CN103336885B - A kind of method solving Weapon-Target Assignment Problem based on differential evolution algorithm - Google Patents

Abstract

The present invention a kind ofly solves the method for Weapon-Target Assignment Problem based on differential evolution algorithm, belongs to Computer Simulation and method optimizes field.On the basis of traditional weapon-target assignment problem, this method with the addition of the detection of sensor to target, and the factors such as the detection transfer time of sensor, the interconnection constraint of target number, sensor and weapon that can simultaneously detect, the reserved observing time of weapon are considered in problem, first determine larger solution space, then according to the constraint of weapon-sensors association, intercept point constraint be set for specific objective reduce solution space; Carry out coding reconstruct to the solution space after reducing, the position can distributed on interval at it by each ammunition of weapon is optimized variable, utilizes differential evolution algorithm to find optimal solution.The present invention, closer to the Weapon-Target Assignment Problem of actual conditions, reduces optimization complicacy, improves optimization efficiency, decreases solution space and taken up space, and operates flexibly more convenient.

Description

Method for solving weapon-target allocation problem based on differential evolution algorithm

Technical Field

The invention belongs to the field of computer simulation and method optimization, and relates to a method for solving a weapon-target distribution problem based on a differential evolution algorithm.

Background

The weapon-target distribution problem is an important subject in combat decision, namely how to reasonably distribute the force of our party to attack the force of the enemy party so as to achieve the optimal combat effect, belongs to a complete problem of NP (Non-deterministic multinomial, a Non-deterministic problem of polynomial complexity), and currently, an effective deterministic solution method is not available. The main purpose of the research is to rapidly and effectively solve the problem of large-scale weapon-target allocation so as to improve the automation level of battlefield command control, namely aiming at a plurality of threat targets, a defender can timely and effectively allocate defense resources, effectively eliminate enemy target threats and minimize the loss of the defender. In general, the weapon-target allocation problem relates to the force resources which are limited to the weapons and targets, and the sensors as the detection resources are not in the force resources.

Solutions to the weapon-target assignment problem have experienced improvements from traditional algorithms to intelligent optimization algorithms, developed to date from the fifties of the 20 th century. The eighties are mainly limited to traditional algorithms such as a hidden enumeration method, a dynamic programming method and the like before, the algorithms are simple, but are complicated to implement, and especially when the target number is increased, the convergence speed is very low. Since the eighties, some optimization algorithms, such as artificial neural networks, chaotic and heuristic search algorithms, and the like, provide new ideas and means for solving complex problems.

The differential evolution algorithm is an optimization algorithm based on a group intelligent theory, and can realize the solution of an optimization problem through cooperation and competition among individuals in a group. Compared with an evolutionary algorithm, the differential evolutionary algorithm reserves a population-based global search strategy, adopts real number coding, simple editing operation based on difference and a one-to-one competition survival strategy, and reduces the complexity of genetic operation. The differential evolution algorithm has the characteristics of memorizing the optimal solution of an individual and sharing information in a middle group, is essentially a greedy genetic algorithm with the blessing idea based on real number coding, is simple and easy to use, has good robustness and strong global search capability, has multiple strategies for selection, and can adjust the search range and the convergence speed as required.

Disclosure of Invention

The invention aims to arrange a sensor in the force resources to be distributed, provides a weapon-target distribution problem which is more in line with the actual situation, and provides a method for solving the weapon-target distribution problem based on a differential evolution algorithm.

The invention relates to a method for solving a weapon-target distribution problem based on a differential evolution algorithm, which adds sensor resources of defense equipment into the weapon-target distribution problem, and the solution specifically comprises the following steps:

the method comprises the following steps: input variables and initialization variables for the weapon-target assignment problem are obtained.

The input variables include: number of targets N, number of weapons M, number of sensors G, resource allocation priority of each target S_iI =1,2, … …, N; the initial or current ammunition quantity B of each weapon_jJ =1,2, … …, M; initial or present number of targets O each sensor can detect simultaneously_kK =1,2, … …, G; the target-weapon engagement matrix comprises the following information: the weapon serial number, the target serial number, the corresponding interceptable time period, the corresponding dischargeable time period and the corresponding distance between the weapon and the target; a detectable matrix of target-sensors containing information of: the method comprises the following steps of (1) detecting a sensor serial number, a target serial number, a detectable time period corresponding to the sensor serial number and a distance between a target and a sensor in the detectable time period; and association constraint of the weapon and the sensor, including associated weapon and sensor information and associated time information.

Initializing variables includes: attribute value C of each object_NiAttribute value C of each weapon_MjAttribute value C of each sensor_GkJth weapon M_jFor the ith target N_iEstimated value P of the killing probability_ijDetection transition time T of each sensor_d_G_kWherein i =1,2, … …, N, j =1,2, … …, M, k =1,2, … …, G; reserved observation time T_d(ii) a Given probability value of killing P_{Given a}(ii) a Given resource allocation priority value S_{Given a}。

Step two: and determining a feasible solution space, comprising the step 2.1 to the step 2.3.

Step 2.1: determining a weapon attack time axis of a target, specifically: finding N from a target-weapon engagement matrix_iCan be weaponized M_jEffective time period of attack MT_ijTo connect MT_ijSplicing according to the time sequence to form a target N_iTime axis MT of weapon attack_iTime axis MT_iThe information stored for each time period of (a) is: a target, a weapon, an attack-capable time period start time, an attack-capable time period end time; wherein i =1,2, … …, N, j =1,2, … …, M.

Step 2.2: determining a time axis of the target which can be detected by the sensor, specifically: finding N from a detectable matrix of sensor-targets_iCan be sensed by sensor G_kThe effective time period GT of the probe_ikTo get GT_ikSplicing according to the time sequence to form a target N_iCan be detected time axis GT_iTime axis GT_iThe information stored for each time period of (a) is: a target, a sensor, a detectable period start time, a detectable period end time; wherein i =1,2, … …, N, k =1,2, … …, G.

Step 2.3: determining an interceptable time axis of the target, specifically: target N_iTime axis MT of weapon attack_iAnd a time axis GT detectable by the sensor_iSorting according to the time sequence, and fusing the overlapped parts on the time axis to obtain a target N_iCan be intercepted time axis T_i. N time axes corresponding to the N targets form an initial solution space A₁。

And recording the information of the offensive weapon and the detectable sensor in each time segment of each target in a binary bit coding mode. The number of coded binary digits recording the weapon information in each time period is the same as the number of the weapons, from right to left, each digit represents the weapon with the serial number of the weapon as the sequence number, the value of each digit is 1 or 0,1 represents that the corresponding weapon can attack the target in the time period, and 0 represents that the corresponding weapon cannot attack the target in the time period. The number of the coded binary bits recording the sensor information in each time period is the same as that of the sensors, from right to left, each bit represents a sensor with the serial number of the sensor as the sequence number, the value of each bit is 1 or 0,1 represents that the corresponding sensor can detect the target in the time period, and 0 represents that the corresponding sensor cannot detect the target in the time period.

Step three: the initial solution space is reduced, including step 3.1 and step 3.2.

