CN114861417A - 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 distributing the weapon targets according to the optimal solution obtained by solving. The method reduces the shooting pressure of a weapon platform by carrying out multi-wave times of planning and striking on the target, establishes a nonlinear integer programming model of a multi-stage weapon target distribution problem by taking the minimum target threat residual error as an optimized target under the condition of weapon resource constraint, designs two feasible solution construction algorithms based on a greedy strategy, provides several disturbance strategies and neighborhood search operators, and improves the distribution efficiency of remote accurate guided weapons.
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
The weapon target distribution problem is one of the most fundamental problems in the field of military operations research. The problem of weapon target distribution refers to distributing a certain number of weapons with damage effect to a plurality of targets of enemies so as to achieve the tactical intention with the maximum damage effect to enemies, and the important strategic resources of the enemies are destroyed to the maximum extent so that the enemies lose the fighting capacity, thereby winning the victory of local wars. From the number of strike periods, weapon target assignment 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 once, and is an ideal distribution scene with abundant weapon resources. The multi-stage problem considers the constraint of weapon resources and the influence of the target striking sequence on subsequent operations, and is closer to the actual operation scene. Most of the current researches on weapon target distribution are focused on the single-stage problem, however, in practical military application, especially in the scene of remote accurate guidance, due to the fact that the types and the number of targets to be hit are large, the maximum hitting capacity of a weapon platform in the same period is exceeded, and the single-stage weapon target distribution algorithm is not suitable for the situation. Therefore, the striking process needs to be divided into a plurality of waves according to the threat degree of the target and the constraints such as the number of the weapon platforms and the fire turning time, and the combat mission is completed by formulating weapon target striking schemes in a plurality of stages, so that the optimal target allocation is realized.
Disclosure of Invention
In view of the above, the present invention aims to provide a multistage weapon target distribution method based on variable neighborhood search. The method reduces the shooting pressure of a weapon platform by carrying out multi-wave planning striking on a target, establishes a non-linear integer programming model of a multi-stage weapon target distribution problem by taking the minimum target threat residual error as an optimized target under the condition of weapon resource constraint, designs two feasible solution construction algorithms based on a greedy strategy, provides several disturbance strategies and neighborhood search operators, and improves the distribution efficiency of remote accurate guided weapons.
The invention aims to realize a multistage weapon target distribution method based on variable neighborhood search, which comprises the following steps:
the multi-stage weapon target distribution model has the following objective functions:
the objective function represents minimizing the sum of threat residuals for all objectives,
the constraint conditions include:
where W ═ 1, …, m } denotes a set of all weapons, any weapon i ∈ W, N ∈ {1,2, …, N } denotes a set of all targets, and any target j ∈ N, V ∈ N j Representing the threat value of the jth target, the more important the target the greater its threat value, x tij Is a binary variable indicating whether the t stage assigns weapon i to target j, p ij Representing the damage probability of the ith weapon to the jth target, D j Represents the attack saturation value corresponding to the jth target, and no weapon is allocated to the jth target after the target reaches the saturation value, wherein S is {1,2, …, S }, the set of all stages, any stage t is belonged to S,representing the set of weapons that can be used during the t phase,representing the set of targets that need to be hit in the t phase, W f 1,2, …, f, representing a weapon launching platform set, wherein the total number of weapon launches in each stage does not exceed 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;
the formula (2) specifies that the damage of all weapons to the target is more than or equal to the attack saturation value specified by the target, and the weapons are stopped being distributed to the target when the damage sum reaches the saturation value; equation (3) specifies that a weapon can only be assigned to a target; equation (4) specifies that the sum of weapons used cannot exceed the inventory of weapons when the distribution is complete; formula (5) limits the firing capability of the weapon platform, and specifies that the number of weapons fired at each stage cannot exceed the limit of the firing platform; equation (6) indicates that the decision variable is a binary number, and in stage t, weapon i is assigned to target j and equals 1, otherwise equals 0.
