A weapon-target assignment optimization method based on improved golden sine algorithm

Abstract

The application discloses a weapon-target assignment optimization method based on an improved golden sine algorithm, and comprises the following steps: establishing a weapon-target damage probability matrix; for a weapon-target assignment problem, a mathematical model comprising a weapon assignment matrix, an objective function and a constraint function is established; an original population satisfying the constraint is generated; the population is optimized by using the improved golden sine algorithm, the population is optimized by updating a golden section coefficient, updating an individual position and using a dynamic random reverse learning strategy, and a better individual is searched until iteration termination. Compared with the prior art, the method improves the position updating formula of the golden sine algorithm, avoids falling into a local optimal solution in the optimization process of the weapon-target assignment problem, simultaneously fuses the dynamic random reverse learning strategy to improve the population diversity, prevents the algorithm from converging too early, and makes the algorithm have strong global search capability and strong ability of jumping out of a local optimal solution.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optimization algorithm and auxiliary decision-making, in particular to a weapon-target assignment optimization method based on improved golden sine algorithm. BACKGROUND

[0002] The research on weapon-target assignment (WTA) problem originated from missile allocation problem (MAP), which is the research on missile defense optimization problem, that is, how to allocate the interceptor missile to achieve the optimal interception of the enemy's attacking missile. After extensive attention and research in the academic field, it gradually developed into the current WTA problem.

[0003] The WTA problem is essentially an N-P complete problem, and the solution space of the WTA problem has a large number of extreme points, so there is no algorithm that can achieve the optimal solution of the WTA problem in polynomial time. For the solution of the WTA problem, there are traditional exact algorithms such as branch and bound method, cutting plane method, and Hungarian method. Such algorithms can find the optimal solution of the WTA problem, but when facing large-scale problems, they will fall into the dilemma of significant increase in solving time. Therefore, the current research on WTA problem solving algorithm mostly focuses on heuristic algorithms such as genetic algorithm (GA) and particle swarm optimization algorithm. However, due to the existence of a large number of extreme points in the solution space of the WTA problem, and the exponential increase of the solution space with the increase of the problem size, these algorithms often have the problem of easily falling into local optimal solution or premature convergence. In order to solve the problem of genetic algorithm easily falling into local optimal solution, natural selection and genetic operator can be designed to obtain better individuals, but this method has high requirements for the design of genetic operator. By improving the position and velocity update formula in the particle swarm optimization algorithm, the problem of premature convergence of the particle swarm can be reduced, but this method will increase the possibility of falling into local optimal solution.

[0004] Golden sine algorithm (GSA) is a new meta-heuristic optimization algorithm, which uses the sine function in mathematics for iterative optimization. The characteristics are fast convergence speed, good robustness, and few parameters to adjust, so it is easy to implement. However, since the weapon-target assignment problem is a 0-1 assignment problem, the new position calculated by the position update formula in the original golden sine algorithm will have the problem of over-constraint, that is, the number 1 target and the number n target will be allocated too many weapons, which will lead the algorithm to fall into local optimal solution in the solving process. SUMMARY

[0005] The purpose of the present application is to improve the golden sine algorithm (RGSA) to optimize weapon-target allocation, which avoids falling into local optimal solution in the optimization process of WTA problem by improving the position update formula of the golden sine algorithm, and improves the population diversity by fusing dynamic random reverse learning strategy, prevents the algorithm from converging too early, so that the algorithm has strong global search ability and strong ability to jump out of local optimal solution.

[0006] The weapon-target allocation optimization method based on the improved golden sine algorithm provided by the present application has the technical scheme comprising the following steps: S1: establishing a weapon-target damage probability matrix for combat scenarios;

[0007] S2: establishing a mathematical model comprising a weapon allocation matrix, an objective function and a constraint function for the weapon-target allocation problem;

[0008] S3: generating an original population satisfying the constraints;

[0009] S4: optimizing the population by using the improved golden sine algorithm, updating the golden section coefficient, updating the individual position, optimizing the population by using the dynamic random reverse learning strategy, and finding better individuals until the iteration is terminated.

[0010] Further, the specific steps in S2 are as follows:

[0011] S201: establishing a weapon allocation matrix;

[0012] S202: taking the highest comprehensive damage probability of weapons to targets under the current allocation scheme as the optimization target, and establishing an objective function;

[0013] S203: establishing a constraint function.

