Adaptive correction weapon target assignment system based on double profile mechanism multi-objective particle swarm optimization algorithm

Abstract

The application discloses a weapon-target distribution system based on a double archive mechanism multi-objective particle swarm optimization algorithm, which comprises a display control module, a host computer, a weapon-target distribution multi-objective optimization problem design module and an optimization module based on the double archive mechanism multi-objective particle swarm optimization algorithm. The weapon-target distribution system based on the double archive mechanism multi-objective optimization algorithm adopts the equipment to search the optimal solution set of the weapon-target distribution problem. The weapon-target distribution system based on the double archive mechanism multi-objective optimization algorithm overcomes the poor convergence and poor balance of diversity of the optimal solution set of the traditional weapon-target distribution system, and is prone to falling into local optimization. The double archive mechanism and the chaotic optimization technology are utilized to improve the global search capability of the weapon-target problem and the balance of convergence and diversity. The adaptive correction strategy is adopted to automatically update the model, so that the accuracy of the system is maintained.

Description

Technical Field

[0001] This invention relates to the field of computer simulation and optimization, and in particular to an adaptive correction weapon target allocation system based on a dual-file mechanism multi-target particle swarm optimization algorithm. Background Technology

[0002] Modern warfare is increasingly evolving towards spatial multidimensionality, diverse combat units, and uncertain operational objectives. Joint operations and overall planning have thus become crucial elements in achieving victory. The Weapon Target Allocation (WTA) problem aims to provide a rational allocation scheme for weaponry, utilizing minimal weapon resources to strike the most strategic targets while maximizing the benefits of the strikes. It is an NP-hard multi-objective constrained optimization problem. Obtaining the global optimal solution to the WTA problem using efficient multi-objective optimization algorithms is a significant research endeavor for operational command, as it will improve operational effectiveness and directly impact the outcome of battles.

[0003] Currently, intelligent algorithms for solving the WTA problem mainly include evolutionary algorithms such as Genetic Algorithm (GA), Gray Wolf Optimization (GW), Fireworks Algorithm, and Particle Swarm Optimization (PSO). These algorithms were originally proposed for single-objective optimization problems, and most can efficiently find the global optimum in the single-objective solution space. However, in multi-objective optimization problems, they often suffer from an imbalance between the convergence and diversity of the optimal solution set, easily getting trapped in local optima. This is because the optimal objective space corresponding to the optimal solution in a multi-objective solution space exists in the form of a hyperplane. The search space usually contains multiple locally optimal hyperplanes, and conventional evolutionary algorithms are prone to getting trapped in local optimum regions due to a lack of means to escape local optima during the optimization process. Similarly, after finding the global optimum, optimization algorithms tend to cluster solutions around it, making it difficult to conduct distributed exploration of the surrounding areas. The convergence and diversity of the optimal solution set are difficult to balance, resulting in a limited range of allocation options for the weapon-allocation problem, which is detrimental to decision-making in dynamic battlefield situations. Summary of the Invention

[0004] To overcome the shortcomings of traditional weapon-target assignment systems, such as poor convergence and diversity balancing of optimal solution sets and a tendency to get trapped in local optima, this invention aims to provide an adaptive correction weapon-target assignment system based on a dual-file mechanism multi-objective particle swarm optimization algorithm. This system improves the global search capability of the multi-objective particle swarm optimization algorithm for weapon-target problems, as well as its ability to balance the convergence and diversity of optimal solution sets. Furthermore, an adaptive correction strategy is employed to automatically update the model and maintain the accuracy of the system.

[0005] The technical solution adopted by this invention to solve its technical problem is: an adaptive correction weapon-target allocation system based on a dual-file mechanism multi-target particle swarm optimization algorithm, which provides a set of alternative optimal solutions for weapon-target optimization. The system includes: a display and control module, a host computer, a weapon-target multi-target optimization problem design module, and an optimization module based on a dual-file mechanism multi-target particle swarm optimization algorithm.

[0006] The operation process of the device includes:

[0007] Step A1: The weapon-target allocation decision-maker inputs the number N of potential targets and their corresponding targets O = {O1,…,} through the display and control module. i ,…, N}, where O i Let represent the i-th potential target, and then input the type M of the weapon to be used for the attack, and its corresponding weapon arsenal W = {W1, ..., ...} j ,…, M} and the j-th (j=1,2,…,M) class of weapon arsenals W j Weapon types available: M j , recorded as Next, input the j-th type of weapon used to strike the i-th potential target O. i The cost of attacking at that time j The probability of hitting is p ij and damage benefits e i Finally, enter the maximum number of weapons L that can be used to attack the same target;

[0008] Step A2: The weapon-target allocation parameters input by the weapon-target allocation decision-maker are transmitted to the host computer through the display and control module for the establishment and optimization solution of the optimization problem;

[0009] Step A3: Weapon-target assignment related parameters are first defined by the weapon-target multi-objective optimization problem design module, which defines the multi-objective optimization problem and the constraint functions.