Specifically, the variable neighborhood search algorithm and a mechanism of alternative selection of multiple neighborhood structures enable the algorithm to explore a solution space in a wider range, and comprises the following steps:
step 201: initializing parameters;
step 202: generating an initial solution s by a decoding algorithm 0 Calculating a corresponding objective function;
step 203: randomly selecting a perturbation operator to perturb the initial target coding sequence to generate a new target coding sequence;
step 204: introducing 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: performing local search on the current solution according to the sequence of neighborhood search operators in the neighborhood search structure;
step 206: if the current neighborhood search operator improves the current solution, jumping back to the first neighborhood search operator to perform search from the beginning; otherwise, executing the next neighborhood search operator in sequence until all neighborhood search operators are finished and no improvement is generated;
step 207: judging whether the termination criterion is reached, if not, repeating the step 202-the step 207 to re-execute the search, and if so, entering the step 208;
step 208: ending the algorithm and outputting a global optimal solution s gb ;
The input of the variable neighborhood searching algorithm is the number and parameters of weapons and targets and an initial target coding sequence; the output is the global optimal solution s gb 。
Furthermore, in the variable neighborhood search algorithm, different neighborhood action alternative search mechanisms are used, a real number coding sequence of a target is used as an operation object of a disturbance operator and a neighborhood search operator, a new solution is searched through local search, if the quality of the new solution is worse than that of the current optimal solution, the next neighborhood search operator is selected, and if the quality of the new solution is better than that of the current optimal solution, the first neighborhood search operator is switched to search for the local optimal solution of the current solution; the disturbance operator comprises a point exchange operator, an overturning operator and a recombination operator, and the neighborhood search operator comprises two exchange operators, an overturning operator and a cross search operator.
Specifically, the point exchange operator is a slight perturbation structure, after an initial target coding sequence is transmitted to the perturbation operator, two points in a target coding sequence group are randomly selected, and the perturbation operation can be completed by exchanging numbers; the turning operator is a disturbance mode for changing a target coding sequence in a large area, and the turning length is determined according to a random number; the recombination operator regards the target coding sequence as a paper tape, randomly designates a segment with a fixed width, and scrambles the numerical sequence of the target coding sequence in the segment by adopting a shuffling mode;
the two exchange operators search a local optimal solution of a neighborhood structure by exchanging a number and neighbors of the number at fixed intervals; the turning operator selects two points with proper spacing and then turns all numbers between the two points to realize the search of a local solution; the cross search operator is divided into three steps: firstly, a target coding sequence is divided into four parts with equal length by adopting a quartering method, secondly, the first quarter of points are traversed, the segments with fixed length are intercepted in sequence, one of the other three parts is randomly selected to execute the same operation, and finally, the front segment and the rear segment are executed with the overturning and crossing operation.
Preferably, the two swapping operators search for the local optimal solution by 2-interval, 3-interval and 4-interval searching methods respectively.
Preferably, the turning operators are designed to be 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 a feasible solution.
Furthermore, a random factor is introduced into the variable neighborhood search algorithm, a feasible solution is constructed by combining a greedy algorithm, distribution of weapons is carried out on each target to be distributed in sequence, and hit weapons are selected in a random mode, wherein the larger the damage probability of the weapons is, the higher the selection probability is, so that the capability of the algorithm for jumping out of a local optimal solution is increased.
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 multi-wave target striking.
Drawings
FIG. 1 is a schematic overall flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating a real number encoding method according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating an example of a cross search operator according to an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the accompanying drawings, but the invention is not limited in any way, and any alterations or substitutions based on the teaching of the invention are within the scope of the invention.
Assuming that an attacker has m weapons, and intends to launch an attack on n targets at a distance, the attack is limited by f weapon launching platforms (f < n), and the attack on all targets is planned to be completed in s stages. In this embodiment, weapons of the same parameters may be considered different weapons, with each projectile causing damage to only one target at a time, but one target may receive the bombings of multiple targets until the corresponding saturation value is reached. And a mixed integer nonlinear programming model of multi-stage weapon target task allocation is established by taking minimized threat residuals of all the hit objects as an optimization target.
