (1) and (2) below then carrying out:
(1) distributes weapon and ammunition.To target N
iCan be blocked time shaft T
iOn all time period T
I.x, calculate in each time period weapon to target N
iAverage kill probability
X is positive integer, x=1,2 ..., expression can be blocked x the time period on the time shaft.Elect section sometime as the time period that intercept point need be set, time period T
I.xWith
Probability be selected.The starting point of selecteed time period is set to intercept point, weapon M on this intercept point
l, l ∈ 1,2 ..., the target N of M}
iThe ammunition number that distributes is B
l* (S
i/ Σ S
i) * (qp), wherein p is M
lTo N
iBut the length of all attack time sections, q is the length of current slot.If the selecteed time period has the plural weapon can be to target N
iAttack, begin to carry out the distribution of ammunition number from the high weapon of kill probability, the distribution ammunition number of gained rounds up.
(2) distribute sensor.If there is the interconnection constraint of weapon and particular sensor, be target N according to interconnection constraint then
iDistribute sensor and detection time, if the onrelevant constraint is target N according to nearby principle then
iAssign sensor; If the selected time period is that (time1～time2), the detection time that then distributes sensor is (time1～time2+T
d_ G
k).
Step 4: to the solution space reconstruct of encoding, comprise step 4.1～step 4.3.
Step 4.1: reconstruct solution space.To solution space A
3The time shaft that can tackle according to weapon is reconstructed, and obtains the solution space A after the reconstruct
4To weapon M
j, at solution space A
3The middle traversal time period, obtain all and contain M
jThe time period of attack information, all time periods that obtain are spliced according to time sequencing, form weapon M
jBut commit time axle TM
jj＝1,2,……,M。
Step 4.2: divide solution space.With weapon M
jBut commit time axle TM
jOn each time period need divide with the time by minimum interception, and will need to reject with the time period of time less than the minimum interception, establish final time shaft TM
jOn live part by ML
jIndividual minimum interception needs to form with the time period, j=1, and 2 ..., M.Described minimum interception needs to comprise with the time T observing time of reservation
d, and T launch time of weapon
fBut with attack time T
lBetween linear relationship.
Step 4.3: solution space coding.To weapon M
j, with TM
jOn ML
jThe individual time period is mapped to ML
jThe real number point set that individual real number is formed 1,2 ..., ML
jOn.Get interval (0, ML
j] as weapon M
jAmmunition can distribute the interval.j=1,2,……,M；.
Step 5: utilize differential evolution algorithm to seek optimal solution, comprise step 5.1～step 5.7.
Step 5.1: selected variable and the objective function optimized.Selected weapon M
jEach ammunition
Can distribute the position on the interval to be the optimization variable at it, s=1,2 ..., B
j; J=1,2 ..., M.
The objective definition function f is:
Wherein: m
iBe target N
iThe quantity of the intercept point that distributes.λ
iBe scale-up factor, determine according to actual conditions.
j
u∈ { j
1..., j
aExpression: the allocation result to certain target intercept point is total a kind weapon j
1..., j
aIt is tackled, and the kill probability value of every kind of weapon is
...,
The ammunition quantity of every kind of weapon distribution is
...,
Step 5.2: produce initial population.
T is for the e in the population individual x
e(t) be expressed as:
x
e(t)=(x
el(t),x
e2(t),...,x
eW(t)),e＝1,2,......,NP；t＝1,2,......,t
max
Wherein, x
e(t) corresponding one of each component is optimized variable, and W constitutes individual chromosome number, namely optimizes the number of variable; NP is population scale; t
MaxIt is maximum evolutionary generation.
Produce NP individuality at random according to the span of optimizing variable.Each individuality in the population produces by the following method:
According to weapon kill probability order from high to low, to weapon M
jAll available ammunitions
(s=1,2 ..., B
j) arrive interval (0, ML by even probability assignments
j] on.For a certain segment, if the interior weapon of this segment can be attacked the target more than 2, then use the mode of roulette, with probability S
i/ Σ S
iSelected one of them target is distributed the ammunition in this segment on the selected target unitedly.With ammunition by the interval of its distribution and Target Assignment on the starting point of its corresponding commit time section, whether have resource to use conflict (sensor resource uses constraint) to the individuality check that generates, if there is conflict then to regenerate.
Add up the intercept point number of each target, calculate each individual fitness value according to objective function.
Step 5.3: produce test vector
From current t for selecting 3 individual x the population at random
P1(t), x
P2(t) and x
P3(t), then t+1 optimizes the corresponding test vector h of variable for r of e population individuality of population
Er(t+1) be:
h
er(t+1)＝x
p1r(t)+F*(x
p2r(t)-x
p3r(t))，e≠p1≠p2≠p3
Wherein,
x
P1r(t), x
P2r(t) and x
P3r(t) represent individual x respectively
P1(t), x
P2(t) and x
P3(t) optimize variable for r;
x
P2r(t)-x
P3r(t) be the differentiation vector; F is zoom factor.
If the test vector that produces is not in the distribution interval of ammunition, regenerate test vector according to the individual production method of population in the step 5.2.
Step 5.4: produce filial generation, r filial generation v of e population individuality
Er(t+1) be:
Wherein, rand l
ErBe the decimal at random between [0,1], CR is crossover probability, and CR ∈ [0,1], rand (e) are the random integers between [1, N].
Whether the filial generation that generates is carried out Target Assignment and checked each individuality to have resource to use conflict, if there is conflict then to regenerate according to the individual production method of population in the step 5.2.
Add up the intercept point number of each target, calculate each individual fitness value in the filial generation according to objective function.
Step 5.5: new population more.The t+1 that upgrades is for the e in the population individual x
e(t+1) be:
Wherein, f (v
El(t+1) ..., v
En(t+1)) be filial generation v
e(t+1) fitness, f (x
E1(t) ..., x
En(t)) be parent x
e(t) fitness.
Whether the individuality of judging fitness optimum in the new population satisfies formula:
If satisfy, termination of iterations returns the fitness optimum individual, otherwise, change step 5.3 and carry out.
Judge perhaps whether t+1 has surpassed iteration upper limit t
Max, if surpass, then termination of iterations returns the fitness optimum individual, carries out otherwise continue to change step 5.3.