[0010] Step A4: The defined weapon-target assignment multi-objective optimization problem will be used as the fitness function of the optimization module of the multi-objective particle swarm optimization algorithm based on the dual-file mechanism for constraint optimization solution;

[0011] Step A5: The optimal solution set and its fitness value of the weapon-target assignment multi-objective optimization problem obtained by the optimization module based on the dual-file mechanism multi-objective particle swarm optimization algorithm will be output to the display control module;

[0012] Step A6: Decision-makers view the optimal weapon-target allocation scheme and its corresponding fitness value obtained through the optimization solution via the display and control module, and further select the weapon-target allocation scheme based on the knowledge of decision experts;

[0013] Step A7: The decision-maker adjusts the relevant parameters of the weapon-target allocation problem through the display and control module. The system will adaptively adjust and reconstruct the multi-objective optimization problem and perform a correction search based on the initial optimal solution set; it can also issue a stop command to the host computer to stop the system from running.

[0014] The design module for the weapon-target allocation multi-objective optimization problem is implemented using the following steps:

[0015] Step B1: Define the optimization objectives of the weapon-target assignment multi-objective optimization problem as maximizing the damage benefit of the strike and minimizing the strike cost;

[0016] Step B2: Define Boolean decision variables and y i ,in Indicates arsenal W j The kth weapon W j k Should potential target O be targeted? i y i Indicates potential target O i Whether to be targeted;

[0017] Step B3: Obtain the Armory W j The kth weapon W j k Strike potential target O i Hit probability P(i,j,k), Armory W j Strike potential target O i The hit probability P(i,j) and the probability of all weapons hitting potential targets O i The hit probability P(i) is as follows:

[0018]

[0019]

[0020]

[0021] Step B4: All weapons obtained from Step B3 engage the potential target O. i The probability of hitting the potential target O is obtained. i Expected damage benefit And the expected damage gain from striking all potential targets. as follows:

[0022]

[0023]

[0024] Step B4: The cost of striking with all weapons It is expressed as follows:

[0025]

[0026] Step B5: To avoid getting trapped in local optima due to the magnitude difference, the expected damage gain and attack cost are normalized based on the sum of the corresponding damage gain and attack cost, as shown below:

[0027]

[0028]

[0029] Where E represents the normalized expected damage gain and C represents the normalized attack cost;

[0030] Step B6: Based on the set upper limit L for the number of weapons that can engage the same target and the total upper limit M for the number of weapons. j The constraints of the weapon-target allocation problem are as follows:

[0031]

[0032]

[0033] Step B7: Based on the established condition that weapons are not allocated to targets not intended for engagement, the following constraints are set:

[0034]

[0035] Step B8: To satisfy the definition of a conventional multi-objective optimization problem, maximizing the expected damage gain E is transformed into minimizing the negative value of the expected damage gain, thus establishing the weapon-target allocation multi-objective optimization problem as follows:

[0036] min{-,C}(12)

[0037]

[0038] The novel optimization module of the multi-objective particle swarm optimization algorithm based on a dual-file mechanism improves the quality of the global optimal solution and the local search capability in the multi-objective particle swarm optimization algorithm. It is implemented through the following steps:

[0039] Step C1: Randomly initialize the particle population. The positions of the particles are randomly assigned using a lower bound vector of all zeros (Lower) and an upper bound vector of all ones (Upper). If the constraint condition of equation (13) is not met, re-initialize until the total number of particles N is satisfied.p ;

[0040] Step C2: Calculate the corresponding objective function - and C based on the position of each particle in the population, and find the non-dominated solution set rep;

[0041] The search process for the non-dominated solution set rep is implemented using the following steps:

[0042] Step C2.1: Traverse the particle population, for particle p i The objective function value is sequentially compared with that of particle p. i+1 arrive By comparison, if there are no particles whose objective function values ​​are all smaller than its own, it is marked as a non-dominated particle;

[0043] Step C2.2: Conversely, mark it as the dominant particle until the particle...

