Double-target dynamic weapon distribution method and system based on simplified double populations

Abstract

The invention provides a double-target dynamic weapon distribution method and system based on simplified double populations, and the method comprises the steps: 1, building a double-target dynamic weapon distribution problem mathematical model which comprises a target function and a constraint condition; 2, on the basis of decimal coding, an initial population 1 meeting constraint conditions is generated through a population generation strategy guided by an objective function, a population 2 meeting the constraint conditions is generated through an uncertainty initialization method, and the population 1 serves as a main population; step 3, sorting the population 1 by using a constraint distribution principle, and sorting the population 2 by rapid non-dominated sorting; and step 4, based on the sorting of the population 1 and the population 2, performing iterative updating on the population 1 and the population 2 by adopting a simplified updating method and a feasible exchange strategy, and obtaining a Pareto frontier solution according to the value of the individual in the population 1. The method is suitable for double-target or multi-target problems of discreteness, large infeasible region and the like.

Description

Technical Field

[0001] The invention relates to a weapon target allocation problem, and in particular to a dual-target dynamic weapon allocation method and system based on simplified dual populations. Background Art

[0002] With the development of new technologies such as artificial intelligence and unmanned systems, more and more scholars are studying the problem of weapon target allocation. The problem of weapon target allocation is to solve the problem of how to allocate multiple combat weapons to multiple strike targets. Among many optimization problems, the problem of weapon target allocation belongs to a large family of nonlinear allocation problems, and its research can often be applied to other optimization problems.

[0003] From the perspective of whether time is considered, the weapon target allocation problem can be divided into static weapon target allocation problem and dynamic weapon target allocation problem; from the perspective of the number of optimization targets, the weapon target allocation problem can be divided into single-target weapon target allocation problem and multi-target weapon target allocation problem. This paper studies the dual-target dynamic weapon target allocation problem. For different weapon target allocation problems, mathematical programming, game theory, graph theory, Markov decision and other methods are used to describe and model the weapon target allocation problem.

[0004] Most scholars consider two aspects in setting the objective function, which can be summarized as maximizing the expected interception rate and minimizing the cost. The dynamic weapon target allocation problem can be divided into two categories: "shoot-observe-shoot" and "two-stage" models. In "shoot-observe-shoot", weapons are assigned to targets in the first engagement, and subsequent engagements allow the remaining weapons to be assigned to any surviving targets; the "two-stage" model can also be called a "multi-stage" model. The difference from the "shoot-observe-shoot" model is that the battlefield situation after a certain stage of engagement is an unknown black box, and only the posterior probability distribution can be obtained.

[0005] The algorithms for solving the dynamic weapon target allocation problem are mainly heuristic algorithms, but there are also some precise algorithms, reinforcement learning, and machine learning algorithms. In single-objective problems, common heuristic algorithms include genetic algorithms (GA), particle swarm optimization (PSO), ant colony optimization (ACO), artificial bee colony algorithm (ABC), etc. In multi-objective problems, NSGA, NSGA-II, and NSGA-III are classic algorithms that are often used to solve the Pareto frontier. In recent years, multi-objective evolutionary algorithms (MOEA) have also been introduced to solve multi-objective weapon target allocation problems.

[0006] The multi-objective dynamic weapon target assignment problem belongs to a discrete constrained multi-objective optimization problem, while the multi-objective evolutionary algorithm mainly solves the unconstrained multi-objective optimization problem. In order to effectively handle constraints, constraint handling techniques (CHTs) are designed to compare feasible and infeasible solutions. However, the combination of the multi-objective evolutionary algorithm and the constraint handling techniques cannot effectively balance the objectives and constraints. Summary of the invention

[0007] The purpose of the present invention is to provide a dual-target dynamic weapon allocation method and system based on simplified dual populations, which can effectively balance targets and constraints and reduce resource consumption of later auxiliary populations.

[0008] The technical solution to achieve the purpose of the present invention is:

[0009] A dual-target dynamic weapon allocation method based on simplified dual populations is applicable to the dual-target dynamic weapon target allocation problem, including:

[0010] Step 1, establish a mathematical model of the dual-objective dynamic weapon allocation problem, including objective functions and constraints;

[0011] Step 2: Based on decimal coding, the objective function-oriented population generation strategy is used to generate the initial population 1 that meets the constraints, and the uncertainty initialization method is used to generate the population 2 that meets the constraints, where population 1 is used as the main population;

[0012] Step 3, sort population 1 using the constraint assignment principle, and sort population 2 using fast non-dominated sorting;

[0013] Step 4: Based on the ranking of population 1 and population 2, a simplified update method and a feasible exchange strategy are used to iteratively update population 1 and population 2 respectively, and the Pareto front solution, i.e., the allocation plan, is obtained according to the values ​​of individuals in population 1.