Step 5.6: distribute surplus resources.
For the optimum individual of selecting, if surplus resources is arranged, under the situation that does not produce conflict, priority allocation is given the high target of priority, or adopts distribution principle distribution nearby.
Step 5.7: the allocation result after the optimization that will obtain is carried out Gray code, determines the intercept point position of Target Assignment and weapon, the sensor resource of distribution.
Advantage of the present invention and good effect are:
1) on the basis of traditional weapon-target assignment problem, added the detection of sensor to target, and factors such as reservation observing time of the interconnection constraint of detection transfer time of sensor, target number, sensor and the weapon that can survey simultaneously, weapon are considered in the problem, the starting point of problem relatively tallies with the actual situation, and can solve more the weapon-target assignment problem close to actual conditions.
2) the proposition method provides the reference of solution aspect for solving the weapon-target assignment problem that adds sensor detection constraint among use the present invention.
3) obtain bigger feasible solution space earlier, dwindle solution space by part constraint again, rather than with a series of constraint all as the constraint condition in the optimization method, greatly reduce the complicacy of optimization method, improved optimization efficient.
4) use the mode of binary digit coding to record in the solution space certain time period and go up assailable weapon and detectable sensor information, perhaps be used for detectable sensor information in the restructuring of record solution space.Compare with general array or vectorial location mode, reduced the shared space of solution space; In the practical operation, more convenient flexibly than array or vector; And just can get information about very much the information that weapon is attacked or sensor is surveyed by a binary number.
5) intercept point is set to optimize variable among the present invention, the reconstruct solution space with the visual angle of time shaft from goal displacement to weapon, successfully finished from the primitive solution space to the conversion of the solution space of importing as differential evolution algorithm, the optimization aim of closely having fitted provides support for further utilizing the differential evolution algorithm optimizing.
Description of drawings
Fig. 1 is the process flow diagram based on differential evolution algorithm solution weapon-target assignment problem method among the present invention;
But Fig. 2 is target-weapon attack time axle;
Fig. 3 is the detectable time shaft of target-sensor;
Fig. 4 is target N
iBe blocked time shaft;
Fig. 5 dwindles the process flow diagram of solution space for the inventive method according to weapon-sensor interconnection constraint;
Fig. 6 dwindles the instance graph of solution space for the inventive method according to weapon-sensor interconnection constraint;
Fig. 7 dwindles the solution space process flow diagram for specific objective arranges the intercept point constraint;
Fig. 8 is reconstruct solution space legend.
Embodiment
Below in conjunction with accompanying drawing, technical scheme of the present invention is further described.
Weapon-target assignment problem to be solved by this invention, on the basis of traditional weapon-target assignment problem, added the detection of sensor to target, and factors such as reservation observing time of the interconnection constraint of detection transfer time of sensor, destination number, sensor and weapon that sensor can be surveyed simultaneously, weapon have been considered in the problem, the starting point of problem relatively tallies with the actual situation, and can solve more close to actual conditions.Weapon-target assignment problem to be solved by this invention is described below:
A collection of offensive weapons is implemented to attack by specific flight path, one cover defend equipment is implemented interception to attacking target, defend equipment comprises weapon and sensor two class resources, the equipment limited amount, requirement provides the optimize resource allocation of defend equipment by certain rule under current intelligence, dynamically guarantee attacking comprehensive belligerent the best as a result of target.
This weapon-target assignment problem is the closing to reality situation more, and sensor is listed among troops' resource to be allocated, and target, weapon, sensor carry out the differentiation of kind by attribute; N altogether of target is with N
i(i=1,2 ..., N) to distinguish, each target has a property value C who characterizes target type
Ni(i=1,2 ..., N), simultaneously, each target all has a priority of resource allocation and is not worth S
i(i=1,2 ..., N), S
iBe the interception order, relevant with the threaten degree of target, S
iThe threaten degree of the more high representative target of value is more high, and the priority level that resource is distributed is also more high.M altogether on weapon is with M
j(j=1,2 ..., M) to distinguish, each weapon has a property value C who characterizes weapon type
Mj(j=1,2 ..., M), G altogether of sensor is with G
k(k=1,2 ..., G) to distinguish, each sensor has a property value C who characterizes sensor type
Gk(k=1 ..., G); J weapon carries ammunition B
j, j=1,2 ..., M.K sensor can detect O simultaneously
kIndividual destination number k=1 ..., G, corresponding one of the sensor of each attribute is surveyed T transfer time
d_ G
k, k=1 ..., G.Survey refer to transfer time when sensor by the transfer time of the detection of certain target being shifted needs for to the detection of another one target the time.
Using differential evolution algorithm to carry out the branch timing of troops' resource, set the goal to one, except distributing weapon hits it, also need distribute sensor that it is surveyed, the sensor that distributes this moment should satisfy the incidence relation of weapon and sensor, also to determine simultaneously the ammunition that weapon uses, and As soon as possible Promising Policy ammunition assignment constraints condition, be not worth S for priority of resource allocation
iBe higher than given priority level value S
GivenTarget, guarantee to distribute at least an intercept point.Final distribution result is the intercept point of each Target Assignment, and the intercept point of a Target Assignment may have a plurality of.
Wherein, the incidence relation of weapon and sensor is: the resource to same target is distributed, should satisfy the incidence relation between weapon and the sensor, the variation that this incidence relation physical presence is very many, can simplify and abstractly be: for the weapon of some attribute, one or two of section must be arranged between weapon and the particular community sensor correlation time, require to have at least m particular community sensor assignment to give detection time section covering section correlation time (being that the detection time section is comprising section correlation time) of this target.M is at least 1, is no more than the sensor sum at most.This interconnection constraint comprises two-layer constraint: the one, and the constraint of weapon and particular community sensor; The 2nd, correlation time section constraint.Section correlation time of weapon and sensor mainly is in order to guarantee accurately to determine the position of target, and target prevents loss.Exemplify for: be C as an attribute
M3Weapon to target N
1When attacking, requiring this moment that m attribute must be arranged is C
G5Sensor, in the process that weapon is desired to attack and attack, this target is surveyed.
