CN114861417B - Multi-stage weapon target distribution method based on variable neighborhood search - Google Patents
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Abstract
The invention discloses a multi-stage weapon target distribution method based on variable neighborhood search, which comprises the following steps: establishing a multi-stage weapon target distribution model; solving the multi-stage weapon target distribution model by adopting a variable neighborhood search algorithm; and carrying out weapon target distribution according to the optimal solution obtained by solving. According to the method, shooting pressure of a weapon platform is relieved by carrying out multi-wave-time planning striking on targets, a minimum target threat residual error is taken as an optimized target under the condition that weapon resources are constrained, a nonlinear integer programming model of a multi-stage weapon target allocation problem is established, two feasible solution construction algorithms based on greedy strategies are designed, a plurality of disturbance strategies and neighborhood search operators are provided, and allocation efficiency of a remote precise guided weapon is improved.
Description
Technical Field
The invention belongs to the technical field of weapon target distribution, and particularly relates to a multi-stage weapon target distribution method based on variable neighborhood search.
Background
Weapon target allocation problem is one of the most fundamental problems in the field of military operations. The weapon target allocation problem is to allocate a certain number of weapons with damage effects to a plurality of targets of the enemy so as to achieve the tactical intention with the maximum damage effects on the enemy, and win the winning of local warfare by destroying important strategic resources of the enemy to the greatest extent so as to lose the fight capability. From the number of strike periods, weapon target task assignments can be divided into two categories: single-stage weapon target task allocation and multi-stage weapon target task allocation. The single-stage problem distributes weapons to all targets at one time, and is an ideal distribution scene with abundant weapons resources. The multi-stage problem considers the constraint of weapon resources and the influence of target striking sequence on subsequent combat, and is closer to the actual combat scene. The current research on weapon target distribution is mostly focused on single-stage problems, however, in practical military applications, especially in remote precise guidance scenes, the single-stage weapon target distribution algorithm is not suitable for the situation because the types and the number of targets to be hit are large and exceed the same-period maximum hitting capability of a weapon platform. Therefore, the striking process is divided into a plurality of wave times according to the threat degree of the targets, the number of weapon platforms, the fire transfer time and other constraints, and the fight task is completed by making weapon target striking schemes of a plurality of stages, so that the optimal target distribution is realized.
Disclosure of Invention
In view of this, it is an object of the present invention to provide a multi-stage weapon target allocation method based on a varying neighborhood search. According to the method, shooting pressure of a weapon platform is relieved by carrying out multi-wave-time planning striking on targets, a minimum target threat residual error is taken as an optimized target under the condition that weapon resources are constrained, a nonlinear integer programming model of a multi-stage weapon target allocation problem is established, two feasible solution construction algorithms based on greedy strategies are designed, several disturbance strategies and neighborhood search operators are provided, and allocation efficiency of a remote precise guided weapon is improved.
The invention aims to realize a multi-stage weapon target distribution method based on variable neighborhood search, which comprises the following steps:
step 1, establishing a multi-stage weapon target distribution model;
Step 2, solving the multi-stage weapon target distribution model by adopting a variable neighborhood search algorithm;
step 3, weapon target distribution is carried out according to the optimal solution obtained by solving;
The multi-stage weapon target distribution model has the target functions of:
The objective function represents minimizing the threat residual sum for all targets,
The constraint conditions include:
Wherein W= {1, …, m }, represents all weapon sets, any weapon i ε W, N= {1,2, …, N }, represents all sets of targets, any target j ε N, V j represents threat value of the jth target, the more important target has a larger threat value, x tij is a binary variable, represents whether weapon i is allocated to target j in the t-th stage, p ij represents damage probability of the ith weapon to the jth target, D j represents attack saturation value corresponding to the jth target, and the targets are not allocated with weapons after reaching saturation value, S= {1,2, …, S }, set of all stages, arbitrary stage t ε S, Representing a set of weapons that can be used at stage t,Representing a target set to be hit in a t stage, wherein W f = {1,2, …, f }, representing a weapon launching platform set, wherein the total number of weapons launched in each stage is not more than f, m represents the total number of weapons, n represents the total number of targets, s represents the total number of stages, and f represents the number of weapon launching platforms;
Equation (2) specifies that all weapons have an attack saturation value greater than or equal to the target specification, and stops distributing weapons to the target when the attack saturation value is reached; equation (3) specifies that a weapon can only be assigned to one target; equation (4) specifies that the sum of the weapons used cannot exceed the weapon inventory when the dispense is complete; equation (5) limits the firing capacity of the weapon platform, providing that the number of weapons fired at each stage cannot exceed the limit of the firing platform; equation (6) shows that the decision variable is a binary number, and that weapon i is assigned to target j at stage t is equal to 1, otherwise equal to 0.