Step 3.1: the solution space is narrowed according to the weapon-sensor association constraints. Eliminating weapon attack information which does not meet association constraint of weapon-sensor, and eliminating time slot which can not be attacked by any weapon in solution space to obtain reduced solution space A₂。

Eliminating time periods which cannot be attacked by any weapon in the solution space, specifically: target N with weapon-sensor association constraint_iFor each weapon-sensor association constraint, the following operations are performed:

setting up weapons M_jAnd a sensor G_kTraversing the target N in the presence of association constraints_iCan be intercepted time axis T_iAll time periods of (c) can be weaponized M_jJudging whether the sensor G is satisfied in a certain time period of the attack_kIf not, on the time axis T_iThe weapon M in the time period_jFor the target N_iRemoving the attacking information, if the attacking information is satisfied, sequentially taking a time period, and if the attacking information is satisfied, enabling the weapon M to be used in the time period_jAttack and satisfaction of sensor G_kUntil it can not be M, then continue to take down a period of time_jAttack or not satisfy sensor G_kThe requirements of (1); at this time, all the weapons M capable of being weaponized are judged_jAttack and satisfaction of sensor G_kIs required for a time period T_i.x1～T_i.x2Whether or not to cover the weapon M_jAnd a sensor G_kIf not, on the time axis T_iWill last time period T_i.x1～T_i.x2Internal weapon M_jFor the target N_iAnd (5) removing the attacked information.

Step 3.2: setting interception point constraint for specific targetA small solution space. Traversing the target to assign a priority S to the resource_iGreater than or equal to a given priority value S_{Given a}At least one interception point is arranged; after all the targets are traversed, updating the states of weapons and sensors and the residual resources; then, removing the time period distributed with the interception point from the solution space, and removing attack information of the weapon with zero residual ammunition amount from the solution space; finally, the time period which can not be attacked by any weapon in the solution space is removed to obtain a reduced solution space A₃。

If the target N_iResource allocation priority value S_i≥S_{Given a}Then, the following operations (1) and (2) are performed:

(1) weapons and munitions are dispensed. For the target N_iInterceptable time axis T_iAll time periods T of_i.xCalculating the weapon pair target N in each time period_iAverage probability of killingx is a positive integer, and x is 1,2 … …, which represents the x-th time segment on the interceptable time axis. Selecting a certain time period as the time period needing to set an interception point, wherein the time period T is_i.xTo be provided withIs selected. Setting the starting point of the selected time segment as an interception point on which the weapon M is located_lL ∈ {1,2, … …, M } vs. target N_iThe number of ammunition dispensed is B_l*(S_i/ΣS_i) (qp), wherein p is M_lTo N_iQ is the length of the current time period. If more than two weapons are capable of targeting target N during the selected time period_iAnd (4) carrying out attack, starting from the weapon with high killing probability, distributing the ammunition number, and rounding up the obtained distributed ammunition number.

(2) A sensor is dispensed. If there is an association constraint of a weapon with a particular sensor, then the association is followedConstraining to a target N_iAllocating sensors and detection time, and taking the sensor and detection time as a target N according to the principle of proximity if no association constraint exists_iAssigning a sensor; if the selected time period is (time 1-time 2), the detection time of the distributed sensor is (time 1-time 2+ T)_d_G_k)。

Step four: and carrying out coding reconstruction on the solution space, wherein the coding reconstruction comprises a step 4.1-a step 4.3.

Step 4.1: a solution space is reconstructed. For solution space A₃Reconstructing according to the time axis of weapon interception to obtain a reconstructed solution space A₄. To weapon M_jIn solution space A₃In the middle traversal time period, all the M-containing components are obtained_jTime periods of attack information are spliced according to time sequence to form a weapon M_jOf an interceptable time axis TM_j。j＝1,2,……,M。

Step 4.2: and partitioning a solution space. Will weapon M_jOf an interceptable time axis TM_jEach time segment is divided according to the minimum interception required time, the time segments smaller than the minimum interception required time are removed, and a final time axis TM is set_jIs composed of ML_jThe minimum interception needs to be made up of time segments, j =1,2, … …, M. The minimum required interception time comprises reserved observation time T_dAnd the firing time T of the weapon_fAnd attack time T_lA linear relationship therebetween.

Step 4.3: and (5) decoding the space coding. To weapon M_jWill TM_jML on_jMapping of individual time periods to ML_jReal number point set {1,2, … …, ML) composed of real numbers_jOn. Taking intervals (0, ML)_j]As weapons M_jThe dispensable interval of ammunition. j =1,2, … …, M; .

Step five: and finding an optimal solution by using a differential evolution algorithm, wherein the optimal solution comprises a step 5.1 and a step 5.7.

Step 5.1: an optimization variable and an objective function are selected. Selected weapon M_jEach ammunition ofThe position in the assignable range is the optimization variable, s is 1,2, … …, B_j;j＝1,2,……,M。

Defining the objective function f as:

wherein: m is_iIs a target N_iNumber of assigned interception points. Lambda [ alpha ]_iIs a proportionality coefficient and is determined according to actual conditions.j_u∈{j₁,...,j_aDenotes: the result of the distribution to a certain target interception point is that a weapons j are shared₁,......,j_aIntercepting the weapon, wherein the probability value of killing of each weapon is......,Each weapon dispenses as many ammunition as......,

Step 5.2: an initial population is generated.

The e-th individual x in the t-th generation population_e(t) is 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 is_e(t) each component corresponds to an optimization variable, W is the number of chromosomes constituting an individual, i.e. the number of optimization variables; NP is the population size; t is t_maxIs the maximum evolutionary algebra.

And randomly generating NP individuals according to the value range of the optimized variable. Each individual in the population was generated as follows:

according to the sequence of the weapon killing probability from high to low, the weapons M are treated_jAll available ammunition(s＝1,2,……,B_j) Is distributed to intervals (0, ML) with uniform probability_j]The above. If the weapon can attack more than 2 targets in a certain section, using roulette mode and probability S_i/ΣS_iOne of the targets is selected, and the ammunition in the interval section is uniformly distributed to the selected target. Distributing ammunition to the starting point of the corresponding interception time period according to the distribution interval and the target of ammunition, checking whether resource use conflict (sensor resource use constraint) exists in the generated individuals, and regenerating if the conflict exists.

And counting the number of interception points of each target, and calculating the fitness value of each individual according to the target function.

Step 5.3: generating test vectors

Randomly selecting 3 individuals x from the current t generation population_p1(t)，x_p2(t) and x_p3(t), the test vector h corresponding to the r-th optimization variable of the e-th population individual of the t + 1-th generation population_er(t +1) is:

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) represents the individuals x, respectively_p1(t)，x_p2(t) and x_p3(t) the r-th optimization variable;

x_p2r(t)-x_p3r(t) is a differentiation vector; f is the scaling factor.

If the test vector is not in the distribution interval of ammunition, the test vector is regenerated according to the individual generation method of the population in step 5.2.

Step 5.4: generating offspring, the r-th offspring v of the e-th population_er(t +1) is:

wherein, randl_erIs [0,1 ]]Random decimal between, CR is the crossover probability, CR ∈ [0,1]And rand (e) is in [1, N ]]Random integer between.

And (5) performing target distribution on the generated filial generation, checking whether each individual has resource use conflict, and if so, regenerating according to the individual generation method of the population in the step 5.2.

And counting the number of interception points of each target, and calculating the fitness value of each individual in the filial generation according to the target function.

Step 5.5: and updating the population. Updated No. e individuals x in the t +1 th generation population_e(t +1) is:

$x_e(t+1)=\left\{\begin{array}{cc}{v}_e(t+1),& f(v_{\mathrm{el}}(t+1),\&CenterDot;\&CenterDot;\&CenterDot;,v_{\mathrm{en}}(t+1))<f(x_{\mathrm{el}}\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;,x_{\mathrm{en}}\left(t\right))\\ x_e\left(t\right),& f(v_{\mathrm{el}}(t+1),\&CenterDot;\&CenterDot;\&CenterDot;,v_{\mathrm{en}}(t+1))\&GreaterEqual;f(x_{\mathrm{el}}\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;,x_{\mathrm{en}}\left(t\right))\end{array}\right.$

wherein, f (v)_el(t+1)，...，v_en(t +1)) is the descendant v_eFitness of (t +1), f (x)_e1(t)，...，x_en(t)) is the parent x_e(t) fitness.