Ammunition assignment constraints condition is: suppose to the allocation result of certain intercept point to be that total a kind weapon is implemented interception, sequence number is j
1, j
2..., j
a, every kind of weapon is respectively the ammunition of this Target Assignment
...,
Individual, the kill probability estimated value of every kind of weapon is respectively
...,
Then should satisfy
Wherein, P
GivenRelevant with the objective attribute target attribute value, during research desirable 0.96.When ammunition was not enough, this condition may be not being met, and the condition that satisfy in the optimization aim this moment gets final product.
As shown in Figure 1, the method that the present invention is based on differential evolution algorithm solution weapon-target assignment problem can be finished according to following steps:
Step 1: initializing variable and the input variable of obtaining weapon-target assignment problem;
Input variable mainly comprises: target, weapon, number of sensors N, M, G; The priority of resource allocation S of each target
i(i=1 ..., N); The ammunition quantity B initial or every kind of current weapon has
j(j=1 ..., M); The destination number O initial or current each sensor can be surveyed simultaneously
k, k=1 ..., G; The belligerent matrix of target-weapon; The detectable matrix of target-sensor; Interconnection constraint between weapon and the particular community sensor comprises related weapon and sensor information, related temporal information.
Every kind of weapon all to target may form belligerent maybe can not form belligerent, after judging according to space-time condition early stage, can obtain the belligerent matrix of target-weapon, the information that comprises in the belligerent matrix has: but but but the weapon of weapon sequence number, target sequence number and corresponding commit time section section launch time intercept point correspondence thereof and target distance from.Because but commit time Duan Yuke section launch time is corresponding and the certain relation of existence one by one, therefore, but the initial conditions when getting the commit time section as problem solving, but distance is that commit time is carried out the discretize result that discretize is handled the correspondence that obtains afterwards.
Each sensor all may form detection to target maybe can not form detection, after judging according to space-time condition early stage, can obtain the detectable matrix of target-sensor, the information that comprises in the matrix has: sensor sequence number, target sequence number and corresponding detectable time period, the target in the detectable time period and the distance between sensor thereof.Distance is that the detectable time is carried out the discretize result that discretize is handled the correspondence that obtains afterwards.
Initializing variable mainly comprises: in order to the property value C of each target of identifying target, weapon, sensor, weapon, sensor
Ni(i=1 ..., N), C
Mj(j=1 ..., M), C
Gk(k=1 ..., G); The estimated value P of the kill probability of the target i of weapon j
Ij(i=1 ..., N; J=1 ..., M); Detection T transfer time of each sensor
d_ G
k(k=1 ..., G); Reserve T observing time
dGiven kill probability value P
GivenGiven priority of resource allocation is not worth S
GivenReserve and to refer to observing time after interception, need to observe whether tackle success, if unsuccessful weapon delivery again implements to tackle, during observing time of reservation is arranged.
Step 2: determine big feasible solution space, specifically comprise step 2.1～step 2.3.
Step 2.1: determine that target can be by the time shaft of weapon attacking, namely target-weapon can belligerent time shaft.
Travel through all targets, from the belligerent matrix of target-weapon of input, find out target N
i(i=1 ..., N) can be by weapon M
j(j=1 ..., M) section MT effective time of Gong Jiing
Ij, i under the identical situation of j, might be a plurality of MT
IjNamely but same weapon may have a plurality of commit time sections to same target.As shown in Figure 2, target N
iCan be by weapon M
1, M
2And M
3Section effective time of attacking is respectively MT
I1, MT
I2And MT
I3, wherein, can be by weapon M
3Section effective time of attacking has two sections MT
I3-1And MT
I3-2With MT
Ij(j=1 ..., M) splice in chronological order, during splicing, arrange according to the zero-time of time period earlier, what zero-time was identical arranged according to the termination time, obtained target N
iCan be by the time shaft MT of weapon attacking
iTime shaft MT
iMay be discontinuous, this time shaft MT
iOn comprise target N
iSometime the section in can be by the information of certain several weapon attacking.Each time period canned data has: but but target, weapon attack time section zero-time attack time section concluding time.As shown in Figure 2, target N
iCan be by the time shaft MT of weapon attacking
iComprise the some time section, for example the 2nd time period can be by weapon M
1And M
2Attack.
Step 2.2: determine the time shaft that target can be surveyed by sensor, i.e. the detectable time shaft of target-sensor.
Travel through all targets, from the detectable matrix of sensor-target, find out N
iCan be by k sensor G
k(k=1 ..., G) section GT effective time of Tan Ceing
IkUnder the identical situation of k, may there be a plurality of GT in i
Ik, namely same sensor may have a plurality of detectable time periods to same target.As shown in Figure 3, target N
iCan be by sensor G
1, G
2, G
3And G
4The section of surveying effective time is respectively GT
I1, GT
I2, GT
I3And GT
I4With GT
IkSplice according to time sequencing, the splicing principle can be consistent by the principle that the attack time axis information adopts with target, forms target N
iBe detected time shaft GT
iTime shaft GT
iMay be discontinuous, comprise target N on this time shaft
iCan be by the information of certain several sensors detection in section sometime.Each time period canned data has: target, sensor, detectable time period zero-time, detectable concluding time time period.As shown in Figure 3, target N
iThe time shaft GT that can be surveyed by sensor
iComprise the some time section, for example the 2nd time period can be by sensor G
1And G
2Survey.
Step 2.3: determine the time shaft that target can be blocked, i.e. the initial solution space of problem.
At first, step 2.1 is obtained target N
i(i=1 ..., N) can be by weapon attacking time shaft MT
i, all time points on the extraction time axle obtain the most original weapon attacking time point information, sort according to time point.
Secondly, the target N that step 2.2 is obtained
i(i=1 ..., be detected time shaft GT N)
i, all time points on the extraction time axle obtain the most original sensor detection time dot information, sort according to time point.
The 3rd, two orderly time point sequences that above two steps are obtained merge arrangement, obtain the new orderly time point sequence that comprises weapon attacking and sensor detection information.The information of identical time point is merged, and the information on the different time points is by judge adding the information that the weapon attacking that lacks accordingly or sensor are surveyed.What obtained this moment is still original object time dot information.