[0014] Furthermore, the objective function is:

[0015]

[0016] Where f1 is the total expected threat value of all targets, f2 is the total expected cost of all weapons, Nstg is the total number of stages considered in the problem, Nwpn is the number of weapons, Ntgt is the number of targets, is the decision variable of the hth stage. If weapon w is assigned to target e of the hth stage, then otherwise v e is the threat value of target e, is the probability that weapon w destroys target e in stage h, c w is the cost of weapon w.

[0017] Furthermore, the constraint condition is:

[0018]

[0019]

[0020] Among them, n h，w is the firing frequency of weapon w at stage h, m h，e is the number of weapons assigned to target e in stage h, a w The amount of ammunition equipped for weapon w, is the matrix of participation feasibility. If weapon w can hit target e in stage h, then otherwise

[0021] Furthermore, in the target function-oriented population generation strategy, each time allocation is performed, first, in the available target set T * Find the target τ with the highest threat level in the target τ, which has the first priority and is assigned to the weapon ω in stage σ, where stage σ and weapon ω are selected according to the highest interception rate; after each valid allocation, update p[σ, ω, τ], υ[τ], μ[σ, τ], α[ω] and T for the next allocation * ; Where p[σ, ω, τ] is the temporary interception success rate copied during the initialization process, v[τ] is the temporary threat level, μ[σ, τ] is the weapon quantity constraint of target τ at stage σ related to constraint formula (4), and α[ω] is the remaining ammunition equipment of weapon ω related to constraint formula (5).

[0022] Furthermore, the population generation strategy guided by the objective function specifically includes:

[0023] Step 5-1, initialize population X = 0 Nstg×Nωpn , initialization parameters T*=T, v=V, μ=M, α=a;

[0024] Step 5-2, except for The goal is e, if Jump to step 9, otherwise execute step 5-3;

[0025] Step 5-3, in the available target set T * Select the target τ with the highest threat level v[τ];

[0026] Step 5-4, determine the stage σ and weapon ω according to the highest interception rate, and obtain the tuple (σ, ω), the stage σ and weapon ω satisfy: x σ，ω =0, α[ω]>0, μ[σ,τ]>0 and has the highest interception rate p[σ,ω,τ];

[0027] Step 5-5, if In T * Remove target τ, i = i + 1, and jump to steps 5-8, otherwise target τ is assigned to weapon ≠ in stage σ;

[0028] Step 5-6, update the temporary parameters x[σ,ω]=τ, α[ω]=α[ω]-1, μ[σ,τ]=μ[σ,τ]-1, v[τ]=v[τ]×p[σ,ω,τ]';

[0029] Step 5-7, let p[σ, ω, e] = 0 for

[0030] Steps 5-8, repeat the above steps until i>Nasn, and obtain population 1, where Nasn is the maximum number of allocations.

[0031] Furthermore, when the uncertainty initialization method generates a population 2 that satisfies the constraints, each time an allocation is made, the weapon ω with the minimum cost is found in the weapon set W, and then all stages σ are traversed to randomly select a weapon ω to ensure that it satisfies the constraint formula (6). After each effective allocation, α[ω], μ[σ, τ] and W are updated for the next allocation. Each time the uncertainty initialization method generates a feasible initial solution, the process is repeated. times, get An initial solution, C IIS is the setting coefficient.

[0032] Furthermore, the maximum number of allocations of the objective function-guided population generation strategy and uncertainty initialization method is Where Nvar=Nstg×Nwpn.

[0033] Furthermore, the simplified updating method specifically includes: in each iteration t of the evolution stage, by comparing with two preset parameters Cg and Cr, updating Each variable in for Each variable in are set to The value with the same index in , HQ or random feasible value x, where HQ is a solution randomly selected from the Pareto front obtained by the constraint assignment principle or fast non-dominated sorting, and the random feasible value x is a random feasible value taken according to the comparison of uniform random number ρ in the range of [0, 1].