[0044] Step C2.3: Copy all particles marked as non-dominated particles to the non-dominated solution set rep;

[0045] Step C3: Create two cooperating external archives, an empty convergence archive CA and a diversity archive DA, and set an upper limit N for the total size of the two archives. CD The objective of CA is to make the approximate Pareto solution set converge to the true Pareto front, while the objective of DA is to make the approximate Pareto solution set uniformly distributed on the Pareto front.

[0046] Step C4: Randomly select the global optimal solution gbest from the non-dominated solution set rep;

[0047] Step C5: Update the particle population, CA, DA, and gbest based on the maximum number of iterations MAX_ITERATION;

[0048] Step C6: After reaching the maximum number of iterations MAX_ITERATION, output the set of CA and DA as the optimal solution set for the weapon target assignment problem.

[0049] The update process for the particle population, CA, DA, and gbest is implemented using the following steps:

[0050] Step D1: Population Update Based on the traditional particle swarm optimization algorithm, the velocity and position of particles in the population are first updated as follows:

[0051] v i,j (t+1)=wv i,j(t)+x1r1(pb i,j (t)-x i,j (t))+c2r2(gb j (t)-x i,j (t)) (14)

[0052] x i,j (t+1)=x i,j (t)+v i,j (t+1) (15)

[0053] Where: v i,j (t+1) represents the velocity value of the i-th particle at time t+1 in the j-th dimension, x i,j (t+1) represents the displacement value of the i-th particle at time t+1 in the j-th dimension, pb i,j (t) represents the individual optimal value of the i-th particle at time t in the j-th dimension, gb j (t) represents the optimal value of the population at time t in the j-th dimension, c1 represents the individual learning factor, c2 represents the population learning factor, ω>0 represents the inertia factor, r1 and r2 represent random numbers between [0,1], and t represents the evolution time.

[0054] Step D2: Constrain the updated particle positions. For particle positions that do not meet the constraints in equation (13), they will be updated again until the constraints are met. Finally, the objective function value is calculated for each updated particle and a new non-dominated solution set rep is obtained as shown in step C2.

[0055] Step D3: The update of the CA and DA dual archives is based on the updated non-dominated solution set rep. Each non-dominated particle from rep will be compared with all members in the CA and DA archives using a fitness function, which will result in three possibilities.

[0056] In the first case, if the particle is dominated by one of the particles in both archives, it is discarded. In the second case, if the particle can dominate some members in both archives, one of the dominated members is randomly removed, and the particle enters CA to replace the non-dominated solution in the original archive. In the third case, if the particle cannot dominate any of the particles in either archive, the particle enters DA to increase the diversity of non-dominated solutions in both archives. This process is repeated until all particles from rep have been traversed.

[0057] After the update is complete, calculate the total size of the two files, CA and DA. If the total size is greater than the upper limit N, then... CD When this happens, a deletion operation is required. The deletion operation only applies to particles in the DA (Data Aspect). First, calculate the Euclidean distance from each particle in the DA to its nearest particle in the CA (Data Cspect). The result is as follows:

[0058] d min (p,CA)=min{EDist(p,q)|q∈CA},p∈DA (16)

[0059] Where p is the position of the particle in DA, d min (p,CA) represents the distance between p and the nearest particle in CA, EDist(,q) represents the Euclidean distance between the two particle positions, and q is the position of the particle in CA. Then, the particle in DA that is closest to CA is iteratively removed until the total size of the two files equals the set capacity limit. This novel approach can maximize the distance between particles representing diversity and convergence in the optimal solution set, achieving a balance between convergence and diversity.

[0060] Step D4: Select the global optimal solution using the CA and DA archives. First, randomly select one parent from the updated CA and DA archives respectively. Then, apply the simulated binary crossover (SBX) operator and the polynomial mutation (PM) operator from the genetic algorithm to the two parents to produce offspring. The mathematical expressions for the two operators are as follows:

[0061] Assumption and If two parents are selected from CA and DA respectively, then the SBX operator can be expressed as:

[0062]

[0063] in, and The parameter γ is calculated as follows to represent the two offspring generated through simulated binary crossover:

[0064]

[0065] Where μ is a random number uniformly distributed on [0,1], and η C The distribution index is p. After simulating binary crossover, the generated offspring are then indexed by p. m The mutation probability is used for polynomial mutation. Taking this as an example, the PM operator is defined as follows:

[0066]

[0067] Among them, u j and l j Let ξ represent the upper and lower bounds of the j-th dimension, respectively. j The calculation method is as follows:

[0068]

[0069]

[0070] Where δ is a random number uniformly distributed on [0,1], and η m This is the distribution index.

