CN111709547A - Weapon-target distribution solution method based on multi-target particle swarm algorithm - Google Patents

Weapon-target distribution solution method based on multi-target particle swarm algorithm Download PDF

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CN111709547A
CN111709547A CN201910710202.8A CN201910710202A CN111709547A CN 111709547 A CN111709547 A CN 111709547A CN 201910710202 A CN201910710202 A CN 201910710202A CN 111709547 A CN111709547 A CN 111709547A
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张大巧
王超
李邦杰
鲜勇
振晓龙
赵久奋
雷刚
张卓
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Abstract

A weapon-target distribution solution based on a multi-target particle swarm algorithm is characterized in that a plurality of optimization target functions are established according to condition data, and a slave population and a master population which are the same in number with the functions are set. And respectively generating feasible solutions for each slave population as population particles and initializing, wherein the master population and the slave populations are evolved by cooperatively using a particle swarm algorithm, the slave populations search non-inferior solutions and transfer the non-inferior solutions to the master population, and the master population repairs gaps among the non-inferior solutions and generates a better Pareto optimal solution set. And iteratively updating the master population and the slave population until termination. The method provided by the invention meets the weapon-target allocation problem, considers a plurality of optimization targets at the same time, meets the requirements of a plurality of fighting intentions, and solves the problems that in the prior art, either the distributivity of the Pareto optimal solution set is poor, or the algorithm is easy to early converge and the solving precision is poor.