The 4th, go on foot the target N that obtains by the 3rd
i(i=1 ..., all time point informations N) obtain target N
i(i=1 ..., N) initial time slice and information thereof forms target N
iBe blocked time shaft T
i, time shaft T
iMay be discontinuous, it comprises target N
iCan be by certain in section sometime several weapon attackings and adoptable sensor is surveyed in this time period information.The be blocked time shaft of all targets has constituted initial solution space A
1
As shown in Figure 4, but information on the detectable time shaft of target-sensor of target-weapon attack time axle of Fig. 2 and Fig. 3 is put in order according to time sequencing, obtain to be blocked time shaft.
In the inventive method, use the mode of binary digit coding to record in the solution space certain time period and go up assailable weapon and detectable sensor information, the coding binary of record weapon information M position altogether represents weapon M from right to left successively in each time period
1..., M
MIf corresponding position is 1, represent that then the weapon of this binary digit correspondence can attack target in the section between can be at this moment; Be that 0 expression can not be attacked.Same, the coding binary of record sensor information G position altogether in each time period, representative sensor G successively from right to left
1..., G
GIf corresponding position is 1, represent that then this binary digit corresponding sensor can survey target in the section between can be at this moment, be 0 and represent that corresponding sensor can not survey target.
Step 3: dwindle the initial solution space, comprise step 3.1 and step 3.2.
Step 3.1 is dwindled solution space according to weapon-sensor interconnection constraint.
In the initial solution space, travel through all targets, for certain target N
i, search whether corresponding interconnection constraint is arranged in that weapon-sensor is intrafascicular approximately, if the interconnection constraint of weapon-sensor is arranged, then at solution space A
1In find this target N
iCorresponding solution---time shaft T
i, establish weapon M
jWith sensor G
kThere is interconnection constraint, travels through all time periods on this time shaft, to can be by weapon M
jCertain time period of attacking, judge whether this time period satisfy particular community sensor G
kRequirement, if do not satisfy, then can be directly with weapon M in this time period
jTo target N
iThe information of attacking is rejected, if satisfy particular community sensor G
kRequirement, next time period of sequential search then is if the next time period can be by weapon M
jAttack, also satisfy particular community sensor G
kRequirement, then again the order search downwards, can not be by M up to finding
jAttack or do not satisfy particular community sensor G
kThe time period that requires.All that this moment, judgement found satisfy particular community sensor G
kThe time period T that requires
I.x1～T
I.x2Whether cover weapon M
jWith sensor G
kSection correlation time, if can not cover section correlation time, then with time shaft T
iOn section T continuous time
I.x1～T
I.x2Middle weapon M
jTo target N
iThe information of attacking is rejected.Idiographic flow as shown in Figure 5.
After top operation, may comprise in the solution space can not be by the time period of any weapon attacking, and these belong to invalid solution space, therefore, also needs and will can not be rejected by the time period of any weapon attacking in the solution space.Further dwindle solution space.
Solution space after note is dwindled is A
2
Below in conjunction with Fig. 5 and Fig. 6, the realization of this step is described with an example.
Target N
iBe blocked time shaft T
iOn time period T
I.1, T
I.2, T
I.3, T
I.4, T
I.5Respectively can be by weapon M
1, sensor G
1, weapon M
1And M
2, sensor G
1, weapon M
2, sensor G
1And G
2, weapon M
3, sensor G
2, weapon M
1, sensor G
3Attack or detect.Suppose that all interconnection constraints are as follows: attribute is C
M1Weapon need be C with 1 attribute
G1The sensor association, and attribute is C
M1Weapon have only M
1, attribute is C
G1Sensor have only G
1, then this moment is associated as weapon M
1Need with sensor G
1Be associated, same, M
3The weapon of corresponding attribute need with 1 G
2The sensor of corresponding attribute is associated.Weapon M
1With sensor G
1Section correlation time, and weapon M
3With sensor G
2Correlation time section as shown in Figure 6.Put down in writing in the temporal information of the association that section is imported in step 1 correlation time.
Interconnection constraint is got in circulation successively, and that circulation for the first time obtains is M
1With G
1Interconnection constraint, obtain in the top time period one by circulation again, be designated as T
I.x(x ∈ 1,2,3,4,5}), parameter TimeSlice is set
1Be used for recording the detectable time period of sensor, it is as follows to carry out step:
A. judge this time period T
I.xCan be by weapon M
1Attack, if cannot be attacked, then order is got T
I.xNext time period T
I. (x+1), proceed this judgement; If can be attacked, then check this time period corresponding sensor detection information, carry out b;
B. judge G
1Can survey it, if can not, then to T
I.xCarry out c, if can survey, then to T
I.xCarry out d;
C. should interior M of time period
1Can from solution space, reject the information that current goal is attacked, judge whether all time periods on the be blocked time shaft of current goal have all traveled through, if do not have, continue to get next time period T
I. (x+1), to T
I. (x+1)Carry out a;
D. note this time period T
I.xTemporal information, TimeSlice is added to
1In, from then on the position begins to get next time period T
I. (x+1), to T
I. (x+1)Carry out e;
E. can the judgement time fragment by weapon M
1Attack, if cannot be attacked, then carry out g, if can be attacked, then check this time period corresponding sensor detection information execution f;
F. judge last G of this time period
1Can be to surveying, if can not, g then carried out.If can survey, then carry out d;
G. judge TimeSlice
1Whether comprise weapon M
1With sensor G
1Section correlation time, if can not, with TimeSlice
1In namely by weapon M
1Attacking again can be by sensor G
1Each time period of surveying is carried out c; Otherwise, illustrate that the detection time of the sensor with interconnection constraint can cover correlation time, satisfy interconnection constraint, keep this time frag info, need not do any processing, judge then whether all time periods on the be blocked time shaft of current goal have all traveled through, if do not have, order is got T
I.xThe next time period, change a then and carry out.