[0071] Based on the SBX and PM operators mentioned above, two offspring are generated from CA and DA. After determining their dominance relationship, a non-dominated solution or a randomly selected offspring is chosen as the global optimal solution gbest. This solution inherits both the convergence and diversity represented by the CA and DA populations, thus improving the quality of the solution.

[0072] Step D5: Introduce chaotic optimization. Further chaotic iteration is performed on the globally optimal solution gbest obtained from CA and DA, enabling the algorithm to escape local optima and approach the true Pareto front. A Logistic chaotic iteration sequence is selected, and its mathematical expression is as follows:

[0073] gbest n+1 =θgbest n (1-gbest n ) n∈{1,2,…} (22)

[0074] Among them, gbest n+1 This represents the position vector of the globally optimal particle after the (n+1)th iteration, where 0 < ≤ 4 represents the control parameter.

[0075] If a solution that can dominate the original gbest is found within n chaotic iterations, then gbest is replaced and the chaotic iteration process is exited, resulting in the global optimal solution for the next particle swarm update.

[0076] The beneficial effects of this invention are mainly reflected in: 1. Improving the quality of the global optimal solution and the local search capability in the multi-objective particle swarm optimization algorithm; 2. Enhancing the balance between convergence and diversity of the optimal solution set of the multi-objective particle swarm optimization algorithm for the WTA problem; 3. Improving the accuracy of adaptive modeling of the system. Attached Figure Description

[0077] Figure 1 This is a schematic diagram of the adaptive correction weapon target allocation system based on a dual-file mechanism multi-target particle swarm optimization algorithm provided by the present invention;

[0078] Figure 2 This is a flowchart of the multi-objective particle swarm optimization algorithm based on a dual-file mechanism provided by the present invention;

[0079] Figure 3 This is a flowchart of the update process for the convergence profile (CA) and diversity profile (DA) provided by the present invention. Detailed Implementation

[0080] The present invention will now be described in detail with reference to the accompanying drawings.

[0081] like Figure 1 As shown, the adaptive correction weapon target allocation system based on the dual-file mechanism multi-target particle swarm optimization algorithm of the present invention consists of a display and control module 01, a host computer 02, a weapon-target multi-target optimization problem design module 03, and an optimization module 04 based on the dual-file mechanism multi-target particle swarm optimization algorithm.

[0082] The operation process of the device includes:

[0083] Step A1: The weapon-target allocation decision-maker inputs the number N of potential targets and their corresponding targets O = {O1,…,} through the display and control module 01. i ,…, N}, where O i Let represent the i-th potential target, and then input the type M of the weapon to be used for the attack, and its corresponding weapon arsenal W = {W1, ..., ...} j ,…, M} and the j-th (j=1,2,…,M) class of weapon arsenals W j Types of weapons available: M j , recorded as Next, input the j-th type of weapon used to strike the i-th potential target O. i The cost of attacking at that time j The probability of hitting is p ij and damage benefits e i Finally, enter the maximum number of weapons L that can be used to attack the same target;

[0084] Step A2: The weapon-target allocation parameters input by the weapon-target allocation decision-maker are transmitted to the host computer 02 through the display and control module 01 for the establishment and optimization solution of the optimization problem;

[0085] Step A3: Weapon-target assignment related parameters are first defined by the weapon-target multi-objective optimization problem design module 03, which defines the multi-objective optimization problem and the constraint functions.

[0086] Step A4: The defined weapon-target assignment multi-objective optimization problem will be used as the fitness function of optimization module 04 of the multi-objective particle swarm optimization algorithm based on the dual-file mechanism for constraint optimization solution;

[0087] Step A5: The optimal solution set and its fitness value of the weapon-target allocation multi-objective optimization problem obtained by the optimization module 04 based on the dual-file mechanism multi-objective particle swarm optimization algorithm will be output to the display control module 01;

[0088] Step A6: The decision-maker views the optimal weapon-target allocation scheme and its corresponding fitness value obtained by the optimization solution through the display and control module 01, and further selects the weapon-target allocation scheme based on the knowledge of decision experts;

[0089] Step A7: The decision-maker adjusts the relevant parameters of the weapon-target allocation problem through the display and control module 01. The system will adaptively adjust and reconstruct the multi-objective optimization problem and perform a correction search based on the initial optimal solution set; it can also issue a stop command to the host computer to stop the system from running.