Description

Weapon-target distribution solution method based on multi-target particle swarm algorithm
Technical Field
The invention relates to a multi-target particle swarm algorithm-based weapon-target distribution solution, and belongs to the field of computer simulation and method optimization.
Background
Weapon-target distribution is a key link in the operation command, directly influences the progress and victory or defeat of the operation, and the core idea is to distribute the weapons to the target to be hit quickly and reasonably to obtain a better scheme meeting the operation intention and optimizing the target. The particle swarm optimization is an optimization algorithm commonly used for solving the weapon-target allocation problem, which has been deeply researched and remarkably developed when aiming at the problem of only one optimization target, but has the problem of slow optimization speed when being applied to the weapon-target allocation of a plurality of optimization targets.
Aiming at solving the weapon-target distribution problem of a plurality of optimization targets, a multi-target evolutionary algorithm based on a Pareto theory is widely adopted for optimization at present. In the prior art, an mpaco (modified particle ant Colony optimization) algorithm based on a new design operator improves a dynamic heuristic information calculation method, a motion probability rule, a dynamic evaporation rate strategy and a global update rule of pheromones. The MPACO algorithm has higher operation efficiency and higher solving precision, but the obtained Pareto optimal solution set has poorer distributivity and cannot better cover a better solution of a weapon-target distribution problem. Another strategy of the prior art to solve the weapon-target assignment problem for solving multiple optimization targets is to improve the particle swarm optimization algorithm. The improved multi-target particle swarm optimization algorithm is easy to implement, high in optimization speed and good in optimization effect, but the diversity of the population is lost rapidly, so that the algorithm is easy to early converge and fall into local optimization, and the problem of poor solving precision exists.
Disclosure of Invention
In view of the defects of the prior art, the invention aims to provide a weapon-target allocation solution based on a multi-target particle swarm algorithm, which is characterized in that a Pareto optimal solution set can better cover a better solution of a weapon-target allocation problem and has good solution precision.
A weapon-target distribution solution method based on multi-target particle swarm optimization comprises the following steps:
s100, modeling according to condition data of weapon-target distribution and an optimization target, determining the number of slave populations according to the number of functions of the optimization target, wherein the number of the slave populations is equal to the number of function models of the optimization target.
S200, respectively generating feasible solutions for each slave population to serve as population particles and initializing, wherein the master population is initialized to be empty.
S300, the main population and the auxiliary population are evolved by cooperatively using a particle swarm algorithm. And updating the particles from the population, searching the optimal solution corresponding to the target function, determining the non-inferior solution in the population and transferring the non-inferior solution to the main population. And after the main population updates the particles, receiving all non-inferior solutions of the slave population, and further searching the non-inferior solutions to generate a Pareto optimal solution set.
S400, judging whether a termination condition is met, if so, outputting a Pareto optimal solution set as a result, and if not, turning to the step S300.
Further, S300 includes randomly selecting one or more non-inferior solution replacement population from other population (S) after the population evolution is completed, wherein the particles have a lower fitness value.
Further, optimizing the target in S100 includes maximizing the operational effectiveness, which is the operational value of the cut target, and minimizing the weapon usage; fighting efficiency f1And weapon dosage f2Are respectively expressed as:
Figure BDA0002153476890000021
and
Figure BDA0002153476890000022
wherein VjTo impair the combat value of the target, pijProbability of damage to the ith target hit by the ith weapon, mijThe number of impacts on the jth target for the ith weapon.
Further, S300 includes limiting the number of particles in the main population; after the master population receives the non-inferior solution of the slave population, each particle x in the master population is calculatedidThe crowding distance may be expressed as:
Figure BDA0002153476890000023
wherein xjdAnd xkdIs equal to xidThe smallest distance particle; if the population size is limited to S, the main population only retains the first S particles with the largest congestion distance.
Further, randomly selecting one of the optimal particles as its local leader for each particle when updating the particles in S300
Figure BDA0002153476890000024
Adding a competition factor r when updating the particles3c3(lid-xid(t)), wherein lidIs composed of
Figure BDA0002153476890000025
Component in d-th dimension of search space, c3To be an acceleration factor, r3Is a random number of 0 to 1 inclusive.
Further, S100 includes normalizing the value coefficient in modeling. The normalization method is to calculate the sum of all the value coefficients and then let the single value coefficient be the ratio of the sum of the value coefficients. By doing so, the effectiveness of battle effectiveness optimization can be compared quickly and concisely after the optimization is finished.
Further, S200 includes that the coding mode does not distinguish the order of the same type weapons striking the same target, and the weapon usage is only expressed by one code, thereby greatly reducing the length of the code.
The technical scheme of the invention has the following beneficial effects: (1) and constructing a master and slave population coevolution model, wherein each slave population corresponds to an objective function, and searching a non-inferior solution of the objective function. And the master population receives the non-inferior solutions of the slave population, and the gaps existing between the non-inferior solutions are repaired to generate a better Pareto optimal solution set. Through the cooperative evolution model of the master and slave populations, the master and slave species groups can simultaneously develop different search areas of problems, so that better diversity of the populations is kept, and efficient cooperation and global search of a plurality of populations can be realized. (2) By using the multi-objective particle swarm algorithm and simultaneously considering a plurality of optimization targets, the distribution scheme can meet a plurality of fighting intentions and optimization targets of a decider. The Pareto optimal solution set obtained by optimizing the technical scheme has better distribution, and can better cover better solution of the WTA problem. (3) A competition factor is introduced into the method for updating the speed of the particles, the particles are guided to compete for searching along multiple directions, and the speed of searching non-inferior solutions by a population and repairing gaps among the non-inferior solutions is increased. Meanwhile, the competition factors also enable the particles to possibly evolve along the direction of the optimal particles in the local optimal area, multi-directional competition optimization of the particles is achieved, the situations of premature convergence and falling into local optimal in the optimization process can be avoided, and the global search efficiency is effectively improved.
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FIG. 1 is a flow chart of steps of an embodiment of the present invention;
FIG. 2 is a Pareto front-end comparison diagram of the calculation results of case 5 in the embodiment of the present invention.
Detailed Description