Finished the processing of dwindling solution space at an interconnection constraint to this, desirable next interconnection constraint is similarly handled, and dwindles solution space.Among Fig. 6, at M
1With G
1Interconnection constraint, at first get time period T
I.1, carry out a, b, d is with T
I.1The temporal information TimeSlice that is added to
1In, get time period T then
I.2Carry out e, f, d is with T
I.2The temporal information TimeSlice that is added to
1In; Continue to get time period T
I.3, carry out e, g; Continue to get time period T
I.4, carry out a; Continue to get time period T
I.5, carry out a, b, c is at time shaft T
iLast deletion time period T
I.5Information.At M
3With G
2Interconnection constraint, time period T
I.1～T
I.3All can not be by weapon M
3Attack time period T
I.4Can be by weapon M
3Attack, and can be by M
3Related sensor G
2Detect, then T
I.4The temporal information TimeSlice that is added to
1In; Because T
I.4Do not cover M
3With G
2Section correlation time, at time shaft T
iLast deletion time period T
I.4Information.
After top operation, may comprise in the solution space can not be by the time period of any weapon attacking, and these belong to invalid solution space, as being labeled as the time period of none among Fig. 6, therefore, also need and to be rejected by the time period of any weapon attacking in the solution space.Further dwindle solution space.Shown in Figure 6, the be blocked time shaft of the target Ni after step 3.1 is dwindled is by T
I.1～T
I.3Form.
Solution space after note is dwindled is A
2
Step 3.2: dwindle solution space for specific objective arranges the intercept point constraint.
Because have constraint: those priority of resource allocation are not worth S
iMore than or equal to given priority level value S
GivenTarget, need to arrange an intercept point at least.
The execution flow process of this step travels through all targets as shown in Figure 7, checks target N
iPriority of resource allocation be not worth S
i, if S
i〉=S
Given, then carry out following first to fourth operation:
The first, calculate average kill probability.To target N
iCan be blocked time shaft T
iOn all time period T
I.x(x=1,2 ...), calculate in each time period weapon to the average kill probability of target
The kill probability of all weapons of this target being attacked in=this time period and/all weapon numbers of this target being attacked in this time period;
The second, the selected time period that intercept point is set.Elect section sometime as the time period that intercept point need be set, time period T
I.xWith
Probability be selected, namely with selected this time period of the mode of roulette.The starting point of selecteed time period is set to intercept point;
The 3rd, distribute the ammunition number.Weapon M on this intercept point
l, l ∈ 1 ..., M} is to this target N
iThe ammunition number that distributes is B
l* (S
i/ Σ S
i) * (qp), wherein p is M
lTo N
iBut the length of all attack time sections, q is the length of the time period of current selection, B
lExpression weapon M
lAmmunition, Σ S
iExpression is to the priority of resource allocation summation of all targets.If this time period has a plurality of weapons can be to target N
iAttack, then begin to carry out the distribution of ammunition number from the high weapon of kill probability, the distribution ammunition number of gained rounds up, and avoids occurring distributing the problem of 0 ammunition.
The 4th, distribute sensor.After weapon and ammunition distribute, need to distribute sensor to target N
iSurvey.If there is the interconnection constraint of weapon and particular sensor, be target N according to interconnection constraint then
iDistribute sensor and detection time, if the onrelevant constraint is target N according to nearby principle then
iAssigning sensor, is target N according to minimum principle
iThe detection time that distributes sensor, but the detection time of specified sensor is selected time period length.For detection time, there is such processing herein: when distributing the sensor detection time, the detection of this sensor is joined in the detection time transfer time, and the selected time period is that (time1～time2), the detection time that then distributes sensor is (time1～time2+T
d_ G
k).For example, distributed sensor G
kSurveyed at the 5th second to the 30th second, then the actual detection time that provides can be the 5th second to (30+T
d_ G
k) survey second.The processing that distributes the sensor detection time has been simplified in such processing, has improved and has distributed the efficient of sensor, and guaranteed that sensor is to surveying the needs of transfer time.
The 5th, upgrade resource status.After having traveled through all targets, change has all taken place in weapon and residue ammunition, sensor and the detectable destination number of residue thereof, needs to upgrade the state of corresponding weapon and sensor, and upgrades remaining available resource.
The 6th, dwindle solution space.To distribute the time period of intercept point from solution space, to reject; Checking the surplus resources of weapon and sensor, is zero weapon if there is the residue ammunition, and the information that this weapon in the time period of solution space is attacked target is rejected; Through after the above step, with not rejected by the time period of any weapon attacking in the solution space, dwindle solution space.
Solution space after note is dwindled is A
3
Step 4: to the solution space reconstruct of encoding.More than each step all be to come time shaft is operated from the angle of target, in order to optimize conveniently, need the solution space reconstruct of encoding namely be operated time shaft from the angle of weapon.Step 4 comprises three sub-steps: step 4.1, reconstruct solution space; Step 4.2 is divided the solution space of reconstruct; Step 4.3 is encoded to solution space.For follow-up optimization is prepared.
Step 4.1: reconstruct solution space.
To solution space A
3The time shaft that can tackle according to weapon is reconstructed.In conjunction with Fig. 8, reconstructing method is explained as follows:
Step 4.1.1 obtains all time periods that weapon can be attacked.Travel through all weapons, for weapon M
j(j=1 ..., M), at solution space A
3In obtain all and comprise M
jTime period, form the initial solution space after the reconstruct; For example among Fig. 8, for M
1, find this weapon to target N
1And N
2The assailable time period.
Step 4.1.2, the fractionation of the initial solution space after the reconstruct being carried out the time period is merged.Need the branch situation to discuss herein, these situations comprise: two time slices overlap fully, and need merge information this moment, and only keep a time slice; Next time slice comprises a time slice, and need to replenish the information of a last time slice this moment, changes the zero-time of next time slice; A last time slice comprises next time slice, needs this moment a last time slice is split into three little time slices, and replenishes weapon and sensor information respectively; Next time slice is the latter half of a last time slice, and need the concluding time of the last time slice of change this moment, replenishes the information of next time slice; The part of occuring simultaneously is the forward part of next time slice, and need split into three this moment with two time slices, and replenishes information separately respectively; Two time slices do not have common factor, and do not need the information of time slice is changed this moment.Form each weapon M
jBut commit time axle TM
j, this time shaft may be discontinuous, comprises weapon M on this time shaft
jTarget and the spendable sensor information that can hit in section sometime, j=1 ..., M.
Step 4.1.3 obtains the solution space of reconstruct.Travel through all weapons, each weapon time corresponding axle is arranged according to time sequencing, obtain the solution space of reconstruct.Solution space after the note reconstruct is A
4
Step 4.2: divide solution space.