[0090] The weapon-target allocation multi-objective optimization problem design module 03 is implemented using the following steps:

[0091] Step B1: Define the optimization objectives of the weapon-target assignment multi-objective optimization problem as maximizing the damage benefit and minimizing the cost of the attack;

[0092] Step B2: Define Boolean decision variables and y i ,in Indicates arsenal W j The kth weapon W j k Should potential target O be targeted? i y i Indicates potential target O i Whether to be targeted;

[0093] Step B3: Obtain the Armory W j The kth weapon W j k Strike potential target O i Hit probability P(i,j,k), Armory W j Strike potential target O i The hit probability P(i,j) and the probability of all weapons hitting potential targets O i The hit probability P(i) is as follows:

[0094]

[0095]

[0096]

[0097] Step B4: All weapons obtained from Step B3 engage the potential target O. i The probability of hitting the potential target O is obtained. i Expected damage benefit And the expected damage gain from striking all potential targets. as follows:

[0098]

[0099]

[0100] Step B4: The cost of striking with all weapons It is expressed as follows:

[0101]

[0102] Step B5: To avoid getting trapped in local optima due to the magnitude difference, the expected damage gain and attack cost are normalized based on the sum of the corresponding damage gain and attack cost, as shown below:

[0103]

[0104]

[0105] Where E represents the normalized expected damage gain and C represents the normalized attack cost;

[0106] Step B6: Based on the set upper limit L for the number of weapons that can engage the same target and the total upper limit M for the number of weapons. J The constraints of the weapon-target allocation problem are as follows:

[0107]

[0108]

[0109] Step B7: Based on the established condition that weapons are not allocated to targets not intended for engagement, the following constraints are set:

[0110]

[0111] Step B8: To satisfy the definition of a conventional multi-objective optimization problem, maximizing the expected damage gain E is transformed into minimizing the negative value of the expected damage gain, thus establishing the weapon-target allocation multi-objective optimization problem as follows:

[0112]

[0113]

[0114] The novel optimization module of the multi-objective particle swarm optimization algorithm based on a dual-file mechanism improves the quality of the global optimal solution and the local search capability in the multi-objective particle swarm optimization algorithm. It is implemented through the following steps: Figure 2 As shown:

[0115] Step C1: Randomly initialize the particle population. The positions of the particles are randomly assigned using a lower bound vector of all zeros (Lower) and an upper bound vector of all ones (Upper). If the constraint condition of equation (13) is not met, re-initialize until the total number of particles N is satisfied. p ;

[0116] Step C2: Calculate the corresponding objective function - and C based on the position of each particle in the population, and find the non-dominated solution set rep;

[0117] The search process for the non-dominated solution set rep is implemented using the following steps:

[0118] Step C2.1: Traverse the particle population, for particle p i The objective function value is sequentially compared with that of particle p. i+1 arrive By comparison, if there are no particles whose objective function values ​​are all smaller than its own, it is marked as a non-dominated particle;

[0119] Step C2.2: Conversely, mark it as the dominant particle until the particle...

[0120] Step C2.3: Copy all particles marked as non-dominated particles to the non-dominated solution set rep;

[0121] Step C3: Create two cooperating external archives, an empty convergence archive CA and a diversity archive DA, and set an upper limit N for the total size of the two archives. CD The objective of CA is to make the approximate Pareto solution set converge to the true Pareto front, while the objective of DA is to make the approximate Pareto solution set uniformly distributed on the Pareto front.

[0122] Step C4: Randomly select the global optimal solution gbest from the non-dominated solution set rep;

[0123] Step C5: Update the particle population, CA, DA, and gbest based on the maximum number of iterations MAX_ITERATION;

[0124] Step C6: After reaching the maximum number of iterations MAX_ITERATION, output the set of CA and DA as the optimal solution set for the weapon target assignment problem.

[0125] The update process for the particle population, CA, DA, and gbest is implemented using the following steps:

[0126] Step D1: Population Update Based on the traditional particle swarm optimization algorithm, the velocity and position of particles in the population are first updated as follows:

[0127] v i,j (t+1)=wv i,j (t)+x1r1(pb i,j (t)-x i,j (t))+c2r2(gb j (t)-x i,j (t)) (14)

[0128] x i,j (t+1)=x i,j (t)+v i,j (t+1) (15)

[0129] Where: v i,j (t+1) represents the velocity value of the i-th particle at time t+1 in the j-th dimension, x i,j (t+1) represents the displacement value of the i-th particle at time t+1 in the j-th dimension, pb i,j (t) represents the individual optimal value of the i-th particle at time t in the j-th dimension, gb j (t) represents the optimal value of the population at time t in the j-th dimension, c1 represents the individual learning factor, c2 represents the population learning factor, ω>0 represents the inertia factor, r1 and r2 represent random numbers between [0,1], and t represents the evolution time.