Specifically, the variable neighborhood search algorithm, a mechanism of alternately selecting a plurality of neighborhood structures, enables the algorithm to explore a wider range of solution space, and comprises the following steps:
Step 201: initializing parameters;
step 202: generating an initial solution s 0 through a decoding algorithm, and calculating a corresponding objective function;
Step 203: randomly selecting a disturbance operator to disturbance the initial target coding sequence to generate a new target coding sequence;
step 204: transmitting the newly generated target coding sequence into a neighborhood searching structure, and calculating a target function value corresponding to the current target coding sequence;
Step 205: carrying out local search on the current solution according to the sequence of the neighborhood searching operators in the neighborhood searching structure;
Step 206: if the current neighborhood search operator improves the current solution, skipping back to the first neighborhood search operator to perform the search from scratch; otherwise, executing the next neighborhood searching operator in sequence until all neighborhood searching operators are walked and no improvement is generated;
Step 207: judging whether the termination criterion is met, if not, repeating the steps 202-207 to re-execute the search, and if so, entering step 208;
Step 208: ending the algorithm, and outputting a global optimal solution s gb;
the input of the variable neighborhood search algorithm is weapon, number of targets, parameters and initial target coding sequence; the output is the global optimal solution s gb.
Furthermore, in the variable neighborhood searching algorithm, different neighborhood action alternate searching mechanisms are used, a real number coding sequence of a target is used as an operation object of a disturbance operator and a neighborhood searching operator, a new solution is searched through local searching, if the quality of the new solution is worse than that of the current optimal solution, a next neighborhood searching operator is selected, and if the new solution is better than that of the current optimal solution, the first neighborhood searching operator is switched to search for the local optimal solution of the current solution; the disturbance operator comprises a point exchange operator, a turnover operator and a recombination operator, and the neighborhood search operator comprises two exchange operators, a turnover operator and a cross search operator.
Specifically, the point intersection scaler is a slight disturbance structure, when an initial target coding sequence is transmitted to a disturbance operator, two points in a target coding sequence array are randomly selected, and the disturbance operation can be completed by exchanging numbers; the turnover operator is a disturbance mode for changing a target coding sequence in a large area, and the turnover length is determined according to random numbers; the recombination operator regards the target coding sequence as a section of paper tape, randomly designates a section with a fixed width, and shuffles the numerical sequence of the target coding sequence in the section;
The two exchange operators search a local optimal solution of a neighborhood structure by exchanging a number and a neighbor with a fixed interval; the turnover operator realizes the search of local solutions by selecting two points with proper spacing and then turning over all numbers between the two points; the cross search operator is divided into three steps: firstly dividing a target coding sequence into four parts with equal length by adopting a quartering method, secondly traversing the front quarter point, sequentially intercepting fragments with fixed length, randomly selecting one from the other three parts to execute the same operation, and finally executing the overturning and crossing operation on the front and rear fragments.
Preferably, the search method of 2 intervals, 3 intervals and 4 intervals in the two exchange operators searches for a local optimal solution.
Preferably, the length of the flipping operator is 0.1 times, 0.15 times and 0.2 times of the length of the target coding sequence.
Preferably, a greedy algorithm is used in the variable neighborhood search algorithm to construct the feasible solution.
Furthermore, a random factor is introduced into the variable neighborhood search algorithm, a greedy algorithm is combined to construct a feasible solution, weapon distribution is sequentially carried out on each target to be distributed, and the hit weapons are selected in a random mode, wherein the larger the damage probability of the weapons is, the higher the probability of being selected is, so that the capability of the algorithm to jump out of a local optimal solution is improved.
The method establishes a multi-stage weapon target distribution model, designs several neighborhood structures and disturbance methods under the framework of a variable neighborhood search algorithm, provides two feasible solution generation strategies, and provides a weapon planning scheme for medium-scale target multi-wave striking.
Drawings
FIG. 1 is a schematic overall flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of a real number encoding method according to an embodiment of the present invention;
FIG. 3 is an exemplary diagram of a cross search operator according to an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings, without limiting the invention in any way, and any alterations or substitutions based on the teachings of the invention are intended to fall within the scope of the invention.