[0034] Furthermore, the feasible exchange strategy is: when λ<C FES When the input solution is a feasible solution, traverse all target tuples (t1, t2) in the solution, and satisfy t1≠t2, and then calculate the cv value of the exchanged solution. The exchanged solution is a feasible solution, where λ is a random number between [0, 1], C FES is a custom swap threshold and C FES ∈(0,1).

[0035] A dual-target dynamic weapon allocation system based on simplified dual populations includes a model building unit, a population initialization unit, a sorting unit and a population optimization unit, wherein:

[0036] The model building unit is used to build a mathematical model of the dual-target dynamic weapon allocation problem, including an objective function and constraint conditions;

[0037] The population initialization unit generates an initial population 1 that meets the constraint conditions based on decimal coding and adopts a population generation strategy guided by an objective function, and generates a population 2 that meets the constraint conditions using an uncertainty initialization method, wherein population 1 is used as a main population;

[0038] The sorting unit sorts population 1 using a constraint allocation principle and sorts population 2 using a fast non-dominated sort;

[0039] The population optimization unit iteratively updates population 1 and population 2 respectively based on the ranking of population 1 and population 2 by using a simplified update method and a feasible exchange strategy, and obtains a Pareto front solution, i.e., an allocation scheme, according to the values ​​of individuals in population 1.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] (1) The simplified update method of the present invention sets the individual evolution method of the population to inheritance, randomness or excellent genes according to a certain probability, so as to achieve a more efficient way of evolving the population;

[0042] (2) The present invention generates two sets of initial solution generation methods, namely, a population generation strategy guided by an objective function and an uncertainty initialization method, through two objective functions in a dual-objective dynamic weapon target allocation model, thereby realizing the generation of several high-quality initial solutions through the knowledge of a specific problem;

[0043] (3) The feasible exchange strategy of the present invention exchanges the targets of feasible allocation. This method ensures that the solutions before and after the exchange are feasible solutions, thereby enhancing the local exploration capability of the simplified dual population algorithm.

[0044] (4) The present invention is applicable to dual-objective or multi-objective problems such as discreteness and large infeasible domain. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 Flowchart of the initialization method for objective function-guided population generation.

[0046] Figure 2 Flowchart of the dual-target dynamic weapon allocation method based on simplified dual populations. DETAILED DESCRIPTION

[0047] Next, the implementation of the present invention will be described in detail with reference to the accompanying drawings.

[0048] See attached Figure 2 The present invention designs a dual-target dynamic weapon allocation method based on simplified dual populations. The method is mainly divided into three parts: 1) simplified update method; 2) objective function-guided population generation method; 3) feasible exchange method. First, according to the DPVAPS algorithm framework, its evolution mode is changed. Secondly, according to the two objective functions, several feasible high-quality solutions are generated for the population. Finally, individuals are exchanged with a certain probability. Specifically, the steps include:

[0049] 1. Establish a mathematical model for the dual-target dynamic weapon allocation problem:

[0050] The objective function of the dual-target dynamic weapon target assignment problem is:

[0051]

[0052] Among them, N stg is the total number of stages considered in the problem, Nwpn is the number of weapons, Ntgt is the number of targets, is the decision variable of the hth stage. If weapon w is assigned to target e of the hth stage, then otherwise v eis the threat value of target e, is the probability that weapon w destroys target e in stage h, c w For the cost of weapons ω.

[0053] The constraints are as follows:

[0054]

[0055] Among them, n h，m is the firing frequency of weapon ω at stage h, m h，e is the number of weapons assigned to target e in stage h, a w The amount of ammunition equipped for weapon w, is the matrix of participation feasibility. If weapon w can hit target e in stage h, then otherwise

[0056] The total expected threat value of all targets is minimized as the objective function f1 of the dual-objective DWTA, as shown in formula (1). The total expected cost of all weapons is minimized as the objective function f2 of the dual-objective DWTA, as shown in formula (2).