Judging whether the individuals with the optimal fitness in the new population meet the formula:if yes, terminating iteration, and returning to the individual with the optimal fitness, otherwise, executing the step 5.3.

Or judging whether t +1 exceeds an iteration upper limit t_maxIf yes, terminating iteration, and returning to the individual with the optimal fitness, otherwise, continuing to execute the step 5.3.

Step 5.6: the remaining resources are allocated.

And for the selected optimal individual, if the selected optimal individual has residual resources, preferentially allocating the selected optimal individual to a target with high priority or allocating the selected optimal individual by adopting a near allocation principle under the condition of not generating conflict.

Step 5.7: and performing inverse coding on the obtained optimized distribution result, and determining the position of an interception point of target distribution and distributed weapon and sensor resources.

The invention has the advantages and positive effects that:

1) on the basis of the traditional weapon-target distribution problem, a sensor is added for detecting targets, and factors such as detection transfer time of the sensor, the number of targets capable of being detected simultaneously, association constraint of the sensor and the weapon, reserved observation time of the weapon and the like are considered in the problem, so that the starting point of the problem is in line with the actual situation, and the weapon-target distribution problem closer to the actual situation can be solved.

2) The method proposed in the present invention provides a solution reference for solving the weapon-target assignment problem with the addition of sensor detection constraints.

3) A larger feasible solution space is obtained first, and then the solution space is reduced through partial constraint instead of taking a series of constraints as constraint conditions in the optimization method, so that the complexity of the optimization method is greatly reduced, and the optimization efficiency is improved.

4) Binary bit-encoded methods are used to record offensive weapons and detectable sensor information over a period of time in solution space or to record detectable sensor information in reconstructed solution space. Compared with a common array or vector storage mode, the space occupied by the understanding space is reduced; in actual operation, the method is more convenient and flexible than an array or a vector; and the information detected by the sensor or the attack of the weapon can be intuitively known through a binary number.

5) In the invention, the interception point is set as an optimization variable, the solution space is reconstructed to transfer the visual angle of the time axis from the target to the weapon, the conversion from the original solution space to the solution space used as the input of the differential evolution algorithm is successfully completed, the optimization target is closely attached, and support is provided for further utilizing the differential evolution algorithm for optimization.

Drawings

FIG. 1 is a flow chart of a method of solving a weapon-target assignment problem based on a differential evolution algorithm in the present invention;

FIG. 2 is a target-weapon aggressable timeline;

FIG. 3 is an object-sensor detectable time axis;

FIG. 4 shows target N_iAn interceptable timeline;

FIG. 5 is a flow chart of the method of the present invention for narrowing the solution space in accordance with the weapon-sensor association constraint;

FIG. 6 is an example diagram of a method of the present invention to reduce the solution space in accordance with the weapon-sensor association constraint;

FIG. 7 is a flow chart of a reduced solution space for a specific target with intercept point constraints;

FIG. 8 is a reconstruction solution space diagram.

Detailed Description

The technical solution of the present invention will be further explained with reference to the accompanying drawings.

The weapon-target distribution problem to be solved by the invention is that on the basis of the traditional weapon-target distribution problem, a sensor is added to detect targets, and factors such as detection transfer time of the sensor, the number of targets which can be detected by the sensor simultaneously, association constraint of the sensor and the weapon, reserved observation time of the weapon and the like are considered in the problem, so that the starting point of the problem is more consistent with the actual situation, and the problem closer to the actual situation can be solved. The weapon-target assignment problem to be solved by the present invention is described as follows:

a batch of offensive weapons implement attack according to a specific flight path, a set of defense equipment intercepts an attacking target, the defense equipment comprises weapons and sensors, the quantity of the equipment is limited, the optimal resource allocation of the defense equipment is required to be given under the dynamic condition according to a certain rule, and the optimal comprehensive engagement result for the attacking target is dynamically ensured.

The weapon-target allocation problem is closer to the actual situation, a sensor is listed in the weapon resources to be allocated, and the target, the weapon and the sensor are classified according to attributes; a total of N targets, in N_i(i =1,2, … …, N), each object having an attribute value C characterizing the type of object_Ni(i =1,2, … …, N), while each target has a resource allocation priority level value S_i(i=1,2,……,N)，S_iI.e. the interception order, is related to the threat level of the target, S_iHigher values represent a higher threat level for the target, and higher priority for resource allocation. A total of M weapons, in M_j(j =1,2, … …, M), each weapon having an attribute value C characterizing the weapon type_Mj(j =1,2, … …, M), a total of G sensors, denoted G_k(k =1,2, … …, G), each sensor having an attribute value C characterizing the type of sensor_Gk(k ═ 1, … …, G); jth weapon carrying ammunition amount B_jJ =1,2, … …, M. The kth sensor can simultaneously detect O_kThe target number k is 1, … …, G, and each sensor of each attribute corresponds to a detection transfer time T_d_G_kK is 1, … …, G. The detection transition time refers to a transition time required when the sensor transitions from detection of a certain object to detection of another object.

When the difference evolution algorithm is used for distributing the weapon force resources, for a certain target, in addition to distributing a weapon to strike the target, a sensor is required to be distributed to detect the target, the distributed sensor should meet the association relation between the weapon and the sensor, the ammunition amount used by the weapon is determined, the ammunition distribution constraint condition is met as far as possible, and the resource distribution priority value S is_iAbove a given priority value S_{Given a}To ensure that at least one interception point is assigned. The final distribution result is the interception point distributed to each target, and the interception point distributed to one target can be multiple.

Wherein, the association relationship between the weapon and the sensor is as follows: the resource allocation to the same target should satisfy the association relationship between the weapon and the sensor, and the association relationship actually has a great variety and can be simplified into the following abstract: for weapons of certain attributes, there must be one or two associated time periods between the weapon and the attribute-specific sensors, requiring that at least m of the attribute-specific sensors have detection time periods assigned to the target that cover the associated time periods (i.e., the detection time periods encompass the associated time periods). m is at least 1 and at most does not exceed the total number of sensors. This associative constraint includes two layers of constraints: first, weapon and specific attribute sensor constraints; the second is the constraint of the associated time period. The association of the weapons and sensors is primarily to ensure that the target is accurately located, preventing the target from being lost. Illustrated by way of example as: if an attribute is C_M3Target N of weapon pair₁When carrying out attack, m attributes are required to be C_G5The sensor detects the target in the process of the weapon to attack and attack.

Ammunition distribution constraints are: suppose that the distribution result of a certain interception point is that a kinds of weapons are totally intercepted, and the serial number is j₁,j₂,……,j_aThe amount of ammunition allocated to the target by each weapon is respectively ......,The estimated damage probability of each weapon is ......,Should satisfy

Wherein, P_{Given a}In relation to the target attribute value, 0.96 may be taken at the time of study. When the amount of ammunition is insufficient, this condition may not be satisfied, and it is sufficient to satisfy the condition in the optimization target at this time.

As shown in FIG. 1, the method for solving the weapon-target assignment problem based on the differential evolution algorithm of the present invention can be accomplished according to the following steps:

the method comprises the following steps: acquiring initialization variables and input variables of a weapon-target distribution problem;

the input variables mainly include: number of targets, weapons, sensors N, M, G; resource allocation priority per target S_i(i ═ 1, … …, N); the initial or current ammunition quantity B of each weapon_j(j ═ 1, … …, M); initial or current number of targets O each sensor can detect simultaneously_k,k＝1，……，G；A target-weapon engagement matrix; a detectable matrix of target-sensors; association constraints between weapons and specific attribute sensors include associated weapons and sensor information, associated time information.