Assuming that the attacking party has m weapons, the attack is to be launched on n targets at a long distance, and is limited by f weapon launching platforms (f < n), the attack on all targets is planned to be completed in s stages. In this embodiment, weapons of the same parameters may be considered as different weapons, each shell only causing damage to one target at a time, but one target may accept the bombings of multiple targets until the corresponding saturation value is reached. And taking threat residuals of the minimum hit objects as optimization targets, and establishing a mixed integer nonlinear programming model of multi-stage weapon target task allocation.
As shown in fig. 1, the multi-stage weapon target allocation method based on the variable neighborhood search includes the following steps:
step 1, establishing a multi-stage weapon target distribution model;
Step 2, solving the multi-stage weapon target distribution model by adopting a search algorithm;
and 3, performing weapon target distribution according to the optimal solution obtained by solving.
The following notation is involved in embodiments to describe a multi-stage weapon target allocation model:
the weapon distribution system is faced with more uncertainty, subject to the complex environment of reality. The multi-stage weapon target allocation method studied in this embodiment makes the following assumptions for reducing complexity:
the number of targets in each scene is fixed, and once the sensing system completes detection, the targets cannot escape or be newly increased;
(II) only one weapon can attack one target, but one target can be attacked by a plurality of weapons;
and (III) any target has a corresponding attack saturation value, and when the target reaches attack saturation, the weapon is stopped being distributed to the target.
Based on the above assumptions, the present embodiment builds a multi-stage weapon target distribution model of the form:
Equation (1) is an objective function, and equations (2) to (6) are constraints. Equation (1) represents minimizing the threat residual sum for all targets. The method is expected to reduce the probability of the target with high threat value surviving in combat so as to achieve better striking effect. Equation (2) specifies that all weapons cause damage to the target not less than the target specified attack saturation value, and stopping assigning weapons to the target when the damage and saturation value are reached; equation (3) is a numerical representation assuming two, specifying that a weapon can only be assigned to one target; equation (4) is a global constraint that specifies that the sum of the armed forces used cannot exceed the weapon inventory when the allocation is complete; equation (5) limits the firing capacity of the weapon platform, providing that the number of weapons fired at each stage cannot exceed the limit of the firing platform; equation (6) shows that the decision variable is a binary number, and that weapon i is assigned to target j at stage t is equal to 1, otherwise equal to 0.
The variable neighborhood search is an improved local search algorithm, and a mechanism for alternately selecting a plurality of neighborhood structures enables the algorithm to explore a larger range of solution space, and the local optimization and the global optimization capabilities are considered, wherein a multi-stage weapon target search algorithm framework based on the variable neighborhood search is as follows:
In algorithm 1, we refer to the mechanism of using different neighborhood actions to search alternately as a variant neighborhood search structure, which contains multiple neighborhood search operators, also called neighborhood actions. In this embodiment, the real number coding list of the target is used as the operation object of the operator, a new solution is found through local search, if the quality of the new solution is worse than that of the current optimal solution, the next neighborhood operator is selected, and if the new solution is better than that of the current solution, the first neighborhood operator is transferred to find the local optimal solution of the current solution. The operator design of the variable neighborhood search structure needs to consider the 'width' and 'precision' of the neighborhood, when solving the small-scale problem, we pay more attention to the precision, and the algorithm can find the optimal solution with higher probability only when the precision is higher. However, as the problem grows in size, high precision local searches may result in unacceptable algorithm execution times, so we need to solve the problem in a coarser search to shorten the solution time.
Coding mode:
For the multi-stage weapon target distribution problem, the binary coding is directly used for constructing the three-dimensional array to execute the searching principle is simple, but the operation is complex, the algorithm needs to execute a large number of repairing operations, and the solving time is greatly prolonged. Therefore, the patent proposes to use a real number coding method based on targets, convert the original data information into a plurality of target lists by means of analysis, and then use a limited number of real numbers to correspond to the lists one by one, and the representation method is shown in fig. 2.
Decoding strategy:
in a variable neighborhood search algorithm, the construction mode of a feasible solution influences the convergence speed and the search quality of the algorithm. The present embodiment proposes to use a greedy algorithm and a greedy algorithm that introduces a random factor to decode the target sequence to construct a feasible solution.
The greedy strategy-based algorithm is a structured heuristic where each step only focuses on the most favorable combinations for the current task in constructing a feasible solution. The following is a pseudo-code representation of the greedy policy algorithm construction initial solution:
In the variable neighborhood search, a greedy algorithm is used for constructing a feasible solution, the probability of the algorithm sinking into the local optimum is high, in order to enable the algorithm to jump out of the local optimum, a random factor is introduced in the second construction method, and the greedy algorithm is combined for constructing the feasible solution. The weapon is distributed to each target to be distributed in turn, the hit weapon is selected in a random mode, wherein the larger the damage probability of the weapon is, the higher the probability of being selected is, so that the capability of the algorithm to jump out of the local optimal solution is increased, and the algorithm framework can refer to the algorithm 2.