[0130] Step D2: Constrain the updated particle positions. For particle positions that do not meet the constraints in equation (13), they will be updated again until the constraints are met. Finally, the objective function value is calculated for each updated particle and a new non-dominated solution set rep is obtained as shown in step C2.

[0131] Step D3: As Figure 3 As shown, the update of the CA and DA dual archives is based on the updated non-dominated solution set rep. Each non-dominated particle from rep will be compared with all members in the CA and DA archives using a fitness function, which will result in three possibilities.

[0132] In the first case, if the particle is dominated by one of the particles in both archives, it is discarded. In the second case, if the particle can dominate some members in both archives, one of the dominated members is randomly removed, and the particle enters CA to replace the non-dominated solution in the original archive. In the third case, if the particle cannot dominate any of the particles in either archive, the particle enters DA to increase the diversity of non-dominated solutions in both archives. This process is repeated until all particles from rep have been traversed.

[0133] After the update is complete, calculate the total size of the two files CA and DA. If the total size is greater than the upper limit N, then... CD When this happens, a deletion operation is required. The deletion operation only applies to particles in the DA (Data Aspect). First, calculate the Euclidean distance from each particle in the DA to its nearest particle in the CA (Data Cspect). The result is as follows:

[0134] d min (p,CA)=min{EDist(p,q)|q∈CA},p∈DA (16)

[0135] Where p is the position of the particle in DA, d min (p,CA) represents the distance between p and the nearest particle in CA, EDist(,q) represents the Euclidean distance between the two particle positions, and q is the position of the particle in CA. Then, the particle in DA that is closest to CA is iteratively removed until the total size of the two files equals the set capacity limit. This novel approach can maximize the distance between particles representing diversity and convergence in the optimal solution set, achieving a balance between convergence and diversity.

[0136] Step D4: Select the global optimal solution using the CA and DA archives. First, randomly select one parent from the updated CA and DA archives respectively. Then, apply the simulated binary crossover (SBX) operator and the polynomial mutation (PM) operator from the genetic algorithm to the two parents to produce offspring. The mathematical expressions for the two operators are as follows:

[0137] Assumption and If two parents are selected from CA and DA respectively, then the SBX operator can be expressed as:

[0138]

[0139] in, and The parameter γ is calculated as follows to represent the two offspring generated through simulated binary crossover:

[0140]

[0141] Where μ is a random number uniformly distributed on [0,1], and η C is the distribution index. After simulating binary crossover, the generated offspring are then indexed by p. m The mutation probability is used for polynomial mutation. The offspring... Taking this as an example, the PM operator is defined as follows:

[0142]

[0143] Among them, u j and l j Let ξ represent the upper and lower bounds of the j-th dimension, respectively. j The calculation method is as follows:

[0144]

[0145]

[0146] Where δ is a random number uniformly distributed on [0,1], and η m This is the distribution index.

[0147] Based on the SBX and PM operators mentioned above, two offspring are generated from CA and DA. After determining their dominance relationship, a non-dominated solution or a randomly selected offspring is chosen as the global optimal solution gbest. This solution inherits both the convergence and diversity represented by the CA and DA populations, thus improving the quality of the solution.

[0148] Step D5: Introduce chaotic optimization. Further chaotic iteration is performed on the globally optimal solution gbest obtained from CA and DA, enabling the algorithm to escape local optima and approach the true Pareto front. A Logistic chaotic iteration sequence is selected, and its mathematical expression is as follows:

[0149] gbest n+1 =θgbest n (1-gbest n ) n∈{1,2,…} (22)

[0150] Among them, gbest n+1 This represents the position vector of the globally optimal particle after the (n+1)th iteration, where 0 < ≤ 4 represents the control parameter.

[0151] If a solution that can dominate the original gbest is found within n chaotic iterations, then gbest is replaced and the chaotic iteration process is exited, resulting in the global optimal solution for the next particle swarm update.