[0014] Further, the objective function formula in S2 is:

[0015]

[0016] In the formula, E is the objective function, m is the number of weapons, n is the number of targets, di,j represents the damage probability of the ith weapon to the jth target, i∈m, j∈n, and the element xij is an element in the weapon allocation matrix. ij ij

[0017] Further, in S2, the constraint function is established under the constraint conditions of "each target is allocated at least one weapon to attack it" and "all weapons need to be used":

[0018]

[0019] ​​Further, the specific steps of generating the original population in S3 are as follows:

[0020] S301: For the convenience of calculation in the iteration process, a coding mode is adopted for the weapon allocation matrix X: the weapon allocation matrix X is coded into a vector P, the size of the vector is the number of weapons m, and the internal elements of the vector are any integers between 1 and n (the number of targets), and the corresponding relationship with the weapon allocation matrix X is: the i-th element in the vector P and its value P[i] indicate that the i-th weapon attacks the P[i]-th target, which corresponds to the element x i,P[i] in the weapon allocation matrix X, the value of which is 1.

[0021] S302: First, an original individual P I is generated, and then the internal elements of the original individual are randomly assigned any integer between 1 and n (the number of targets), and then the number of individuals (popsize) in the population is copied to form the population.

[0022] Further, the specific steps in S4 are as follows:

[0023] S401: Calculate the initial golden section ratio;

[0024] S402: Calculate the target function value of each individual, and obtain the current optimal target function value and the corresponding individual;

[0025] S403: Update the individual position using the improved golden sine algorithm position update formula; calculate the target function value of each individual after the golden sine position update, and update the current optimal target function value and the corresponding individual;

[0026] S404: Update the individual position using the dynamic random reverse learning strategy; calculate the target function value of each individual after the reverse learning, and update the current optimal target function value and the corresponding individual;

[0027] S405: Update the golden section coefficient;

[0028] S406: Determine whether the iteration is ended, if not, repeat S403 and enter the iteration calculation again; if the iteration is ended, output the final target function value and the allocation scheme.

[0029] Further, in S402, the updated target function is as follows:

[0030]

[0031] where F I is the target function value of the I-th individual, where I is the I-th individual in the population, and D is the damage probability matrix in S1, D(i, P I[i]) is the i-th weapon of the I-th individual to hit the P I [i] target damage probability.

[0032] Further, in S403, the individual position update formula is as follows:

[0033] P I (t+1) = P I (t) |sin(R1)| + R3R2sin(R1)|x1P B (t) - x2P I (t) |,

[0034] Wherein, P I (t) represents the position of the I-th individual at the t-th iteration, P B (t) represents the position of the optimal individual at the t-th iteration, R1 is a distance random number, R2 is a direction random number, and R3 is a scaling random number.

[0035] Further, S404 includes:

[0036] (1) Adopting a dynamic random reverse learning strategy for each individual to update the individual position;

[0037] (2) Calculate the objective function value of each individual after reverse learning, and update the current optimal objective function value and the corresponding individual.

[0038] Further, the dynamic reverse learning strategy is as follows:

[0039]

[0040] Wherein r is a reverse learning random number, P NEWI (t) is the position of the I-th individual after reverse learning at the t-th iteration, L and U are the upper and lower bounds of the solution, L and U values are 1 and n, and p is a dynamic reverse learning probability;

[0041] For the t max -th iteration with a maximum iteration number of t max , the calculation formula is:

[0042] p = t / t max .

[0043] The beneficial effects of the present application are that: aiming at the problems existing in the current weapon-target allocation problem, a weapon-target allocation optimization method based on improved golden sine algorithm is proposed, first, the population is initialized, then the improved golden sine algorithm is used to optimize the population, in the optimization process, through the improved golden sine algorithm position updating formula, the over-constraint problem of the original golden sine algorithm in the weapon-target allocation problem is solved; at the same time, a dynamic random reverse learning strategy is proposed, so that the individuals meeting the dynamic reverse learning requirements randomly use global dynamic reverse learning or elite reverse learning, further increasing the exploration ability of the algorithm to the solution space. BRIEF DESCRIPTION OF DRAWINGS

[0044] Figure 1 is the algorithm flow chart of the improved golden sine algorithm (RGSA) for optimizing weapon-target allocation.