In the multi-stage weapon target allocation method, two parts need to design an operator, wherein the first part is a disturbance operator design, and the other part is a neighborhood search operator contained in a variable neighborhood structure. This patent has designed three kinds of operators for disturbance structure. Three types of operators are designed for the variable neighborhood part, and seven neighborhood search operators are obtained in total through changing the shape parameter values.
Disturbance operator:
(1) Point exchange operator: the point exchange operator is a slight disturbance structure, and when the initial target code is transferred to the disturbance operator, two points in the array are randomly selected, and the disturbance operation can be completed by exchanging numbers.
(2) The inversion operator: unlike the point exchange operator, the inversion operator is a disturbance mode for changing the original sequence in a large area, the inversion length is determined according to random numbers, and the large change is helpful to the problem of jumping out of multiple local optimal solutions, but the probability of skipping over global optimal solutions is also large.
(3) Recombination operators: in order to achieve the balance between the ability to jump out of local optimum and the search accuracy, a reorganization operator is designed. The target sequence is regarded as a piece of paper tape, a piece with a fixed width is randomly assigned, and the numerical sequence is disturbed by shuffling inside the piece. The method can not only reserve the original structural characteristics to a certain extent, but also can relatively severely disturb the current sequence.
Neighborhood search operator
(1) Two exchange operators: the two-swap operation is a traditional neighborhood search method that searches for a locally optimal solution of a neighborhood structure by swapping a number with its fixed-interval neighbors. In the algorithm, a 2-interval, a 3-interval and a 4-interval searching method are adopted to find a local optimal solution.
(2) The inversion operator: the inversion operator performs a search for a local solution by selecting two points of appropriate spacing and then inverting all numbers between the two points. In this algorithm we have designed roll-over operators with lengths of 0.1 times, 0.15 times and 0.2 times the total target sequence length.
(3) Cross search operator: the crossover search operator is divided into three steps: firstly, dividing the original sequence into four equal-length parts by adopting a quartering method, secondly traversing the front quarter point, sequentially intercepting fragments with fixed length, randomly selecting one from the other three parts to execute the same operation, and finally executing the overturning and crossing operation on the front and rear fragments, as shown in figure 3.
According to the invention, aiming at the problems of limited number of remote accurate guided weapon transmitting platforms and high ammunition cost in large-scale military operations, the invention provides a multi-stage weapon target distribution method, shooting pressure of a weapon platform is relieved by carrying out multi-wave-time planning striking on targets, a nonlinear integer programming model of the multi-stage weapon target distribution problem is established by taking a minimum target threat residual error as an optimization target under the condition of constraint of weapon resources, two feasible solution construction algorithms based on greedy strategies are designed, a plurality of disturbance strategies and neighborhood search operators are provided, and the distribution efficiency of remote accurate guided weapons is improved.
Claims (8)
1. A multi-stage weapon target allocation method based on a variable neighborhood search, comprising the steps of:
step 1, establishing a multi-stage weapon target distribution model;
Step 2, solving the multi-stage weapon target distribution model by adopting a variable neighborhood search algorithm;
step 3, weapon target distribution is carried out according to the optimal solution obtained by solving;
The multi-stage weapon target distribution model has the target functions of:
The objective function represents minimizing the threat residual sum for all targets,
The constraint conditions include:
Wherein W= {1, …, m }, represents all weapon sets, any weapon i ε W, N= {1,2, …, N }, represents all sets of targets, any target j ε N, V j represents threat value of the jth target, the more important target has a larger threat value, x tij is a binary variable, represents whether weapon i is allocated to target j in the t-th stage, p ij represents damage probability of the ith weapon to the jth target, D j represents attack saturation value corresponding to the jth target, and the targets are not allocated with weapons after reaching saturation value, S= {1,2, …, S }, set of all stages, arbitrary stage t ε S, Representing a set of weapons that can be used at stage t,Representing a target set to be hit in a t stage, wherein W f = {1,2, …, f }, representing a weapon launching platform set, wherein the total number of weapons launched in each stage is not more than f, m represents the total number of weapons, n represents the total number of targets, s represents the total number of stages, and f represents the number of weapon launching platforms;
Equation (2) specifies that all weapons have an attack saturation value greater than or equal to the target specification, and stops distributing weapons to the target when the attack saturation value is reached; equation (3) specifies that a weapon can only be assigned to one target; equation (4) specifies that the sum of the weapons used cannot exceed the weapon inventory when the dispense is complete; equation (5) limits the firing capacity of the weapon platform, providing that the number of weapons fired at each stage cannot exceed the limit of the firing platform; equation (6) shows that the decision variable is a binary number, and that weapon i is assigned to target j at stage t is equal to 1, otherwise equal to 0.