Claims

1. An adaptive correction weapon target allocation system based on a dual-file mechanism multi-target particle swarm optimization algorithm, characterized in that, The system includes: a display and control module, a host computer, a design module for the weapon-target allocation multi-target optimization problem, and an optimization module based on a dual-file mechanism multi-target particle swarm optimization algorithm; The system operation process includes: Step A1: The weapon-target allocation decision-maker inputs the number of potential targets via the display and control module. and their corresponding targets ,in Indicates the first Enter a list of potential targets, then input the type of weapon to be used to strike them. Its corresponding arsenal and the Armory Types of weapons available , recorded as Then enter the number Type of weapon used to strike the first A potential target Cost of attack at that time The probability of hitting is and the benefits of attack and destruction Finally, enter the maximum number of weapons that can be used to attack the same target. ; Step A2: The weapon-target allocation parameters input by the weapon-target allocation decision-maker are transmitted to the host computer through the display and control module for the establishment and optimization solution of the optimization problem; Step A3: Weapon-target assignment related parameters are first defined by the weapon-target multi-objective optimization problem design module, which defines the multi-objective optimization problem and the constraint functions. Step A4: The defined weapon-target assignment multi-objective optimization problem will be used as the fitness function of the optimization module of the multi-objective particle swarm optimization algorithm based on the dual-file mechanism for constraint optimization solution; Step A5: The optimal solution set and its fitness value of the weapon-target assignment multi-objective optimization problem obtained by the optimization module based on the dual-file mechanism multi-objective particle swarm optimization algorithm will be output to the display control module; Step A6: Decision-makers view the optimal weapon-target allocation scheme and its corresponding fitness value obtained through the optimization solution via the display and control module, and further select the weapon-target allocation scheme based on the knowledge of decision experts; Step A7: The decision-maker adjusts the relevant parameters of the weapon-target allocation problem through the display and control module; the system will adaptively adjust and reconstruct the multi-objective optimization problem, and perform a correction search based on the initial optimal solution set, and can also issue a stop command to the host computer to stop the system operation; The design module for the weapon-target assignment multi-objective optimization problem is implemented using the following steps: Step B1: Define the optimization objectives of the weapon-target assignment multi-objective optimization problem as maximizing the damage benefit and minimizing the cost of the attack; Step B2: Define Boolean decision variables as well as ,in Armory The first in One weapon Should potential targets be targeted? , Indicate potential target Whether to be targeted; Step B3: Obtain the Armory The first in One weapon Strike potential targets Hit probability Armory Strike potential targets Hit probability and all weapons strike potential targets Hit probability as follows: (1) (2) (3) Step B4: All weapons obtained from Step B3 engage potential targets. The probability of hitting the potential target is increased. Expected damage benefit And the expected damage gain from striking all potential targets. as follows: (4) (5) Step B4: The cost of striking with all weapons It is expressed as follows: (6) Step B5: To avoid getting trapped in local optima due to the magnitude difference, the expected damage gain and attack cost are normalized based on the sum of the corresponding damage gain and attack cost, as shown below: (7) (8) in, This represents the normalized expected damage gain. This represents the normalized cost of attack; Step B6: Based on the set maximum number of weapons that can engage the same target. and the total upper limit of the number of weapons The constraints of the weapon-target allocation problem are as follows: (9) (10) Step B7: Based on the established condition that weapons are not allocated to targets not intended for engagement, the following constraints are set: (11) Step B8: To satisfy the definition of a conventional multi-objective optimization problem, maximize the expected damage gain. This is transformed into minimizing the negative value of the expected damage gain, thus establishing the following weapon-target allocation multi-objective optimization problem: (12) (13)； The optimization module of the multi-objective particle swarm optimization algorithm based on the dual-file mechanism improves the quality of the global optimal solution and the local search capability in the multi-objective particle swarm optimization algorithm, and is implemented through the following steps: Step C1: Randomly initialize the particle population. The positions of the particles are randomly assigned using the lower bound vector (all zeros) and the upper bound vector (all ones). If the constraint condition of equation (13) is not met, re-initialize until the total number of particles is satisfied. ; Step C2: Calculate the corresponding objective function based on the position of each particle in the population. and Find the non-dominated solution set rep; The search process for the non-dominated solution set rep is implemented using the following steps: Step C2.1: Traverse the particle population, for each particle... The objective function value is sequentially compared with the particle. arrive By comparison, if there are no particles whose objective function values ​​are all smaller than its own, it is marked as a non-dominated particle; Step C2.2: Conversely, mark it as the dominant particle until the particle... ; Step C2.3: Copy all particles marked as non-dominated particles to the non-dominated solution set rep; Step C3: Create two cooperative external archives, an empty convergence archive CA and a diversity archive DA, and set an upper limit on the total size of the two archives. The objective of CA is to make the approximate Pareto solution set converge to the true Pareto front, while the objective of DA is to make the approximate Pareto solution set uniformly distributed on the Pareto front. Step C4: Randomly select the global optimal solution gbest from the non-dominated solution set rep; Step C5: Update the particle population, CA, DA, and gbest based on the maximum number of iterations MAX_ITERATION; Step C6: After reaching the maximum number of iterations MAX_ITERATION, output the set of CA and DA as the optimal solution set for the weapon target assignment problem.