At first, calculate minimum interception and need use the time.Minimum interception needs with T observing time that comprises reservation in the time
d, and T launch time of weapon
fBut with attack time T
lBetween linear relationship.As T launch time
fBut with attack time T
lBetween during for the simplest linear relationship, minimum interception needs can be expressed as with the time: minimum interception needs with time=T
d+ | T
l-T
f|.
Secondly, to weapon M
j(j=1 ..., M), with time shaft TM
jOn each time period need divide with the time by minimum interception, and will need reject in solution space with the time period of time less than the minimum interception.
At last, computing time axle TM
jOn the minimum interception that is cut into of live part need add up to ML with the time period
jIndividual.
Step 4.3: solution space coding.
Travel through all weapons, for weapon M
j(j=1 ..., M):
At first, obtain M
jTime shaft TM
jOn the time period sum, be designated as ML
j
Secondly, with TM
jThe time period of going up all interceptings is mapped to ML
jThe integer point set that individual real number is formed 1,2 ..., ML
jOn;
At last, get interval (0, ML
j], with this interval as weapon M
jAmmunition can distribute the interval.
Step 5: utilize differential evolution algorithm to seek optimal solution.
Step 5.1: selected variable and the objective function optimized.
Selected weapon M
jEach ammunition can distribute position on the interval for optimizing variable at it.Then optimize the total W=Σ B of variable
j(j=1,2 ..., M) individual.Ammunition
(s=1,2 ..., B
j) the interval distributed at (0, ML
j] on, allocation result is a real number, and this real number is rounded up, obtain point set 1,2 ..., ML
jOn sequence number.Herein
(s=1,2 ..., B
j) in s represent weapon M
jAll ammunitions (from 1 to B
j), be to weapon M
jAll ammunitions identify.
Optimizing variable is weapon M
j(j=1 ..., each ammunition M)
(s=1,2 ..., B
j; J=1,2 ..., M) can distribute the position on the interval to be the optimization variable at it.
Objective function is:
Wherein: m
iBe target N
iThe quantity of the intercept point that distributes.λ
iBe scale-up factor, determine according to actual conditions.Allocation result to certain target intercept point is total a kind weapon j
1..., j
aIt is tackled, and the kill probability value of every kind of weapon is
...,
The ammunition quantity of every kind of weapon distribution is
...,
Step 5.2: produce initial population according to certain principle.
If make x
e(t) be that t is individual for e in the population, then
x
e(t)=(x
el(t),x
e2(t),...,x
eW(t)),e＝1,2,......,NP；t＝1,2,......,t
max
Wherein, x
e(t) corresponding one of each component is optimized variable, and W constitutes individual chromosome number, namely optimizes the number of variable; NP is population scale; t
MaxIt is maximum evolutionary generation.
Produce NP individuality at random according to the span of optimizing variable.
Each individuality in the population produces by the following method:
Obtain weapon M successively according to weapon kill probability order from high to low
j, to weapon M
jAll available ammunitions
(s=1,2 ..., B
j) arrive interval (0, ML by even probability assignments
j] on.
For a certain segment, if weapon can zeal in this segment, then use the mode of roulette, with probability S
i/ Σ S
iSome in selected these targets distributed the ammunition in this segment on the selected target unitedly.
With ammunition by the interval of its distribution and Target Assignment on the starting point of its corresponding commit time section, whether there is resource to use conflict (sensor resource uses constraint) to the individuality check that generates, if conflict is arranged, even distribute by this scheme, target number that this time period inner sensor can be surveyed has simultaneously surpassed the quantity of the target that sensor can survey simultaneously, then regenerates.
Add up the intercept point number of each target, calculate each individual fitness value according to objective function.
Step 5.3: produce test vector.
From current t for selecting 3 individual x the population at random
P1(t), x
P2(t) and x
P3(t), then t+1 optimizes the corresponding test vector h of variable for r of e population individuality of population
Er(t+1) be:
h
er(t+1)＝x
p1r(t)+F*(x
p2r(t)-x
p3r(t))，e≠p1≠p2≠p3
Wherein,
x
P1r(t), x
P2r(t) and x
P3r(t) represent individual x respectively
P1(t), x
P2(t) and x
P3(t) optimize variable for r;
x
P2r(t)-x
P3r(t) be the differentiation vector; F is zoom factor.
During evolution, for the validity that guarantees to separate, must judge whether test vector satisfies boundary condition, if do not satisfy boundary condition, then regenerate test vector with random device, the generation method is identical with the individual production method of initial population in the step 5.2.Boundary condition refers to the distribution interval of ammunition.
Step 5.4: produce filial generation.
Use the t+1 of crossover operator generation in the population, r filial generation v of e population individuality
Er(t+1) be:
Wherein, rand l
ErBe the decimal at random between [0,1], CR is crossover probability, CR ∈ [0,1], and rand (e) is the random integers between [1, N], this Crossover Strategy can be guaranteed x
e(t+1) have one-component and x at least
e(t) respective component is relevant.
Whether the filial generation that generates is carried out Target Assignment and checked each individuality to have resource to use conflict, regenerate with random device if having then, the generation method is identical with the individual production method of initial population in the step 5.2.
Add up the intercept point number of each target, calculate each individual fitness value in the filial generation.
Step 5.5: new population more.With filial generation v
e(t+1) and parent x
e(t) fitness compares, and the t+1 of renewal is for the e in the population individual x
e(t+1) be:
Wherein, f (v
El(t+1) ..., v
En(t+1)) be filial generation v
e(t+1) fitness, f (x
El(t) ..., x
En(t)) be parent x
e(t) fitness.
Then, whether check obtains optimal result.
Whether the individuality of judging fitness optimum in the new population satisfies formula (1), if satisfy, then termination of iterations returns the fitness optimum individual, otherwise, change step 5.3 and carry out.
Judge perhaps whether t+1 has surpassed iteration upper limit t
Max, if surpassed the iteration upper limit, then termination of iterations.Return the fitness optimum individual this moment, otherwise, return step 5.3 and continue to carry out.
Step 5.6: distribute surplus resources.
For the optimum individual of selecting, if surplus resources is arranged, under the situation that does not produce conflict, priority allocation is given the high target of priority, or adopts distribution principle distribution nearby.