[0045] Figure 2 is the fitness curve diagram of the improved golden sine algorithm (RGSA) combined with reverse learning in the present application and the genetic algorithm (GA) and the golden sine algorithm (GSA) for optimizing the 20*8 scale WTA problem.

[0046] Figure 3 is the over-constraint phenomenon existing in the golden sine algorithm for optimizing the WTA problem and the objective function curve and corresponding weapon allocation situation not meeting the minimum allocation number. DETAILED DESCRIPTION

[0047] Please refer to Figure 1 The flow chart shows that the present application provides a weapon-target allocation optimization method based on improved golden sine algorithm. In order to achieve the above purpose, the present application provides the following technical scheme including the following steps:

[0048] S1. For the WTA scene of m weapons attacking n targets, a weapon-target damage probability matrix D is established;

[0049]

[0050] Wherein, m is the number of weapons, n is the number of targets; d ij represents the damage probability of the i th weapon to the j th target (i e m, j e n), the specific value is determined by the combat performance of our weapon and the target to be attacked by the enemy;

[0051] S2: For the weapon-target allocation problem, a mathematical model including weapon allocation matrix, objective function and constraint function is established;

[0052] S201: Establish a weapon allocation matrix X: the elements x ij of the weapon allocation matrix X are Boolean numbers (x ij = {0, 1}), x ij= 1 represents that the ith weapon attacks the jth target, x ij = 0 represents that the ith weapon does not attack the jth target; wherein i e m, j e n;

[0053]

[0054] S202: Taking the highest comprehensive damage probability of the weapon to the target under the current allocation scheme as the optimization target, a target function E is established:

[0055]

[0056] S203: A constraint function is established for the constraints "each target is allocated at least one weapon to attack it" and "all weapons need to be used":

[0057]

[0058] S3: Generate an original population that satisfies the constraints;

[0059] S301: For convenience in the iteration process, a coding method is used for the weapon allocation matrix X: the weapon allocation matrix X is coded into a vector P, the size of the vector is the number of weapons m, and the internal elements of the vector are any integers between 1 and n (the number of targets). The correspondence between the weapon allocation matrix X and the vector P is as follows: the ith element in the vector P and its value P[i] represent that the ith weapon attacks the P[i]th target, and the value of the element x i,P[i] in the weapon allocation matrix X is 1.

[0060] S302: First, an original individual P I is generated, and then the internal elements of the original individual are randomly assigned any integer between 1 and n (the number of targets). Subsequently, the number of individuals (popsize) in the population is copied to form the population by reordering the elements in each individual.

[0061] S4: The improved golden section algorithm is used to optimize the population. By updating the golden section coefficient, updating the individual position, and using a dynamic random reverse learning strategy to optimize the population, a better individual is found until the iteration is terminated.

[0062] S401: Calculate the initial golden section rate, which is as follows:

[0063]

[0064] where a and b are the golden section proportional search values, τ is the golden section proportion, and c1 and c2 are the golden section coefficients.

[0065] S402: Calculate the objective function value of each individual, and obtain the current optimal objective function value and the corresponding individual; calculate the objective function value F of each individual I , find the highest value of the objective function F B and the corresponding weapon allocation scheme P B , update the objective function as follows according to the encoding mode adopted in S301:

[0066]

[0067] Where F I is the objective function value of the Ith individual, I is the Ith individual in the population, D is the damage probability matrix in S1, D(i, P I [i]) is the damage probability of the Ith individual in the Ith weapon striking the P I [i] target.

[0068] S403: Update the individual position using the improved golden sine algorithm position update formula; calculate the objective function value of each individual after golden sine position update, and update the current optimal objective function value and the corresponding individual;

[0069] (1) Start iteration, for each iteration, first update the position of each individual according to the improved golden sine algorithm position update formula, the position update formula is as follows:

[0070] P I (t+1)=P I (t)|sin(R1)|+R3R2sin(R1)|x1P B (t)-x2P I (t)|

[0071] Where P I (t) represents the position of the Ith individual at the tth iteration, P B (t) represents the position of the optimal individual at the tth iteration, R1 is a distance random number ranging from 0 to 2π, R2 is a direction random number ranging from 0 to π, and R3 is a scaling random number ranging from 0 to 1.