2. The adaptive correction weapon target allocation system based on the dual-file mechanism multi-target particle swarm optimization algorithm according to claim 1, characterized in that, The update process for the particle population, CA, DA, and gbest is implemented using the following steps: Step D1: Population Update Based on the traditional particle swarm optimization algorithm, the velocity and position of particles in the population are first updated as follows: (14) (15) in: Indicates the first The particle in the first In each dimension The velocity value at that moment, Indicates the first The particle in the first In each dimension Displacement value at time t. Indicates the first The particle in the first In each dimension The individual optimal value at time t. Indicates the first Dimensions The group optimal value at time t. Represents individual learning factors. Represents the group learning factor. Indicates the inertia factor. and express Random numbers between, Indicates the moment of evolution; Step D2: Constrain the updated particle positions. For particle positions that do not meet the constraints in equation (13), they will be updated again until the constraints are met. Finally, the objective function value is calculated for each updated particle and a new non-dominated solution set rep is obtained as shown in step C2. Step D3: The update of the CA and DA dual archives is based on the updated non-dominated solution set rep. Each non-dominated particle from rep will be compared with all members in the CA and DA archives using the fitness function, which will have three possibilities. In the first case, if the particle is dominated by one of the particles in the two archives, it is discarded. In the second case, if the particle can dominate some members in the two archives, one of the dominated members will be randomly removed, and the particle will enter CA to replace the non-dominated solution in the original archive. In the third case, if the particle and the particles in both archives cannot dominate each other, the particle will enter DA to increase the diversity of non-dominated solutions in the two archives. Repeat the above process until all particles from rep have been traversed. After the update is complete, calculate the total size of the CA and DA files. If the total size exceeds the upper limit... When this happens, a deletion operation is required. The deletion operation only applies to particles in DA. First, calculate the Euclidean distance from each particle in DA to its nearest particle in CA, as shown below: (16) in, It is the position of the particle in DA. express Distance to the nearest particle in CA This represents the Euclidean distance between the positions of two particles. The position of the particle in CA is used; then the particle in DA that is closest to CA is iteratively deleted until the total size of the two files is equal to the set capacity limit. This novel approach can maximize the distance between particles representing diversity and convergence in the optimal solution set, achieving a balance between convergence and diversity. Step D4: Select the globally optimal solution using the CA and DA archives. First, randomly select one parent from both the updated CA and DA archives. Then, apply the simulated binary crossover (SBX) operator and the polynomial mutation (PM) operator from the genetic algorithm to the two parents to produce offspring. The mathematical expressions for the two operators are as follows: Assumption and If two parents are selected from CA and DA respectively, then the SBX operator can be expressed as: (17) in, and For the two offspring generated by simulating binary crossover, the parameters are... The calculation method is as follows: (18) in, for Random numbers that are uniformly distributed on the upper surface. The distribution index is used; after simulating binary crossover, the generated offspring are then... Polynomial mutation is performed on the mutation probability of offspring; Taking this as an example, the PM operator is defined as follows: (19) in, and They represent the first Upper and lower bounds of each dimension, parameters The calculation method is as follows: (20) (21) in, for Random numbers that are uniformly distributed on the upper surface. The distribution index; Based on the above SBX and PM operators, two offspring are generated from CA and DA. After determining their dominance relationship, a non-dominated solution or a randomly selected offspring is chosen as the global optimal solution gbest. This solution inherits the convergence and diversity represented by the CA and DA populations, thus improving the quality of the solution. Step D5: Introduce chaotic optimization by further iterating the globally optimal solution gbest obtained from CA and DA, enabling the algorithm to escape local optima and approach the true Pareto front; a Logistic chaotic iteration sequence is selected, the mathematical expression of which is as follows: (22) in, This represents the position vector of the globally optimal particle after the (n+1)th iteration. Indicates control parameters; exist Within each chaotic iteration, if a solution that can dominate the original gbest is found, then gbest is replaced, and the chaotic iteration process is exited, resulting in the global optimal solution for the next particle swarm update.

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