The weapon-target allocation solution based on the multi-target particle swarm algorithm of the invention will be further described in detail with reference to the drawings and specific embodiments of the specification.
The multi-target particle swarm algorithm-based weapon-target distribution solution is applied to the typical weapon-target distribution problem. Different cases are set based on the same background, optimization solution is respectively carried out by the method, and the weapon consumption value and the optimization consumption time which are finally optimized by the method are compared with other methods in the prior art.
The case background is that there are a total of ten different types of weapons striking twelve targets. The available amount of each weapon, the value coefficient of each target, and the maximum number of weapons that can be used per target are shown in table 1. The probability of damage to the target for each type of weapon is shown in table 2.
Figure BDA0002153476890000041
TABLE 1
Figure BDA0002153476890000042
TABLE 2
Based on the above background, 5 different cases were set, and each case included a usable type of weapon and a target of attack as shown in table 3.
Figure BDA0002153476890000051
TABLE 3
Aiming at each case, under the same software and hardware conditions, Matlab software is used for programming and simulating the case problem respectively by using the method, the method based on the MPACO algorithm and the method based on the improved particle swarm optimization algorithm, and the time (unit: second) consumed by optimizing the three algorithms and the optimized distribution result are recorded.
The programming and writing for optimization is performed with reference to the flow chart of fig. 1. First, S101 is executed to determine a plurality of optimization objectives for solving the case problem, which are required to be optimized with the greatest operational efficiency and the least weapon consumption. The effectiveness of the battle is to cut down the value of the target, and the value of the individual targets that can be weakened is Vj。
The effectiveness of combat can be expressed as:
Figure BDA0002153476890000052
this is the first optimization objectiveA function of (b), wherein pijProbability of damage to the ith target hit by the ith weapon, mijThe number of the ith weapon acting on the jth target is shown.
And carrying out normalization processing on the value coefficient for the subsequent quick and concise comparison of the optimization effect of the combat effectiveness. The normalization method is to calculate the sum of all the merit coefficients and then divide the single merit coefficient by the sum of the merit coefficients.
Weapon use may be expressed as:
Figure BDA0002153476890000053
this is a function of the second optimization objective.
Referring to Table 1, the maximum usage of type i weapons is NiThe aggressor uses C to the jth target at mostjA weapon. The functions of both optimization objectives satisfy
Figure BDA0002153476890000054
And
Figure BDA0002153476890000055
the conditions of (1).
Next, S102 is entered, because two functions of the optimization goal are determined in S101, corresponding slave population and a master population are respectively established for the two functions.
Next, S201 is executed to initialize the slave population. Different from the single-target optimization problem, the multi-target optimization problem does not have a unique optimal solution, and the optimal solution becomes a solution set which may contain infinite solutions and has mutually independent solutions, namely a Pareto optimal solution set. And calculating feasible solutions as particles of the slave population according to a Pareto principle and a function of target optimization. The main population is initially empty.
The feasible solution is coded in an integer coding mode based on the hit target, the length of the coding is N × M, namely the dimension D is N × M, wherein P1,P2,…,PN×1Representing the allocation of all N-weapons to the first target, PN+1,PN+2,…,PN×2Representing the allocation of all N-weapons to a second target, PN×(M-1)+1,PN×(M-2)+1,…,PN×MRepresenting the allocation of all N-weapons to target M, PiIs an integer not less than 0, i is 1,2, …, N × M.
And after the initialization of the master population and the slave population is finished, iterative updating based on a particle swarm algorithm is started. And S301 is executed, the particles are updated from the population, and the optimal solution corresponding to the objective function is searched.
Randomly selecting one of the optimal particles as its local leader for each particle when updating the particle
Figure BDA0002153476890000061
Adding a competition factor r when updating the particles3c3(lid-xid(t)), wherein c3To be an acceleration factor, r3Is a random number of 0 to 1 inclusive. The particle update method can be expressed as:
xid(t+1)＝xid(t)+wvid(t)+r1c1(pid-xid(t))+r2c2(gd-xid(t))+r3c3(lid-xid(t))
wherein p isidThe optimal solution, g, found for the particle itselfdFor the best solution currently found for the whole population,/idIs composed of
Figure BDA0002153476890000062
The component in the d-th dimension of the search space.
And determining non-inferior solutions in the slave population, transferring the non-inferior solutions to the master population, and randomly selecting one or more particles with lower fitness values in the non-inferior solution replacement population from other slave populations after the evolution of the slave population is completed.
Next, step S302 is executed, after the master population receives the non-inferior solutions from the slave population, the master population receives all the non-inferior solutions from the slave population, and generates a better Pareto optimal solution set by updating the particles to patch gaps existing between the non-inferior solutions. The particle update method of the master population is the same as that of the slave population.
Calculating each particle x in the main populationidThe crowding distance may be expressed as:
Figure BDA0002153476890000063
wherein xjdAnd xkdIs equal to xidThe smallest distance particle. If the population size is limited to S, the main population only retains the first S particles with the largest congestion distance.
And entering S401 after the iterative updating of the main population and the slave population is finished, checking whether the Pareto optimal solution set generated by the main population in S302 meets a preset iteration termination condition, if so, entering S402 to output the Pareto optimal solution set as an optimization finding result, and if not, returning to S301 to continue the iteration.
Figure BDA0002153476890000071
TABLE 4
Comparing the shortest time consumption, the longest time consumption and the time consumption of the three weapon-target distribution problem solution methods in the table 4, the time consumption of the method of the present invention is much less than that of the method in the prior art, and the optimization speed can be greatly increased when the weapon-target distribution problem with a plurality of optimization targets is solved by using the method of the present invention.
Fig. 2 shows a visualization result Pareto front end of the Pareto optimal solution set obtained by resolving case 5 respectively by using the method of the present invention, the method based on the MPACO algorithm, and the method based on the improved particle swarm algorithm, i.e. an optimized numerical relationship between the maximum operational effectiveness and the minimum weapon consumption. Compared with the weapon-target distribution problem solution method in the prior art, the Pareto front end optimized by the algorithm of the invention is closer to the real Pareto front end. The weapon-target distribution solution method based on the multi-target particle swarm algorithm is correct and effective, the distribution of the Pareto optimal solution set is good, premature convergence is not easy to occur in the optimization process, the solution precision is high, and good optimization results can still be obtained along with the increase of the problem scale.
It will be apparent to those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention also encompasses these modifications and variations.