[0057] Formula (3) is the capability constraint of the weapon. It limits the number of targets that the weapon can attack at each stage. Usually, n w The value of is set to 1 because most weapons can only attack one target at a time. Special weapons that can attack multiple targets at the same time can be considered as multiple independent weapons. Formula (4) ensures that at most m can be assigned to target e at stage h. h，e Formula (5) ensures that the ammunition consumption of a weapon w in all stages cannot exceed its predefined allowance a w . Formula (6) is the time window constraint, which takes into account the impact of the time window on the attack feasibility of the weapon. It ensures that any shot fired by the weapon at each stage must meet the attack feasibility. According to formula (2), it is easy to see that the cost is minimum when no weapon is assigned to the target. However, this is usually inconsistent with the actual situation. Therefore, formula (7) is proposed, which requires that the weapon must make a certain number of effective allocations. Finally, all decision variables All must be binary.

[0058] 2. Use decimal encoding to encode and decode the population. Initialize population 1 through the objective function-guided population generation strategy, and randomly initialize population 2. The objective function-guided population generation strategy can be described as:

[0059] The objective function-guided population generation strategy aims to generate a good initial solution through problem-specific knowledge to improve the quality of the solution and the convergence speed, e.g. Figure 1 As shown in Figure 2. In dual-objective DWTA, there are two objective functions, corresponding to two initialization schemes: deterministic initialization method and uncertain initialization method. In both schemes, the maximum number of allocations, i.e., Nasn, is given by Determine, where Nvar=Nstg×Nwpn.

[0060] In the deterministic initialization method, in each allocation, first, we need to find the target set T in the available target set. * Find the target ω with the highest threat level in the target τ, which will be assigned to the weapon ω with the first priority in stage σ, where the stage σ and weapon ω are selected according to the highest interception rate. And as long as the interception rate is greater than 0, it is guaranteed that the assignment satisfies constraint (6). After each valid assignment, p[σ, ω, τ], υ[τ], μ[σ, τ], α[ω] and T need to be updated for the next assignment. * Among them, p[σ, ω, τ] is the temporary interception success rate copied during the initialization process, υ[τ] is the temporary threat level, μ[σ, τ] is the target τ related to constraint (4) at stage σ weapon quantity constraint, α[ω] is the remaining ammunition equipment of weapon ω related to constraint (5). The specific pseudo code is as follows:

[0061]

[0062] Since objective function 1 has more parameters and a more complex form, the initial solution can be generated deterministically. However, objective function 2 is only affected by the cost matrix and the participation feasibility matrix, which inevitably introduces randomness in the selection process, resulting in the number of initial solutions generated by the uncertain initialization method being non-unique. Considering that the number of generated initial solutions is uncertain, the coefficient C is introduced here IIS , which indicates that the number of initial solutions generated by the uncertain initialization method is in the total population number N pop The proportion of each time Algorithm 2 can generate a feasible initial solution, and repeat the operation times, you can get An initial solution.

[0063] In the uncertain initialization method, for each allocation, find the weapon ω with the minimum cost in the weapon set W. Then traverse all stages σ and randomly select weapons ω to ensure that they satisfy constraint (6). After each valid allocation, update α[ω], μ[σ, τ] and W for the next allocation. Where α[ω] and μ[σ, τ] are defined the same as in the deterministic initialization method, so as to avoid violating constraints (4), (5), (6). The specific pseudo code is as follows:

[0064]

[0065]

[0066] 3. Sort population 1 and population 2 using the constrained assignment principle and fast non-dominated sort respectively.

[0067] 4. Enter the population update main loop, and use the simplified update method and feasible exchange strategy to update population 1 and population 2 respectively. Finally, output the Pareto front solution to obtain population 1. The simplified update method and feasible exchange strategy can be described as:

[0068] The simplified update method is: in each iteration t of the evolution stage, by comparing with two preset parameters Cg and Cr, here Cg = 0.6, Cr = 0.61, update one by one Each variable in Specifically, for Each variable in It is in turn set to The value of the same index in , HQ, or a random feasible value x taken according to the comparison of a uniform random number ρ in the range [0, 1]. Where HQ is a randomly selected solution from the Pareto front obtained by the constraint domination principle (CDP) or fast non-dominated sorting. It is designated as a high-quality solution and is passed to the next generation with a certain probability. The simplified update method can be expressed by formula (9).

[0069]

[0070] in, is the i-th solution in the population at the t-th iteration, Nvar is the total number of variables in the solution, Npop is the number of solutions in the population, HQ is a high-quality solution randomly selected from the Pareto front, and x is a random integer in the range [0, Ntgt].