Each weapon may or may not form a battle on the target, and the target-weapon battle matrix can be obtained after the early stage is judged according to the space-time conditions, wherein the information contained in the battle matrix is as follows: the weapon serial number, the target serial number and the corresponding interceptable time period, the corresponding dischargeable time period and the corresponding distance between the weapon and the target. The interceptable time periods are in one-to-one correspondence with the transmittable time periods and have a certain relationship, so that the interceptable time periods are taken as input conditions during problem solving, and the distance is a corresponding discretization result obtained after discretization processing is performed on the interceptable time.

Each sensor may or may not detect the target, and after the early stage of judgment according to the space-time condition, a detectable matrix of the target-sensor can be obtained, wherein the matrix contains the following information: the device comprises a sensor serial number, a target serial number and a corresponding detectable time period, and a distance between a target and a sensor in the detectable time period. The distance is a corresponding discretization result obtained after discretizing the detectable time.

The initialization variables mainly include: attribute value C for each target, weapon, sensor to identify target, weapon, sensor_Ni(i＝1,……,N)、C_Mj(j＝1,……,M)、C_Gk(k ═ 1, … …, G); estimate P of the probability of weapon j killing target i_ij(i-1, … …, N; j-1, … …, M); detection transition time T of each sensor_d_G_k(k ═ 1, … …, G); reserved observation time T_d(ii) a Given probability value of killing P_{Given a}(ii) a Given resource allocation priority value S_{Given a}. The reserved observation time refers to observation time which is reserved during the process that whether interception is successful needs to be observed after interception, and if interception is not successful, a weapon is transmitted for interception.

Step two: and determining a larger feasible solution space, and specifically comprising the steps of 2.1-2.3.

Step 2.1: and determining a time axis of the target which can be attacked by the weapon, namely a target-weapon engagement time axis.

Traversing all targets, and finding target N from input target-weapon engagement matrix_i(i =1, … …, N) may be weaponized M_j(j ═ 1, … …, M) valid period MT of attack_ijIf i, j are the same, there may be a plurality of MTs_ijThat is, the same weapon may have multiple interceptable time periods for the same target. As shown in FIG. 2, target N_iCan be weaponized M₁、M₂And M₃Effective time periods of the attacks are MT respectively_i1、MT_i2And MT_i3Wherein the weapon M₃The effective period of attack has two MT sections_i3-1And MT_i3-2. Will MT_ij(j 1.... times.m) are spliced according to a time sequence, and when the target N is obtained, the target N is obtained by arranging according to the starting time of the time period and arranging according to the ending time of the same starting time_iTime axis MT of weapon attack_i. Time axis MT_iMay be discontinuous, such as time axis MT_iUpper includes a target N_iInformation that can be attacked by several weapons within a certain time period. The information stored for each time segment is: target, weapon, attack-capable time period start time, attack-capable time period end time. As shown in FIG. 2, target N_iTime axis MT capable of being attacked by weapon_iInvolving several time periods, e.g. 2 nd time period can be weaponized M₁And M₂And (5) attacking.

Step 2.2: the time axis in which the object can be detected by the sensor, i.e. the object-sensor detectable time axis, is determined.

Traversing all targets, finding N from the sensor-target detectable matrix_iCan be detected by the kth sensor G_k(k 1, … …, G) detected valid time period GT_ik. in the case where i, k are the same, there may be a plurality of GT s_ikI.e. the same sensor may have multiple detectable time periods for the same target. As shown in FIG. 3, target N_iCan be sensed by sensor G₁、G₂、G₃And G₄The effective time periods of the detection are GT respectively_i1、GT_i2、GT_i3And GT_i4. Combining GT with a tube_ikSplicing according to the time sequence, wherein the splicing principle is consistent with the principle adopted by the time shaft information of the target which can be attacked, and a target N is formed_iCan be detected time axis GT_i. Time axis GT_iMay be discontinuous, with the time axis containing the target N_iInformation that can be detected by several sensors during a certain period of time. The information stored for each time segment is: target, sensor, detectable period start time, detectable period end time. As shown in FIG. 3, target N_iTime axis GT detectable by a sensor_iInvolving several time periods, e.g. 2 nd time period can be sensed by sensor G₁And G₂And (6) detecting.

Step 2.3: a time axis is determined in which the target can be intercepted, i.e. the initial solution space of the problem.

Firstly, the target N is obtained in the step 2.1_iWeapons assault time axis MT of (i ═ 1, … …, N)_iAnd extracting all time points on the time axis to obtain the most original weapon attack time point information, and sequencing according to the time points.

Secondly, the target N obtained in the step 2.2_iDetectable time axis GT of (i 1, … …, N)_iAnd extracting all time points on the time axis to obtain the most original information of the detection time points of the sensor, and sequencing according to the time points.

And thirdly, fusing and sorting the two ordered time point sequences obtained in the two steps to obtain a new ordered time point sequence containing weapon attack and sensor detection information. And information at the same time point is fused, and information at different time points is judged and added with corresponding lacking weapon attack or information detected by a sensor. The original target time point information is obtained at this time.

Fourth, the target N obtained from the third step_i(i is 1, … …, N) to obtain the target N_i(i-1, … …, N) initial time slice and its information, forming target N_iCan be intercepted time axis T_iTime axis T_iMay be discontinuous and include a target N_iThe information that can be attacked by several weapons during a certain period of time and that can be detected by sensors used during this period of time. The interceptable time axes of all objects constitute the initial solution space A₁。

As shown in fig. 4, the target-weapon attack timeline of fig. 2 and the target-sensor detection timeline of fig. 3 are organized in time order to obtain an interception-capable timeline.

In the method, a binary bit coding mode is used for recording offensive weapons and detectable sensor information in a certain time period in a solution space, the coded binary system of the weapon information in each time period has M bits, and the weapon M is represented from right to left in sequence₁,……,M_MIf the corresponding bit is 1, the weapon corresponding to the binary bit can attack the target in the time period; a value of 0 indicates that the attack cannot be performed. Similarly, the coded binary system of the sensor information recorded in each time period is G bits, and represents the sensor G from right to left in turn₁,......,G_GIf the corresponding bit is 1, it indicates that the sensor corresponding to the binary bit can detect the target in this time period, and if the corresponding bit is 0, it indicates that the corresponding sensor cannot detect the target.

Step three: the initial solution space is reduced, including step 3.1 and step 3.2.

And 3.1, reducing a solution space according to weapon-sensor association constraint.

In the initial solution space, all targets are traversed, for a certain target N_iSearching whether corresponding association constraint exists in weapon-sensor constraint, if so, searching for association constraintWeapon-sensor association constraint, then in solution space A₁To find the target N_iCorresponding solution-time axis T_iIs provided with a weapon M_jAnd a sensor G_kThere is a correlation constraint that traverses all time periods on this time axis, can be weaponized M_jJudging whether the time period of attack meets the specific attribute sensor G or not_kIf not, the weapon M in the time period can be directly used_jFor the target N_iRemoving the attacking information, if the specific attribute is satisfied, the sensor G_kIf the next time slot can be weapon M, then the next time slot is searched in sequence_jAttack, also satisfying specific properties sensor G_kThen search down in sequence until finding that can not be M_jSensor G attacking or not satisfying a particular attribute_kThe required period of time. At this time, all the searched sensors G meeting the specific attribute are judged_kRequired time period T_i.x1～T_i.x2Whether to cover the weapon M_jAnd a sensor G_kIf the associated time period cannot be covered, the time axis T is set_iOn a continuous time period T_i.x1～T_i.x2Middle weapon M_jFor the target N_iAnd eliminating the attacked information. The specific flow is shown in fig. 5.