As shown in fig. 1, the multi-stage weapon target distribution method based on variable neighborhood search comprises the following steps:
and 3, distributing the weapon targets according to the optimal solution obtained by solving.
The following notation is involved in the embodiments to describe a multi-stage weapon target assignment model:
the weapon distribution system faces more uncertainty, subject to realistic complex environments. The multi-stage weapon target distribution method studied in this embodiment makes the following assumptions in order to reduce complexity:
the number of targets in each scene is fixed, and once the sensing system finishes detection, the targets cannot escape or be newly added;
(II) one weapon can only 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 the target stops being allocated with the weapon when reaching the attack saturation value.
In accordance with the above assumptions, the present embodiment builds a multi-stage weapon target assignment model of the form:
equation (1) is an objective function, and equations (2) to (6) are constraints. Equation (1) represents minimizing the sum of threat residuals for all targets. The method is expected to reduce the survival probability of the target with the high threat value in the battle so as to achieve a better attack effect. The formula (2) specifies that the damage of all weapons to the target is not lower than the attack saturation value specified by the target, and the weapons are stopped being distributed to the target when the damage sum reaches the saturation value; 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 weapons used cannot exceed the inventory of weapons when the allocation is complete; formula (5) limits the firing capability of the weapon platform, and specifies that the number of weapons fired at each stage cannot exceed the limit of the firing platform; equation (6) indicates that the decision variable is a binary number, and in stage t, weapon i is assigned to target j and equals 1, otherwise equals 0.
The variable neighborhood search is an improved local search algorithm, a mechanism of alternative selection of various neighborhood structures enables the algorithm to explore a solution space in a wider range, and the local optimization and global optimization capacities are considered, wherein a multi-stage weapon target search algorithm frame based on the variable neighborhood search is as follows:
in algorithm 1, a mechanism of alternately searching by using different neighborhood actions is called a variable neighborhood searching structure, and comprises a plurality of neighborhood searching operators, also called neighborhood actions. In this embodiment, a real number encoding list of a target is used as an operation object of an operator, a new solution is searched through local search, if the quality of the new solution is worse than the current optimal solution, a next neighborhood operation operator is selected, and if the quality of the new solution is better than the current solution, the first neighborhood operator is switched to search for the local optimal solution of the current solution. The operator design of the variable neighborhood search structure needs to consider the width and the precision of a neighborhood, when a small-scale problem is solved, people pay more attention to the precision, and an algorithm can find an optimal solution with a higher probability only when the precision is higher. However, when the scale of the problem becomes larger, the high-precision local search results in unacceptable algorithm execution time, so we need to solve the problem in a coarser search manner to shorten the solution time.
The encoding mode comprises the following steps:
for the multi-stage weapon target distribution problem, the binary code is directly used for constructing the three-dimensional array to execute the search principle, 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 encoding method based on the target to 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 to one, and the representation method is shown in fig. 2.
Decoding strategy:
in the variable neighborhood search algorithm, the convergence speed and the search quality of the algorithm are influenced by the construction mode of feasible solution. The present embodiment proposes to construct a feasible solution using a greedy algorithm and a greedy algorithm that introduces a random factor to decode the target sequence.
The greedy strategy-based algorithm is a structured heuristic algorithm, and only the most favorable combination for the current task is concerned in each step in the process of constructing a feasible solution. The following is a pseudo-code representation of the greedy strategy algorithm to construct the initial solution:
in the variable neighborhood search, a feasible solution is constructed by using a greedy algorithm, the probability of trapping the algorithm into local optimum is higher, in order to enable the algorithm to jump out of the local optimum, a random factor is introduced into the second construction method, and the feasible solution is constructed by combining the greedy algorithm. And sequentially distributing the weapons to each target to be distributed, and selecting the hit weapons in a random mode, wherein the larger the damage probability of the weapons is, the higher the probability of selection 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 distribution method, two parts are needed to design an operation operator, wherein the first part is a perturbation 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 the disturbance structure. Three types of operators are designed for the variable neighborhood part, and seven neighborhood search operators are obtained in total by changing the shape parameter value.