Step 5.7: the Gray code result that is optimized.
Allocation result after the optimization that obtains is carried out Gray code, and namely the process with step 4.3 is opposite, determines the intercept point position of Target Assignment and weapon, the sensor resource of distribution.
So far, finished the resource of weapon, sensor and target has been distributed.
Claims (3)
1. the method based on differential evolution algorithm solution weapon-target assignment problem is characterized in that, with the sensor resource adding weapon-target assignment problem of defend equipment, solution specifically comprises the steps:
Step 1: the input variable and the initializing variable that obtain weapon-target assignment problem;
Input variable comprises: target number N, weapon number M, sensor number G; The priority of resource allocation S of each target
i, i=1,2 ..., N; The ammunition quantity B initial or every kind of current weapon has
j, j=1,2 ..., M; The destination number O initial or each current sensor can be surveyed simultaneously
k, k=1,2 ..., G; The belligerent matrix of target-weapon, comprising information has: but but but the weapon of weapon sequence number, target sequence number and corresponding commit time section section launch time intercept point correspondence thereof and target distance from; The detectable matrix of target-sensor, comprising information has: sensor sequence number, target sequence number and corresponding detectable time period, the target in the detectable time period and the distance between sensor thereof; The interconnection constraint of weapon and sensor comprises related weapon and sensor information, related temporal information;
Initializing variable comprises: the property value C of each target
Ni, the property value C of each weapon
Mj, the property value C of each sensor
Gk, j weapon M
jTo i target N
iThe estimated value P of kill probability
Ij, detection T transfer time of each sensor
d_ G
k, wherein, i=1,2 ..., N, j=1,2 ..., M, k=1,2 ..., G; Reserve T observing time
dGiven kill probability value P
GivenGiven priority of resource allocation is not worth S
Given
Step 2: determine big feasible solution space, comprise step 2.1～step 2.3;
Step 2.1: determine that target can be by the time shaft of weapon attacking, specifically: from the belligerent matrix of target-weapon, find i target N
iCan be by weapon M
jSection MT effective time that attacks
Ij, with MT
IjSplice in chronological order, form target N
iCan be by the time shaft MT of weapon attacking
i, time shaft MT
iOn each time period canned data have: but but target, weapon attack time section zero-time attack time section concluding time; Wherein, i=1,2 ..., N, j=1,2 ..., M;
Step 2.2: determine the time shaft that target can be surveyed by sensor, specifically: from the detectable matrix of sensor-target, find out N
iCan be by sensor G
kSection GT effective time that surveys
Ik, with GT
IkSplice according to time sequencing, form target N
iBe detected time shaft GT
i, time shaft GT
iOn each time period canned data have: target, sensor, detectable time period zero-time, detectable concluding time time period; Wherein, i=1,2 ..., N, k=1,2 ..., G;
Step 2.3: with target N
iCan be by weapon attacking time shaft MT
iWith can be by sensor detection time axle GT
iPut in order according to time sequencing, will have overlapping part to merge on the time shaft, obtain target N
iBe blocked time shaft T
iThe N of a N target correspondence time shaft has constituted initial solution space A
1Wherein, i=1,2 ..., N;
Use the mode of binary digit coding to record weapon and the sensor information of each target in each time period; The coding binary figure place of record weapon information is identical with the number of weapon in each time period, from right to left, each represents the weapon that the weapon sequence number is serial number, every value is 1 or 0, the corresponding weapon of 1 expression can be attacked target in this time period, and the corresponding weapon of 0 expression can not be attacked target in this time period.The coding binary figure place of record sensor information is identical with number of sensors in each time period, from right to left, each representative sensor sequence number is the sensor of serial number, every value is 1 or 0,1 expression respective sensor can be surveyed target in this time period, and 0 expression respective sensor can not be surveyed target in this time period;
Step 3: dwindle the initial solution space, comprise step 3.1～step 3.2;
Step 3.1: the be blocked time shaft that travels through the target of the interconnection constraint that weapon-sensor is arranged, reject the weapon attacking information of the interconnection constraint of not satisfying weapon-sensor, to can not be rejected the solution space A that obtains dwindling by the time period of any weapon attacking in the solution space then
2
Step 3.2: the traversal target is priority of resource allocation S
iMore than or equal to given priority level value S
GivenTarget, an intercept point is set at least; After having traveled through all targets, the more state of modern weapons and sensor, and surplus resources; Then, will distributing the time period of intercept point to reject from solution space, be that the attack information of zero weapon is rejected in solution space with the residue ammunition; To can not be rejected the solution space A that obtains dwindling by the time period of any weapon attacking in the solution space at last
3
Step 4: to the solution space reconstruct of encoding, comprise step 4.1～step 4.3;
Step 4.1: to solution space A
3The time shaft that can tackle according to weapon is reconstructed, and obtains the solution space A after the reconstruct
4To weapon M
j, at solution space A
3The middle traversal time period, obtain all and contain M
jThe time period of attack information, all time periods that obtain are spliced according to time sequencing, form weapon M
jBut commit time axle TM
j, j=1,2 ..., M;
Step 4.2: with weapon M
jBut commit time axle TM
jOn each time period need divide with the time by minimum interception, and will need to reject final time shaft TM with the time period of time less than the minimum interception
jBy ML
jIndividual minimum interception needs to form with the time period, j=1, and 2 ..., M; Described minimum interception needs to comprise with the time T observing time of reservation
d, and T launch time of weapon
fBut with attack time T
lBetween linear relationship;
Step 4.3: with weapon M
jBut commit time axle TM
jOn ML
jThe individual time period is mapped to ML
jThe real number point set that individual real number is formed 1,2 ..., ML
jOn; Get interval (0, ML
j] as weapon M
jAmmunition can distribute the interval; J=1,2 ..., M;
Step 5: utilize differential evolution algorithm to seek optimal solution, comprise step 5.1～step 5.7;
Step 5.1: selected weapon M
jEach ammunition
Can distribute the position on the interval to be the optimization variable at it, j=1,2 ..., M, s=1,2 ..., B
jThe objective definition function f is:
Wherein, m
iBe target N