After the above operations, the solution space may contain time slots that cannot be attacked by any weapon, and these time slots belong to invalid solution space, so that the time slots that cannot be attacked by any weapon in the solution space also need to be eliminated. Further reducing the solution space.

Noting the reduced solution space as A₂。

The implementation of this step is described below with reference to fig. 5 and 6 as an example.

Target N_iCan be intercepted time axis T_iTime period T of_i.1，T_i.2，T_i.3，T_i.4，T_i.5Respectively can be weaponized M₁And a sensor G₁Weapon M₁And M₂And a sensor G₁Weapon M₂And a sensor G₁And G₂Weapon M₃And a sensor G₂Weapon M₁And a sensor G₃Attack or detection. Assume all association constraints are as follows: attribute is C_M1Is required to associate 1 attribute with C_G1Is associated with a sensor of attribute C_M1Only M of the weapon₁Attribute is C_G1Has only G₁Then the association at this time is weapon M₁Need to be connected with a sensor G₁Associated, likewise, M₃Corresponding to the attribute of weapon required 1G₂The sensors of the corresponding attributes are associated. Weapon M₁And a sensor G₁And a weapon M₃And a sensor G₂The associated time period of (a) is as shown in fig. 6. The associated time period is described in the associated time information input in step 1.

The association constraint is taken in a sequential loop, and M is taken in the first loop₁And G₁And then one of the above time periods is obtained through circulation and is marked as T_i.x(x ∈ {1,2,3,4,5}), setting the parameter TimeSlice₁For recording the time period detectable by the sensor, the following steps are carried out:

a. judging the time period T_i.xWhether can be weaponized M₁Attack, if can not be attacked, then sequentially fetch T_i.xFor the next time period T_i.(x+1)Continuing the determination; if the attack can be made, checking the sensor detection information corresponding to the time period, and executing step b;

b. judgment G₁Whether it can be detected, if not, then T is detected_i.xC is executed, if probing can be carried out, then T is processed_i.xExecuting d;

c. m within the time period₁Information capable of attacking the current target is removed from the solution space, whether all time periods on the intercepted time axis of the current target are traversed or not is judged, and if not, the next target is continuously takenA time period T_i.(x+1)To T_i.(x+1)Executing a;

d. record this time period T_i.xTo the TimeSlice₁From this position, a time period T is removed_i.(x+1)To T_i.(x+1)Executing e;

e. judging whether the time slice can be weaponized M₁If the attack can be carried out, checking sensor detection information corresponding to the time period to execute f;

f. determine G in the time period₁And whether the detection can be carried out or not, and if not, executing g. If the detection can be carried out, executing d;

g. judging Timeslice₁Whether or not to include a weapon M₁And a sensor G₁If not, the TimeSlice is used₁Chinese weapon M₁Attack can be further detected by the sensor G₁C, executing each detected time period; otherwise, the detection time of the sensor with the association constraint can cover the association time, the association constraint is satisfied, the time slice information is reserved without any processing, and then whether all time slices on the time axis of the current target which can be intercepted are traversed or not is judged, if not, T is sequentially selected_i.xThen a is performed.

To this end, the process of reducing the solution space for one association constraint may be performed, and a similar process may be performed for one association constraint to reduce the solution space. In FIG. 6, for M₁And G₁First, a time period T is taken_i.1A, b, d, and T_i.1Time information of (2) is superimposed to TimeSlice₁Then taking the time period T_i.2(ii) a Performing e, f, d, and mixing T_i.2Time information of (2) is superimposed to TimeSlice₁Performing the following steps; continuously taking time period T_i.3Executing e, g; continuously taking time period T_i.4Executing a; continuously taking time period T_i.5A, b, c are performed on a time axis T_iLast deletion periodT_i.5The information of (1). For M₃And G₂Is associated with a constraint of time period T_i.1～T_i.3Can not be weaponized M₃Attack, time period T_i.4Can be weaponized M₃Attack and can be M₃Associated sensor G₂If detected, then T_i.4Time information of (2) is superimposed to TimeSlice₁Performing the following steps; due to T_i.4Uncovered M₃And G₂At the time axis T_iUpper deletion period of time T_i.4The information of (1).

After the above operations, the solution space may contain time periods that cannot be attacked by any weapon, which belong to an invalid solution space, such as the time period marked by none in fig. 6, and therefore, the time periods that cannot be attacked by any weapon in the solution space also need to be eliminated. Further reducing the solution space. FIG. 6 shows the interceptable time axis of the target Ni scaled down in step 3.1 from T_i.1～T_i.3And (4) forming.

Noting the reduced solution space as A₂。

Step 3.2: setting the intercept point constraint for a particular target reduces the solution space.

Due to the constraints: those resource allocation priority values S_iGreater than or equal to a given priority value S_{Given a}At least one interception point is required.

The execution flow of this step is shown in FIG. 7, which traverses all targets, checks target N_iResource allocation priority value S_iIf S is_i≥S_{Given a}Then, the following first to fourth operations are performed:

first, the average killing probability is calculated. For the target N_iInterceptable time axis T_iAll time periods T of_i.x(x ═ 1,2 … …), calculating the average probability of destruction of the weapon to the target in each time segment = the probability of killing of all weapons attacking the target during this time period and/or the number of all weapons attacking the target during this time period;

second, the time period for setting the interception point is selected. Selecting a certain time period as the time period needing to set an interception point, wherein the time period T is_i.xTo be provided withIs selected, i.e. the roulette is used to select this time period. Setting the starting point of the selected time period as an interception point;

third, the number of charges dispensed. Weapon M on the interception point_lL ∈ {1, … …, M } for the target N_iThe number of ammunition dispensed is B_l*(S_i/ΣS_i) (qp), wherein p is M_lTo N_iQ is the length of the currently selected time period, B_lRepresenting a weapon M_lAmount of ammunition of ∑ S_iIndicating the summation of resource allocation priorities over all targets. If there are multiple weapons available for target N during this period_iAnd when the attack is carried out, the ammunition number is distributed from the weapon with high killing probability, and the obtained distributed ammunition number is rounded up, so that the problem of distributing 0 ammunition amount is avoided.

Fourth, a sensor is assigned. After the weapon and ammunition are dispensed, the dispensing sensor is required to target N_iAnd detecting. If there is an association constraint of the weapon with a particular sensor, then the target N is identified according to the association constraint_iAllocating sensors and detection time, and taking the sensor and detection time as a target N according to the principle of proximity if no association constraint exists_iAssign sensors to target N on a minimum basis_iThe detection time of the sensor is assigned, and the detection time of the sensor can be designated as the selected time period. For the detection time, there is a process here: when assigning sensor detection time, when shifting the detection of this sensorAdding the time into the detection time, wherein the selected time period is (time 1-time 2), and the detection time of the distribution sensor is (time 1-time 2+ T)_d_G_k). For example, a sensor G is assigned_kThe detection is performed from the 5 th to the 30 th seconds, the actual detection time will be from the 5 th to the (30 + T) th seconds_d_G_k) And detecting in seconds. Such processing simplifies the processing of assigning sensor detection times, improves the efficiency of assigning sensors, and ensures sensor need for detection transfer times.

And fifthly, updating the resource state. After all targets have been traversed, the weapon and its remaining ammunition amount, the sensors and their remaining detectable target number are changed, requiring updating of the state of the corresponding weapon and sensors, and updating of the remaining available resources.