And (3) disturbance operator:
(1) a point exchange operator: the point exchange operator is a slight disturbance structure, after the initial target code is transmitted to the disturbance operator, two points in the array are randomly selected, and the disturbance operation can be completed by exchanging numbers.
(2) And (3) turning over an operator: different from a point exchange operator, the turnover operator is a disturbance mode for changing an original sequence in a large area, the turnover length is determined according to random numbers, the large change is helpful for jumping out of a multi-local optimal solution, but the probability of jumping over the global optimal solution is also large.
(3) And (3) recombination operator: in order to achieve the balance between the ability of jumping out of local optimum and the search precision, a recombination operator is designed. The target sequence is regarded as a paper tape, a segment with a fixed width is randomly assigned, and the numerical sequence is disturbed in the segment by adopting a shuffling mode. The method can not only retain the original structural characteristics to a certain extent, but also can disturb the current sequence more violently.
Neighborhood search operator
(1) Two swap operators: two-exchange operation is a traditional neighborhood search method, which searches for a locally optimal solution of a neighborhood structure by exchanging a number with its neighbors at fixed intervals. In the algorithm, 2-interval, 3-interval and 4-interval searching methods are respectively adopted to find local optimal solutions.
(2) And (3) turning over an operator: the flip operator performs the search of the local solution by selecting two points with a suitable spacing and then flipping all numbers between the two points. In this algorithm we have designed flip operators with lengths of 0.1, 0.15 and 0.2 times the total target sequence length.
(3) And (3) a cross search operator: the cross search operator is divided into three steps: firstly, an original sequence is divided into four parts with equal length by adopting a quartering method, secondly, the first quarter of points are traversed, the fragments with fixed length are intercepted in sequence, one fragment is randomly selected from the other three parts to execute the same operation, and finally, the front fragment and the rear fragment are executed with overturning cross operation, as shown in figure 3.
According to the content and the embodiment of the invention, aiming at the problems of limitation of the number of remote accurate guided weapon launching platforms and high ammunition cost in large-scale military operation, the invention provides a multi-stage weapon target distribution method, the shooting pressure of the weapon platform is reduced by carrying out multi-wave planning striking on targets, a non-linear integer programming model of the multi-stage weapon target distribution problem is established by taking the minimum target threat residual error as an optimized target under the condition of constraint of weapon resources, two feasible solution construction algorithms based on a greedy strategy 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. The multi-stage weapon target distribution method based on variable neighborhood search is characterized by comprising 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, carrying out weapon target distribution according to the optimal solution obtained by solving;
the multi-stage weapon target distribution model has the following objective functions:
the objective function represents minimizing the sum of threat residuals for all objectives,
the constraint conditions include:
where W ═ 1, …, m } denotes a set of all weapons, any weapon i ∈ W, N ∈ {1,2, …, N } denotes a set of all targets, and any target j ∈ N, V ∈ N j Representing the threat value of the jth target, the more important the target the greater its threat value, x tij Is a binary variable indicating whether the t stage assigns weapon i to target j, p ij Representing the damage probability of the ith weapon to the jth target, D j Represents the attack saturation value corresponding to the jth target, and no weapon is allocated to the jth target after the target reaches the saturation value, wherein S is {1,2, …, S }, the set of all stages, any stage t is belonged to S,representing the set of weapons that can be used during the t phase,representing the set of targets that need to be hit in the t phase, W f 1,2, …, f, representing a weapon launching platform set, wherein the total number of weapon launches in each stage does not exceed 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;
the formula (2) specifies that the damage of all weapons to the target is more than or equal to the attack saturation value specified by the target, and the weapons are stopped being distributed to the target when the damage sum reaches the saturation value; equation (3) specifies that a weapon can only be assigned to a target; equation (4) specifies that the sum of weapons used cannot exceed the inventory of weapons when the distribution is complete; formula (5) limits the firing capability of the weapon platform, and specifies that the number of weapons fired at each stage cannot exceed the limit of the firing platform; equation (6) indicates that the decision variable is a binary number, and in stage t, weapon i is assigned to target j and equals 1, otherwise equals 0.