2. The multi-stage weapon target allocation method based on variable neighborhood search according to claim 1, wherein the variable neighborhood search algorithm, the mechanism of multiple neighborhood structure alternate selection allows the algorithm to explore a wider range of solution spaces, comprising the steps of:
Step 201: initializing parameters;
step 202: generating an initial solution s 0 through a decoding algorithm, and calculating a corresponding objective function;
Step 203: randomly selecting a disturbance operator to disturbance the initial target coding sequence to generate a new target coding sequence;
step 204: transmitting the newly generated target coding sequence into a neighborhood searching structure, and calculating a target function value corresponding to the current target coding sequence;
Step 205: carrying out local search on the current solution according to the sequence of the neighborhood searching operators in the neighborhood searching structure;
Step 206: if the current neighborhood search operator improves the current solution, skipping back to the first neighborhood search operator to perform the search from scratch; otherwise, executing the next neighborhood searching operator in sequence until all neighborhood searching operators are walked and no improvement is generated;
Step 207: judging whether the termination criterion is met, if not, repeating the steps 202-207 to re-execute the search, and if so, entering step 208;
Step 208: ending the algorithm, and outputting a global optimal solution s gb;
the input of the variable neighborhood search algorithm is weapon, number of targets, parameters and initial target coding sequence; the output is the global optimal solution s gb.
3. The multi-stage weapon goal distribution method based on variable neighborhood search according to claim 2, wherein in the variable neighborhood search algorithm, different neighborhood action alternate search mechanisms are used, real number coding sequences of the goals are used as operation objects of disturbance operators and neighborhood search operators, new solutions are found through local search, if the quality of the new solutions is worse than that of the current optimal solution, the next neighborhood search operator is selected, and if the new solutions are better than that of the current solution, the first neighborhood search operator is transferred to find the local optimal solution of the current solution; the disturbance operator comprises a point exchange operator, a turnover operator and a recombination operator, and the neighborhood search operator comprises two exchange operators, a turnover operator and a cross search operator.
4. The multi-stage weapon target distribution method based on variable neighborhood search according to claim 3, wherein the point cross converter is a slight disturbance structure, when the initial target coding sequence is transferred to the disturbance operator, two points in the target coding sequence array are randomly selected, and the disturbance operation can be completed by exchanging numbers; the turnover operator is a disturbance mode for changing a target coding sequence in a large area, and the turnover length is determined according to random numbers; the recombination operator regards the target coding sequence as a section of paper tape, randomly designates a section with a fixed width, and shuffles the numerical sequence of the target coding sequence in the section;
The two exchange operators search a local optimal solution of a neighborhood structure by exchanging a number and a neighbor with a fixed interval; the turnover operator realizes the search of local solutions by selecting two points with proper spacing and then turning over all numbers between the two points; the cross search operator is divided into three steps: firstly dividing a target coding sequence into four parts with equal length by adopting a quartering method, secondly traversing the front quarter point, sequentially intercepting fragments with fixed length, randomly selecting one from the other three parts to execute the same operation, and finally executing the overturning and crossing operation on the front and rear fragments.
5. The multi-stage weapon target allocation method based on variable neighborhood search according to claim 4, wherein the two exchange operators search for a local optimal solution by 2-interval, 3-interval and 4-interval search methods respectively.
6. The multi-stage weapon target allocation method based on variable neighborhood search according to claim 4, wherein the flipping operators are designed with lengths which are 0.1 times, 0.15 times and 0.2 times the length of the target coding sequence.
7. The multi-stage weapon target allocation method based on variable neighborhood search according to claim 2, wherein a greedy algorithm is used in the variable neighborhood search algorithm to construct a feasible solution.
8. The multi-stage weapon target allocation method based on variable neighborhood search according to claim 2, wherein a random factor is introduced into the variable neighborhood search algorithm, and a greedy algorithm is combined to construct a feasible solution, weapon allocation is sequentially carried out on each target to be allocated, and hit weapons are selected in a random manner, wherein the larger the damage probability of the weapons is, the higher the probability of being selected is, so that the capability of the algorithm to jump out of a local optimal solution is increased.
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