Sixth, the solution space is reduced. Removing the time period of which the interception point is distributed from the solution space; checking the residual resources of the weapon and the sensor, and if the weapon with zero residual ammunition exists, removing the information of the target attacked by the weapon in the time period of the solution space; after the steps, the time period which cannot be attacked by any weapon in the solution space is eliminated, and the solution space is reduced.

Noting the reduced solution space as A₃。

Step four: and carrying out coding reconstruction on the solution space. All the above steps are performed from the perspective of a target on the time axis, and for optimization convenience, encoding reconstruction needs to be performed on a solution space, that is, the time axis is performed from the perspective of a weapon. The fourth step comprises three substeps: step 4.1, reconstructing a solution space; step 4.2, dividing the reconstructed solution space; and 4.3, coding the solution space. Preparation is made for subsequent optimization.

Step 4.1: a solution space is reconstructed.

For solution space A₃The reconstruction is performed according to a time axis in which the weapon can be intercepted. With reference to fig. 8, the reconstruction method is explained as follows:

step 4.1.1, all time periods during which the weapon can attack are taken. Traverse all weapons, for weapon M_j(j ═ 1, … …, M), in solution space a₃In which all the contents M are obtained_jForming a reconstructed initial solution space; for example, in FIG. 8, for M₁Find the weapon target N₁And N₂Time period of attackability.

And 4.1.2, splitting and fusing the reconstructed initial solution space in a time period. This is discussed in cases including: the two time segments are completely overlapped, at the moment, information needs to be fused, and only one time segment is reserved; the next time segment comprises the previous time segment, and the information of the previous time segment needs to be supplemented at the moment, so that the starting time of the next time segment is changed; the last time segment comprises the next time segment, and at the moment, the last time segment needs to be split into three small time segments, and weapon and sensor information is respectively supplemented; the next time slice is the latter half of the previous time slice, and the end time of the previous time slice needs to be changed at the moment to supplement the information of the next time slice; the intersection part is the front part of the next time segment, and at this time, two time segments need to be split into three time segments and respectively supplemented with respective information; the two time segments have no intersection, and the information of the time segments does not need to be changed. Forming each weapon M_jOf an interceptable time axis TM_jPossibly discontinuous, the time axis containing the weapon M_jA target that can be hit within a certain period of time and sensor information that can be used, j ═ 1, … …, M.

And 4.1.3, obtaining a reconstructed solution space. And traversing all weapons, and arranging time axes corresponding to all weapons according to the time sequence to obtain a reconstructed solution space. Recording the reconstructed solution space as A₄。

Step 4.2: and partitioning a solution space.

First, the minimum intercept time is calculated. Minimum intercept requirementObservation time T including reservation in time_dAnd the firing time T of the weapon_fAnd attack time T_lA linear relationship therebetween. When transmitting time T_fAnd attack time T_lThe simplest linear relationship between the two, the minimum interception required time can be expressed as: minimum intercept required time = T_d+|T_l-T_f|。

Secondly, to the weapon M_j(j ═ 1, … …, M), the time axis TM_jEach time period is divided according to the minimum required interception time, and the time periods smaller than the minimum required interception time are removed from the solution space.

Finally, the time axis TM is calculated_jThe minimum required time period for interception truncated by the effective part is ML_jAnd (4) respectively.

Step 4.3: and (5) decoding the space coding.

Traverse all weapons, for weapon M_j(j＝1，……，M)：

First, M is obtained_jTime axis TM of_jTotal number of time periods above, denoted as ML_j；

Secondly, mix TM_jMapping of all truncated time segments to ML_jInteger point set {1,2, … …, ML) consisting of real numbers_jOn is multiplied;

finally, take the interval (0, ML)_j]Using the interval as weapon M_jThe dispensable interval of ammunition.

Step five: and finding an optimal solution by using a differential evolution algorithm.

Step 5.1: an optimization variable and an objective function are selected.

Selected weapon M_jThe position of each ammunition in its assignable interval is an optimization variable. The optimization variable has W ═ Σ B in common_j(j =1,2, … …, M). Ammunition(s＝1,2,……,B_j) Can be allocated in (0, ML)_j]In the above, the assignment result is a real number, and the real number is rounded up to obtain the values in the point set {1,2, … …, ML_jThe sequence number on. Here, the(s＝1,2,……,B_j) S in denotes weapon M_jAll ammunition (from 1 to B)_j) Is to the weapon M_jIs identified.

Optimizing variables to weapon M_j(j-1, … …, M) of each ammunition(s＝1,2,……,B_jJ ═ 1,2, … …, M) is an optimization variable at its assignable interval.

The objective function is:

wherein: m is_iIs a target N_iNumber of assigned interception points. Lambda [ alpha ]_iIs a proportionality coefficient and is determined according to actual conditions. The result of the distribution to a certain target interception point is that a weapons j are shared₁,......,j_aIntercepting the weapon, wherein the probability value of killing of each weapon is......,Each weapon dispenses as many ammunition as......,

Step 5.2: generating an initial population according to a certain principle.

If x is ordered_e(t) is the e-th individual in the t-th generation 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 is_e(t) each component corresponds to an optimization variable, W is the number of chromosomes constituting an individual, i.e. the number of optimization variables; NP is the population size; t is t_maxIs the maximum evolutionary algebra.

And randomly generating NP individuals according to the value range of the optimized variable.

Each individual in the population was generated as follows:

the weapons M are taken in turn according to the sequence of the weapon killing probability from high to low_jTo weapon M_jAll available ammunition(s＝1,2,……,B_j) Is distributed to intervals (0, ML) with uniform probability_j]The above.

For a certain time section, if the weapon in the time section can attack a plurality of targets, a roulette mode is used to play with probability S_i/ΣS_iOne of the targets is selected, and the ammunition in the section is uniformly distributed to the selected target.

Distributing ammunition to the starting point of the corresponding interception time period according to the distribution interval and the targets of the ammunition, checking whether the generated individuals have resource use conflict (sensor resource use constraint), and if the ammunition has conflict, namely if the ammunition is distributed according to the scheme, the number of the targets which can be simultaneously detected by the sensors in the time period exceeds the number of the targets which can be simultaneously detected by the sensors, and then regenerating the ammunition.

And counting the number of interception points of each target, and calculating the fitness value of each individual according to the target function.

Step 5.3: test vectors are generated.

Randomly selecting 3 individuals x from the current t generation population_p1(t)，x_p2(t) and x_p3(t), the test vector h corresponding to the r-th optimization variable of the e-th population individual of the t + 1-th generation population_er(t +1) is:

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) represents the individuals x, respectively_p1(t)，x_p2(t) and x_p3(t) the r-th optimization variable;

x_p2r(t)-x_p3r(t) is a differentiation vector; f is the scaling factor.

In the evolution process, in order to ensure the validity of the solution, it is necessary to judge whether the test vector meets the boundary condition, and if not, the test vector is regenerated by a random method, and the generation method is the same as the individual generation method of the initial population in step 5.2. The boundary condition refers to the distribution interval of ammunition.

Step 5.4: generating the offspring.

The r sub-generation v of the e population individuals in the t +1 generation population generated by the cross operator_er(t +1) is:

wherein, randl_erIs [0,1 ]]Random decimal between, CR is the crossover probability, CR ∈ [0,1]And rand (e) is in [1, N ]]Random integer between, such a crossover strategy may ensurex_e(t +1) has at least one component with x_eThe respective components of (t) are related.

And (5) performing target distribution on the generated filial generation, checking whether each individual has resource use conflict, and if so, regenerating by using a random method, wherein the generation method is the same as the individual generation method of the initial population in the step 5.2.