iThe quantity of the intercept point that distributes; λ
iBe scale-up factor;
j
u∈ { j
1..., j
aExpression: to target N
iThe allocation result of intercept point is total a kind weapon j
1..., j
aIt is tackled, and the kill probability value of every kind of weapon is
...,
The ammunition quantity of every kind of weapon distribution is
...,
Step 5.2: produce initial population;
T is for the e in the population individual x
e(t) be expressed as:
x
e(t)=(x
e1(t),x
e2(t),...,x
eW(t)),e＝1,2,......,NP；t＝1,2,......,t
max
Wherein, x
e(t) corresponding one of each component is optimized variable, and W constitutes individual chromosome number, and NP is population scale, t
MaxIt is maximum evolutionary generation;
Each individuality in the population produces by the following method: according to weapon kill probability order from high to low, to weapon M
jAll available ammunitions
(s=1,2 ..., B
j) arrive interval (0, ML by even probability assignments
j] on; If weapon can be attacked the target more than 2 in a certain segment, with probability S
i/ Σ S
iSelected one of them target is distributed the ammunition in this segment on the selected target unitedly; With ammunition by the interval of its distribution and Target Assignment on the starting point of corresponding commit time section, whether have resource to use conflict to the individuality check that generates, if there is conflict then to regenerate;
Add up the intercept point number of each target, calculate each individual fitness value according to objective function;
Step 5.3: produce test vector, specifically: from current t for selecting 3 individual x the population at random
P1(t), x
P2(t) and x
P3(t), then t+1 optimizes the corresponding test vector h of variable for r of e population individuality of population
Er(t+1) be:
h
er(t+1)＝x
p1r(t)+F*(x
p2r(t)-x
p3r(t))，e≠p1≠p2≠p3
Wherein, x
P1r(t), x
P2r(t) and x
P3r(t) represent individual x respectively
P1(t), x
P2(t) and x
P3(t) optimize variable for r; x
P2r(t)-x
P3r(t) be the differentiation vector; F is zoom factor;
If the test vector that produces is not in the distribution interval of ammunition, then the individual production method according to population in the step 5.2 regenerates test vector;
Step 5.4: produce filial generation, r filial generation v of e population individuality
Er(t+1) be:
Wherein, rand l
ErBe the decimal at random between [0,1], CR is crossover probability, and CR ∈ [0,1], rand (e) are the random integers between [1, N];
Whether the filial generation that generates is carried out Target Assignment and checked each individuality to have resource to use conflict, if there is conflict then to regenerate according to the individual production method of population in the step 5.2;
Add up the intercept point number of each target, calculate each individual fitness value in the filial generation according to objective function;
Step 5.5: new population more: upgrade t+1 for the e in the population individual x
e(t+1) be:
F (v
El(t+1) ..., v
En(t+1)) be filial generation v
e(t+1) fitness, f (x
El(t) ..., x
En(t)) be parent x
e(t) fitness;
Whether the individuality of judging fitness optimum in the new population satisfies formula:
If satisfy, termination of iterations returns the fitness optimum individual, otherwise, change step 5.3 and carry out;
Judge perhaps whether t+1 has surpassed iteration upper limit t
Max, if surpass, then termination of iterations returns the fitness optimum individual, otherwise, change step 5.3 and carry out;
Step 5.6: for the optimum individual of selecting, if surplus resources is arranged, under the situation that does not produce conflict, priority allocation is given the high target of priority, or adopts distribution principle distribution nearby;
Step 5.7: the allocation result after the optimization that will obtain is carried out Gray code, determines the intercept point position of Target Assignment and weapon, the sensor resource of distribution.
2. the method that solves weapon-target assignment problem based on differential evolution algorithm according to claim 1, it is characterized in that, the weapon attacking information of the interconnection constraint of weapon-sensor is not satisfied in rejecting described in the step 3.1, and the specific implementation method is: to the target N of interconnection constraint that weapon-sensor is arranged
i, at the interconnection constraint of every weapon-sensor, carry out following operation:
If weapon M
jWith sensor G
kThere is interconnection constraint, traversal target N
iBe blocked time shaft T
iOn all time periods, to can be by weapon M
jCertain time period of attacking, judge whether satisfy sensor G in this time period
kRequirement, if do not satisfy, then at time shaft T
iOn should the time period in weapon M
jTo target N
iThe information of attacking is rejected, if satisfy, order is got the next time period, if can be by weapon M in this time period
jAttack and satisfy sensor G again
kRequirement, then continue to take off a time period, up to can not be by M
jAttack or do not satisfy sensor G
kRequirement; At this moment, judge that all can be by weapon M
jAttack and satisfy sensor G again
kThe time period T of requirement
I.x1～T
I.x2, whether cover weapon M
jWith sensor G
kSection correlation time, if not, then at time shaft T
iGo up time period T
I.x1～T
I.x2Interior weapon M
jTo target N
iThe information of attacking is rejected.
3. the method based on differential evolution algorithm solution weapon-target assignment problem according to claim 1 is characterized in that described step 3.2 specific implementation method is: travel through all targets, check target N
iPriority of resource allocation be not worth S
i, if S
i〉=S
Given, the operation of (1) and (2) below then carrying out:
(1) distributes weapon and ammunition: to target N
iCan be blocked time shaft T
iOn all time period T
I.x(x=1,2 ...), calculate in each time period weapon to target N
iAverage kill probability
Then with probability
Select time section T
I.xThe time period of intercept point is set as needs; The starting point of the time period of selecting is set to intercept point, weapon M on this intercept point
l, l ∈ 1 ..., the target N of M}
iThe ammunition number that distributes is B
l* (S
i/ Σ S
i) * (qp), wherein, p is M
lTo target N
iBut the length of all attack time sections, q is the length of the time period of current selection, B
lExpression weapon M
lAmmunition; If there is the plural weapon can be to target N in the selecteed time period
iAttack, begin to carry out the distribution of ammunition number from the high weapon of kill probability, the distribution ammunition number of gained rounds up;
(2) distribute sensor; If there is the interconnection constraint of weapon and particular sensor, be target N according to interconnection constraint then
iDistribute sensor and detection time, if the onrelevant constraint is target N according to nearby principle then
iAssign sensor; If the selected time period is that (time1～time2), the detection time that then distributes sensor is (time1～time2+T
d_ G
k).
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