[0071] The feasible exchange strategy focuses on the exploration ability of the neighborhood of the current solution. FES When the input solution is a feasible solution, traverse all target tuples (t1, t2) in the solution. To ensure effective exchange, t1≠t2 must be satisfied. Then calculate the cv value of the exchanged solution to ensure that the exchanged solution is a feasible solution. FES is a custom swap threshold and C FES ∈(0,1).

[0072] This embodiment also provides a dual-target dynamic weapon allocation system based on a simplified dual population, including a model building unit, a population initialization unit, a sorting unit and a population optimization unit, wherein:

[0073] The model building unit is used to build a mathematical model of the dual-target dynamic weapon allocation problem, including an objective function and constraint conditions;

[0074] The population initialization unit generates an initial population 1 that meets the constraint conditions based on decimal coding and adopts a population generation strategy guided by an objective function, and generates a population 2 that meets the constraint conditions using an uncertainty initialization method, wherein population 1 is used as a main population;

[0075] The sorting unit sorts population 1 using a constraint allocation principle and sorts population 2 using a fast non-dominated sort;

[0076] The population optimization unit iteratively updates population 1 and population 2 respectively based on the ranking of population 1 and population 2 by using a simplified update method and a feasible exchange strategy, and obtains a Pareto front solution, i.e., an allocation scheme, according to the values ​​of individuals in population 1.

[0077] The present invention uses the method to generate a set of dual-target dynamic weapon target allocation problem data with 5 stages, 20 weapons and 60 targets, and uses NSGA2, DPVAPS and simplified dual population algorithm (SDP) to conduct comparative experiments. Each algorithm runs independently 10 times and calculates the average value, and limits the population size to 100, and limits the number of objective function calculations to 5*10e4. Inverse generation distance (IGD), generation distance (GD) and diversification index (DM) are used as evaluation indicators. The results are shown in the table:

[0078]

[0079] From the table results, we can see that compared with NSGA2 and DPVAPS, the SDP algorithm has the lowest IGD and GD values ​​and the highest DM value, indicating that the SDP algorithm proposed in this application has the best convergence, exploration ability and diversity.

[0080] Based on the dual-population variable assisted population sizing (DPVAPS) algorithm with variable auxiliary population size, the present invention proposes a dynamic population size reduction mechanism, which can reduce the resource consumption of the later auxiliary population and introduce an external archived auxiliary population to provide more feasible solutions for the main population.

[0081] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A dual-target dynamic weapon allocation method based on simplified dual population, characterized in that: include: Step 1, establish a mathematical model of the dual-objective dynamic weapon allocation problem, including objective functions and constraints; Step 2: Based on decimal coding, the objective function-oriented population generation strategy is used to generate the initial population 1 that meets the constraints, and the uncertainty initialization method is used to generate the population 2 that meets the constraints, where population 1 is used as the main population; Step 3, sort population 1 using the constraint assignment principle, and sort population 2 using fast non-dominated sorting; Step 4: Based on the ranking of population 1 and population 2, a simplified update method and a feasible exchange strategy are used to iteratively update population 1 and population 2 respectively, and the Pareto front solution, i.e., the allocation plan, is obtained according to the values ​​of individuals in population 1.

2. A dual-target dynamic weapon allocation method based on simplified dual population according to claim 1, characterized in that: The objective function is: Where f1 is the total expected threat value of all targets, f2 is the total expected cost of all weapons, Nstg is the total number of stages considered in the problem, Nwpn is the number of weapons, Ntgt is the number of targets, is the decision variable of the hth stage. If weapon w is assigned to target e of the hth stage, then otherwise v e is the threat value of target e, is the probability that weapon w destroys target e in stage h, c w is the cost of weapon w.

3. A dual-target dynamic weapon allocation method based on simplified dual population according to claim 2, characterized in that: The constraints are: Among them, n h，w is the firing frequency of weapon w at stage h, m h，e is the number of weapons assigned to target e in stage h, a w The amount of ammunition equipped for weapon w, is the matrix of participation feasibility. If weapon w can hit target e in stage h, then otherwise 4. The method for dynamic weapon allocation for dual targets based on simplified dual population according to claim 3, characterized in that: In the target function-guided population generation strategy, each time an allocation is made, the target τ with the highest threat level is first found in the available target set T*, and the target τ is allocated to the weapon ω with the first priority at stage σ, where the stage σ and the weapon ω are selected according to the highest interception rate; after each effective allocation, p[σ, ω, τ], υ[τ], μ[σ, τ], α[ω] and T are updated for the next allocation. * ; Where p[σ, ω, τ] is the temporary interception success rate copied during the initialization process, υ[τ] is the temporary threat level, μ[σ, τ] is the weapon quantity constraint of target τ at stage σ related to constraint formula (4), and α[ω] is the remaining ammunition equipment of weapon ω related to constraint formula (5).