And counting the number of interception points of each target, and calculating the fitness value of each individual in the filial generation.

Step 5.5: and updating the population. The offspring v_e(t +1) and parent x_e(t) comparing the fitness of the population to update the e-th individual x in the t +1 th generation population_e(t +1) is:

$x_e(t+1)=\left\{\begin{array}{cc}{v}_e(t+1),& f(v_{\mathrm{el}}(t+1),\&CenterDot;\&CenterDot;\&CenterDot;,v_{\mathrm{en}}(t+1))<f(x_{\mathrm{el}}\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;,x_{\mathrm{en}}\left(t\right))\\ x_e\left(t\right),& f(v_{\mathrm{el}}(t+1),\&CenterDot;\&CenterDot;\&CenterDot;,v_{\mathrm{en}}(t+1))\&GreaterEqual;f(x_{\mathrm{el}}\left(t\right),\&CenterDot;\&CenterDot;\&CenterDot;,x_{\mathrm{en}}\left(t\right))\end{array}\right.---\left(4\right)$

wherein, f (v)_el(t+1),...,v_en(t +1)) is the descendant v_eFitness of (t +1), f (x)_el(t),...,x_en(t)) is the parent x_e(t) fitness.

Then, it is checked whether an optimum result is obtained.

And (3) judging whether the individual with the optimal fitness in the new population meets the formula (1), if so, terminating iteration, and returning the individual with the optimal fitness, otherwise, executing the step 5.3.

Or judging whether t +1 exceeds an iteration upper limit t_maxIf the upper iteration limit is exceeded, the iteration is terminated. And returning to the individual with the optimal fitness at the moment, and otherwise, returning to the step 5.3 to continue executing.

Step 5.6: the remaining resources are allocated.

And for the selected optimal individual, if the selected optimal individual has residual resources, preferentially allocating the selected optimal individual to a target with high priority or allocating the selected optimal individual by adopting a near allocation principle under the condition of not generating conflict.

Step 5.7: and performing inverse coding to obtain an optimized result.

And (4) performing inverse coding on the obtained optimized distribution result, namely determining the position of an interception point distributed by the target and distributed weapons and sensor resources in a process opposite to the process of the step 4.3.

Thus, the resource allocation of weapons, sensors, and targets is completed.

Claims (2)

1. A method for solving a weapon-target allocation problem based on a differential evolution algorithm is characterized in that sensor resources of defense equipment are added to the weapon-target allocation problem, and the solution specifically comprises the following steps:

the method comprises the following steps: acquiring input variables and initialization variables of a weapon-target distribution problem;

the input variables include: the number of targets N, the number of weapons M and the number of sensors G; resource allocation priority per target S_iI ═ 1,2, … …, N; number of ammunition each weapon initially or currently availableQuantity B_jJ ═ 1,2, … …, M; initial or present number of targets O each sensor can detect simultaneously_kK is 1,2, … …, G; the target-weapon engagement matrix comprises the following information: the weapon serial number, the target serial number, the corresponding interceptable time period, the corresponding dischargeable time period and the corresponding distance between the weapon and the target; a detectable matrix of target-sensors containing information of: the method comprises the following steps of (1) detecting a sensor serial number, a target serial number, a detectable time period corresponding to the sensor serial number and a distance between a target and a sensor in the detectable time period; weapon and sensor association constraints including associated weapon and sensor information, associated time information;

initializing variables includes: attribute value C of each object_NiAttribute value C of each weapon_MjAttribute value C of each sensor_GkJth weapon M_jFor the ith target N_iEstimated value P of the killing probability_ijDetection transition time T of each sensor_d_G_kWherein i is 1,2, … …, N, j is 1,2, … …, M, k is 1,2, … …, G; reserved observation time T_d(ii) a Given probability value of killing P_{Given a}(ii) a Given resource allocation priority value S_{Given a}；

Step two: determining a larger feasible solution space, comprising the steps of 2.1-2.3;

step 2.1: determining a time axis of the target which can be attacked by the weapon, specifically: finding the ith target N from the target-weapon engagement matrix_iCan be weaponized M_jEffective time period of attack MT_ijTo connect MT_ijSplicing according to the time sequence to form a target N_iTime axis MT of weapon attack_iTime axis MT_iThe information stored for each time period of (a) is: a target, a weapon, an attack-capable time period start time, an attack-capable time period end time; wherein i is 1,2, … …, N, j is 1,2, … …, M;

step 2.2: determining a time axis in which the target can be detected by the sensor, specifically: finding N from a detectable matrix of sensor-targets_iCan be sensed by sensor G_kThe effective time period GT of the probe_ikWill beGT_ikSplicing according to the time sequence to form a target N_iCan be detected time axis GT_iTime axis GT_iThe information stored for each time period of (a) is: a target, a sensor, a detectable period start time, a detectable period end time; wherein i is 1,2, … …, N, k is 1,2, … …, G;

step 2.3: target N_iTime axis MT of weapon attack_iAnd a time axis GT detectable by the sensor_iSorting according to the time sequence, and fusing the overlapped parts on the time axis to obtain a target N_iCan be intercepted time axis T_i(ii) a N time axes corresponding to the N targets form an initial solution space A₁(ii) a Wherein i is 1,2, … …, N;

recording weapon and sensor information in each time segment of each target in a binary bit coding mode; the number of coded binary digits recording weapon information in each time period is the same as the number of weapons, from right to left, each digit represents a weapon with a weapon serial number as a sequence number, the value of each digit is 1 or 0,1 represents that the corresponding weapon can attack the target in the time period, and 0 represents that the corresponding weapon cannot attack the target in the time period; the number of coded binary bits for recording sensor information in each time period is the same as that of the sensors, from right to left, each bit represents a sensor with the serial number of the sensor as the sequence number, the value of each bit is 1 or 0,1 represents that the corresponding sensor can detect the target in the time period, and 0 represents that the corresponding sensor cannot detect the target in the time period;

step three: reducing the initial solution space, including step 3.1-step 3.2;

step 3.1: traversing the time axis which can be intercepted of the target with the association constraint of the weapon-sensor, and eliminating the weapon attack information which does not meet the association constraint of the weapon-sensor, wherein the specific implementation method comprises the following steps: target N with weapon-sensor association constraint_iFor each weapon-sensor association constraint, the following operations are performed:

setting up weapons M_jAnd a sensor G_kTraversing the target N in the presence of association constraints_iOfIntercepted time axis T_iAll time periods of (c) can be weaponized M_jJudging whether the sensor G is satisfied in a certain time period of the attack_kIf not, on the time axis T_iThe weapon M in the time period_jFor the target N_iRemoving the attacking information, if the attacking information is satisfied, sequentially taking a time period, and if the attacking information is satisfied, enabling the weapon M to be used in the time period_jAttack and satisfaction of sensor G_kUntil it can not be M, then continue to take down a period of time_jAttack or not satisfy sensor G_kThe requirements of (1); at this time, all the weapons M capable of being weaponized are judged_jAttack and satisfaction of sensor G_kIs required for a time period T_i.x1～T_i.x2Whether or not to cover the weapon M_jAnd a sensor G_kIf not, on the time axis T_iWill last time period T_i.x1～T_i.x2Internal weapon M_jFor the target N_iRemoving the information of the attack;

then eliminating the time period which can not be attacked by any weapon in the solution space to obtain a reduced solution space A₂；