2. The method for assigning a multi-stage weapon target based on variable neighborhood search according to claim 1, wherein the variable neighborhood search algorithm, a mechanism for alternately selecting multiple neighborhood structures, enables the algorithm to explore a wider solution space, comprising the following steps:
step 201: initializing parameters;
step 202: generating an initial solution s by a decoding algorithm 0 Calculating a corresponding objective function;
step 203: randomly selecting a perturbation operator to perturb the initial target coding sequence to generate a new target coding sequence;
step 204: introducing 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: performing local search on the current solution according to the sequence of neighborhood search operators in the neighborhood search structure;
step 206: if the current neighborhood searching operator improves the current solution, jumping back to the first neighborhood searching operator to perform searching from the beginning; otherwise, executing next neighborhood searching operator in sequence until all neighborhood searching operators are finished and no improvement is generated;
step 207: judging whether the termination criterion is reached, if not, repeating the step 202-the step 207 to re-execute the search, and if so, entering the step 208;
step 208: ending the algorithm and outputting a global optimal solution s gb ;
The input of the variable neighborhood searching algorithm is the number and parameters of weapons and targets and an initial target coding sequence; the output is the global optimal solution s gb 。
3. The method for assigning targets to weapons in multiple stages based on variable neighborhood search according to claim 2 wherein, in the variable neighborhood search algorithm, a different mechanism of alternative neighborhood search is used, the real coded sequence of targets is used as the operation object of the perturbation operator and the neighborhood search operator, a new solution is found by local search, if the quality of the new solution is worse than the current optimal solution, the next neighborhood search operator is selected, and if the quality of the new solution is better than the current solution, the first neighborhood search operator is switched to find the local optimal solution of the current solution; the disturbance operator comprises a point exchange operator, an overturning operator and a recombination operator, and the neighborhood search operator comprises two exchange operators, an overturning operator and a cross search operator.
4. The method of claim 3, wherein the point exchange operator is a slightly perturbed structure, and when the initial target code sequence is transmitted to the perturbing operator, two points in the target code sequence set are randomly selected, and the perturbation operation can be completed by exchanging numbers; the turning operator is a disturbance mode for changing a target coding sequence in a large area, and the turning length is determined according to a random number; the recombination operator regards the target coding sequence as a paper tape, randomly designates a segment with a fixed width, and scrambles the numerical sequence of the target coding sequence in the segment by adopting a shuffling mode;
the two exchange operators search a local optimal solution of a neighborhood structure by exchanging a number and neighbors of the number at fixed intervals; the turning operator selects two points with proper spacing and then turns all numbers between the two points to realize the search of a local solution; the cross search operator is divided into three steps: firstly, a target coding sequence is divided into four parts with equal length by adopting a quartering method, secondly, the first quarter of points are traversed, the fragments with fixed length are intercepted in sequence, one fragment is randomly selected from the other three parts to execute the same operation, and finally, the front fragment and the rear fragment are executed with overturning cross operation.
5. The method of claim 4, wherein the two swap operators search for locally optimal solution at 2, 3 and 4 intervals, respectively.
6. The method of claim 4, wherein the flipping operators are designed to have lengths of 0.1, 0.15 and 0.2 times the length of the target coding sequence.
7. The method of claim 2, wherein a greedy algorithm is used in the variable neighborhood search algorithm to construct the feasible solution.
8. The multi-stage weapon target distribution method based on variable neighborhood search according to claim 2, characterized in that a random factor is introduced into the variable neighborhood search algorithm, a feasible solution is constructed by combining with a greedy algorithm, distribution of weapons is performed on each target to be distributed in sequence, 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 as to increase the ability of the algorithm to jump out of the local optimal solution.
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