5. The method for dynamic weapon allocation for dual targets based on simplified dual population according to claim 4, characterized in that: The population generation strategy guided by the objective function specifically includes: Step 5-1, initialize population X = 0 Nstg×Nwpn , initialization parameter T * , v, μ and α; Step 5-2, remove the satisfied The goal is e, if Jump to step 9, otherwise execute step 5-3; Step 5-3, select the target τ with the highest threat level v[τ] from the available target set T*; Step 5-4, determine the stage σ and weapon ω according to the highest interception rate, and obtain the tuple (σ, ω), the stage σ and weapon ω satisfy: x σ，ω =0, α[ω]>0, μ[σ,τ]>0 and has the highest interception rate p[σ,ω,τ]; Step 5-5, if Remove target τ from T*, i=i+1, and jump to steps 5-8, otherwise target τ is assigned to weapon ω in stage σ; Step 5-6, update the temporary parameters x[σ,ω]=τ, α[ω]=α[ω]-1, μ[σ,τ]=μ[σ,τ]-1, v[τ]=v[τ]×p[σ,ω,τ]; Step 5-7, let p[σ, ω, e] = 0 for i=i+1; Steps 5-8, repeat the above steps until i>Nasn, and obtain population 1, where Nasn is the maximum number of allocations.

6. The method for dynamic weapon allocation for dual targets based on simplified dual population according to claim 3, characterized in that: When the uncertainty initialization method generates a population 2 that satisfies the constraints, each time an allocation is made, the weapon ω with the minimum cost is found in the weapon set w, and then all stages σ are traversed to randomly select a weapon ω to ensure that it satisfies the constraint formula (6). After each effective allocation, α[ω], μ[σ, τ] and W are updated for the next allocation. Each time the uncertainty initialization method generates a feasible initial solution, the process is repeated. times, get An initial solution, C IIs is the setting coefficient.

7. The method for dynamic weapon allocation for dual targets based on simplified dual population according to claim 1, characterized in that: The maximum number of allocations for the population generation strategy guided by the objective function and the uncertainty initialization method Where Nvar-Nstg×Nwpn.

8. The method for dynamic weapon allocation for dual targets based on simplified dual population according to claim 1, characterized in that: The simplified updating method specifically includes: in each iteration t of the evolution stage, by comparing with two preset parameters Cg and Cr, Cg = 0.6, Cr = 0.61, updating one by one Each variable in for Each variable in are set to The value with the same index in , HQ or random feasible value x, where HQ is a solution randomly selected from the Pareto front obtained by the constraint assignment principle or fast non-dominated sorting, and the random feasible value x is a random feasible value taken according to the comparison of uniform random number ρ in the range of [0, 1].

9. The method for dynamic weapon allocation for dual targets based on simplified dual population according to claim 1, characterized in that: The feasible exchange strategy is: when λ<C FES When the input solution is a feasible solution, traverse all target tuples (t1, t2) in the solution, and satisfy t1≠t2, and then calculate the cv value of the exchanged solution. The exchanged solution is a feasible solution, where λ is a random number between [0, 1], C FES is a custom swap threshold and C FES ∈(0,1).

10. A dual-target dynamic weapon allocation system based on simplified dual populations for implementing any of the methods described in claims 1-9, characterized in that: It includes a model building unit, a population initialization unit, a sorting unit and a population optimization unit, among which: The model building unit is used to build a mathematical model of the dual-target dynamic weapon allocation problem, including an objective function and constraint conditions; The population initialization unit generates an initial population 1 that meets the constraint conditions based on decimal coding and adopts a population generation strategy guided by an objective function, and generates a population 2 that meets the constraint conditions using an uncertainty initialization method, wherein population 1 is used as a main population; The sorting unit sorts population 1 using a constraint allocation principle and sorts population 2 using a fast non-dominated sort; The population optimization unit uses a simplified update method and a feasible exchange strategy to iteratively update population 1 and population 2 based on the ranking of population 1 and population 2, and obtains a Pareto front solution according to the values ​​of individuals in population 1.

Images