Step 3.2: traversing the target to assign a priority S to the resource_iGreater than or equal to a given priority value S_{Given a}At least one interception point is arranged; after all the targets are traversed, updating the states of weapons and sensors and the residual resources; then, removing the time period distributed with the interception point from the solution space, and removing attack information of the weapon with zero residual ammunition amount from the solution space; finally, the time period which can not be attacked by any weapon in the solution space is removed to obtain a reduced solution space A₃；

Step four: encoding and reconstructing a solution space, wherein the encoding and reconstructing process comprises a step 4.1 to a step 4.3;

step 4.1: for solution space A₃Reconstructing according to the time axis of weapon interception to obtain a reconstructed solution space A₄(ii) a To weapon M_jIn solution space A₃In the middle traversal time period, all the M-containing components are obtained_jAttack the time section of the information, and carry out all the obtained time sections according to the time sequenceLine splicing to form a weapon M_jOf an interceptable time axis TM_j，j＝1,2,……,M；

Step 4.2: will weapon M_jOf an interceptable time axis TM_jEach time segment is divided according to the minimum interception required time, the time segments smaller than the minimum interception required time are removed, and finally the time axis TM_jBy ML_jEach minimum interception needs to be formed by time periods, j is 1,2, … …, M; the minimum required interception time comprises reserved observation time T_dAnd the firing time T of the weapon_fAnd attack time T_lA linear relationship therebetween;

step 4.3: will weapon M_jOf an interceptable time axis TM_jML on_jMapping of individual time periods to ML_jReal number point set {1,2, … …, ML) composed of real numbers_jOn is multiplied; taking intervals (0, ML)_j]As weapons M_jThe ammunition dispensable interval of (a); j ═ 1,2, … …, M;

step five: searching an optimal solution by using a differential evolution algorithm, wherein the optimal solution comprises the steps of 5.1-5.7;

step 5.1: selected weapon M_jEach ammunition B of_jsThe position in the assignable interval is an optimized variable, j is 1,2, … …, M, s is 1,2, … …, B_j(ii) a Defining the objective function f as:

wherein m is_iIs a target N_iThe number of assigned interception points; lambda [ alpha ]_iIs a proportionality coefficient; b_ju,j_u∈{j₁,...,j_aDenotes: for the target N_iThe distribution result of the interception points is that a weapons j are shared₁,......，j_aIntercepting the weapon, wherein the probability value of killing of each weapon isEach weapon dispenses as many ammunition as

Step 5.2: generating an initial population;

the e-th individual x in the t-th generation population_e(t) is 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 is_e(t) each component corresponds to an optimization variable, W is the number of chromosomes constituting an individual, NP is the population size, t_maxIs the maximum evolution algebra;

each individual in the population was generated as follows: according to the sequence of the weapon killing probability from high to low, the weapons M are treated_jAll available ammunition B_js(s＝1,2,……,B_j) Is distributed to intervals (0, ML) with uniform probability_j]The above step (1); if the weapon can attack more than 2 targets in a certain time interval, the probability S is used_i/ΣS_iSelecting one target, and uniformly distributing the ammunition in the interval section to the selected target; distributing ammunition to the starting point of the corresponding interception time period according to the distribution interval and the target of the ammunition, checking whether resource use conflict exists in the generated individuals, and regenerating the ammunition if the conflict exists;

counting the number of interception points of each target, and calculating the fitness value of each individual according to a target function;

step 5.3: generating a test vector, specifically: randomly selecting 3 individuals x from the current t generation population_p1(t)，x_p2(t) and x_p3(t), the test vector h corresponding to the r-th optimization variable of the e-th population individual of the t + 1-th generation population_er(t +1) is:

h_er(t+1)＝x_p1r(t)+F*(x_p2r(t)-x_p3r(t))，e≠p1≠p2≠p3

wherein x is_p1r(t)，x_p2r(t) and x_p3r(t) represents the individuals x, respectively_p1(t)，x_p2(t) and x_p3(t) the r-th optimization variable; x is the number of_p2r(t)-x_p3r(t) is a differentiation vector; f is a zoom factorA seed;

if the generated test vector is not in the distribution interval of the ammunition, regenerating the test vector according to the individual generation method of the population in the step 5.2;

step 5.4: generating offspring, the r-th offspring v of the e-th population_er(t +1) is:

wherein, randl_erIs [0,1 ]]Random decimal between, CR is the crossover probability, CR ∈ [0,1]And rand (e) is in [1, N ]]Random integers in between;

performing target distribution on the generated filial generation and checking whether each individual has resource use conflict, and if so, regenerating according to the individual generation method of the population in the step 5.2;

counting the number of interception points of each target, and calculating the fitness value of each individual in the filial generation according to the target function;

step 5.5: updating the population: updating the e-th individual x in the t + 1-th generation population_e(t +1) is:

$x_e(t+1)=\left\{\begin{array}{cc}{v}_e(t+1),& f\left(v_{e1}\right(t+1),...,v_{en}(t+1\left)\right)<f\left(x_{e1}\right(t),...,x_{en}(t\left)\right)\\ x_e\left(t\right),& f\left(v_{e1}\right(t+1),...,v_{en}(t+1\left)\right)\&GreaterEqual;f\left(x_{e1}\right(t),...,x_{en}(t\left)\right)\end{array}\right.$

f(v_e1(t+1),…,v_en(t +1)) is the descendant v_eFitness of (t +1), f (x)_e1(t),…,x_en(t)) is the parent x_e(t) fitness;

judging whether the individuals with the optimal fitness in the new population meet the formula:if yes, terminating iteration, returning to the individual with the optimal fitness, otherwise, executing the step 5.3;

or judging whether t +1 exceeds an iteration upper limit t_maxIf yes, terminating iteration and returning to the individual with the optimal fitness, otherwise, executing the step 5.3;

step 5.6: for the selected optimal individual, if the selected optimal individual has residual resources, the selected optimal individual is preferentially allocated to a target with high priority or allocated by adopting a near allocation principle under the condition of not generating conflict;

step 5.7: and performing inverse coding on the obtained optimized distribution result, and determining the position of an interception point of target distribution and distributed weapon and sensor resources.

2. The method for solving the weapon-target assignment problem based on the differential evolution algorithm as claimed in claim 1, wherein traversing the targets in step 3.2 assigns the resource with priority S_iGreater than or equal to a given priority value S_{Given a}The target of (2) is to set at least one interception point, and the specific implementation method is as follows: go through all targets, look over target N_iResource allocation priority value S_iIf S is_i≥S_{Given a}Then, the following operations (1) and (2) are performed:

(1) dispensing weapons and munitions: for the target N_iInterceptable time axis T_iAll time periods T of_i.x(x ═ 1,2 … …), calculating weapon pair target N for each time segment_iAverage probability of killingThen with probabilitySelecting a time period T_i.xAs a time period for which interception points need to be set; setting the start of the selected time period as an interception point, the interception point being pointed atMachine M_lL ∈ {1, … …, M } vs. target N_iThe number of ammunition dispensed is B_l*(S_i/ΣS_i) (q/p), wherein p is M_lFor the target N_iQ is the length of the currently selected time period, B_lRepresenting a weapon M_lThe amount of ammunition of (a); if more than two weapons are capable of targeting target N within the selected time period_iCarrying out attack, starting to distribute ammunition number from a weapon with high killing probability, and rounding up the obtained distributed ammunition number;

(2) a dispensing sensor; if there is an association constraint of the weapon with a particular sensor, then the target N is identified according to the association constraint_iAllocating sensors and detection time, and taking the sensor and detection time as a target N according to the principle of proximity if no association constraint exists_iAssigning a sensor; if the selected time period is (time 1-time 2), the detection time of the distributed sensor is (time 1-time 2+ T)_d_G_k)。