Claims (7)

1. A weapon-target distribution solution method based on a multi-target particle swarm algorithm comprises the following steps:
s100, modeling according to condition data of weapon-target distribution and an optimization target, determining the number of slave populations according to the number of functions of the optimization target, wherein the number of the slave populations is equal to the number of function models of the optimization target;
s200, respectively generating feasible solutions for each slave population as population particles and initializing; initializing the main population to be empty;
s300, the main population and the auxiliary population are evolved by cooperatively using a particle swarm algorithm; updating particles from the population, searching the optimal solution corresponding to the target function, determining the non-inferior solution in the population and transferring the non-inferior solution to the main population; after the master population updates the particles, receiving all non-inferior solutions of the slave population, and further searching the non-inferior solutions to generate a Pareto optimal solution set;
s400, judging whether a termination condition is met, if so, outputting the Pareto optimal solution set as a result, and otherwise, turning to the step S300.
2. The multi-target particle swarm algorithm-based weapon-target distribution solution of claim 1, wherein S300 comprises randomly selecting one or more non-inferior solutions from other populations to replace the particles with lower fitness value in the population after population evolution is completed.
3. The multi-objective particle swarm optimization-based weapon-objective distribution solution as claimed in claim 1, wherein the optimization of objectives in S100 includes maximization of operational effectiveness and minimization of weapon consumption, and the operational effectiveness is reduction of objectivesThe value of the battle; fighting efficiency f1And weapon dosage f2Are respectively expressed as:
Figure FDA0002153476880000011
and
Figure FDA0002153476880000012
wherein VjTo impair the combat value of the target, pijProbability of damage to the ith target hit by the ith weapon, mijThe number of impacts on the jth target for the ith weapon.
4. The multi-target particle swarm algorithm-based weapon-target distribution solution of claim 2, wherein S300 comprises limiting the number of particles in the main population; after the master population receives the non-inferior solution of the slave population, each particle x in the master population is calculatedidThe crowding distance may be expressed as:
Figure FDA0002153476880000013
wherein xjdAnd xkdIs equal to xidThe smallest distance particle; if the population size is limited to S, only the first S particles with the largest crowding distance are retained in the main population.
5. The multi-target particle swarm algorithm-based weapon-target distribution solution as claimed in claim 3, wherein in S300, when updating the particles, for each particle, one of the optimal particles is randomly selected as its local leader
Figure FDA0002153476880000022
Adding a competition factor r when updating the particles3c3(lid-xid(t)), wherein lidIs composed of
Figure FDA0002153476880000021
Component in d-th dimension of search space, c3To be an acceleration factor, r3Is a random number of 0 to 1 inclusive.
6. The multi-target particle swarm algorithm-based weapon-target distribution solution as claimed in any one of claims 2 to 5, wherein S100 comprises normalization of the cost coefficients during modeling by calculating the sum of all the cost coefficients and then making the single cost coefficient as the ratio of the sum of the cost coefficients.
7. The multi-target particle swarm algorithm-based weapon-target distribution solution of any one of claims 1 to 5, wherein S200 comprises encoding the feasible solution based on hit targets in an integer encoding manner.
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