[0072] In order to avoid the situation that part of the elements in the individual exceed the boundary after position update, after position update, a boundary checking step is added, the value of the element exceeding the lower boundary 1 is taken as 1, the value of the element exceeding the upper boundary n is taken as n, and the non-integer situation of each element in the position update process is taken as an integer operation.

[0073] (2) Calculate the objective function value of each individual after golden sine position update, and update the current optimal objective function value and the corresponding individual;

[0074] For each iteration, after the population is updated by the improved golden section algorithm position update formula, the target function value of each individual is calculated according to the updated target function in S402, and the current optimal individual and the optimal target function value are updated.

[0075] S404: the individual position is updated by using a dynamic random reverse learning strategy; the target function value of each individual after reverse learning is calculated, and the current optimal target function value and the corresponding individual are updated.

[0076] (1) for each individual, the individual position is updated by using a dynamic random reverse learning strategy;

[0077] By introducing a dynamic reverse learning probability, a higher probability of generating reverse individuals to explore unknown areas in the solution space in the early iterations is generated, the global search ability of the algorithm is enhanced, and the number of reverse learning in the later iterations is reduced to reduce the computational amount of the algorithm; at the same time, by introducing a random reverse learning probability, global reverse learning and elite reverse learning are combined, when the individual performs reverse learning, global reverse learning or elite reverse learning is randomly performed, and the exploration ability of the algorithm to the solution space is further increased. The dynamic reverse learning strategy is as follows:

[0078]

[0079] Wherein r is a reverse learning random number in the range of [0, 1], P NEWI (t) is the position of the Ith individual after reverse learning in the tth iteration, L, U are the upper and lower bounds of the solution, L, U values are 1 and n, p is a dynamic reverse learning probability, for the tth iteration with a maximum iteration number of t max The calculation formula is:

[0080] p=t / t max .

[0081] (2) the target function value of each individual after reverse learning is calculated, and the current optimal target function value and the corresponding individual are updated.

[0082] After the dynamic random reverse learning is completed, the target function value of each individual is calculated according to the updated target function in S402, and the current optimal individual and the optimal target function value are updated.

[0083] S405: update the golden section coefficient;

[0084] The update function of the golden section coefficient is as follows:

[0085] The update function of the golden section coefficient of the non-current local optimal individual is as follows:

[0086]

[0087] The golden section coefficient update function of the current local optimal individual is as follows:

[0088]

[0089] When the golden section coefficient c1(t+1) = c2(t+1) occurs, the following formula is used for updating:

[0090]

[0091] Wherein r1, r2 are golden section coefficient update random numbers in the range of [0, 1].

[0092] S406: Determine whether the iteration is ended, if not, repeat S403, S404, S405; if the iteration is ended, output the final objective function value and the allocation scheme.

[0093] Embodiment

[0094] The improved weapon-target allocation method of the golden sine algorithm of the application is further described below in combination with examples. For the WTA problem, three simulation scenarios are given, and the simulation scenario settings are shown in Table 1. The improved golden sine algorithm (RGSA) of the application, the original golden sine algorithm (GSA) and the genetic algorithm (GA) are used for solving, and the simulation results are compared and analyzed.

[0095] Table 1 Simulation scenario settings

[0096]

[0097] Table 2 Simulation result comparison

[0098]

[0099] From Figure 2 As can be seen from Table 2, the improved golden sine algorithm (RGSA) of the application has a higher optimal fitness value compared with other algorithms. Although the average iteration number of the GA algorithm is less, the optimal fitness value, the minimum value and the average value of the GA algorithm are all less than those of the GSA algorithm and the RGSA algorithm. The optimal fitness value, the minimum value and the average value of the RGSA algorithm are better than those of the GSA algorithm as a whole. At the same time, the GSA algorithm is prone to over-constraint and not meeting the single target weapon allocation number constraint problem in the solving process. As shown in Table 2, the analysis shows that the convergence speed of the method of the application is slower, but the improved position update algorithm and the dynamic random reverse learning strategy enhance the ability of the algorithm to find the global optimal solution and jump out of the local optimal solution, and solve the over-constraint and the problem of not meeting the single target weapon allocation number constraint in the solving process of the GSA algorithm, so that the algorithm has a significant improvement in solving accuracy. Figure 3 ​

Claims

1. A weapon-target allocation optimization method based on an improved golden sine algorithm, characterized in that, Includes the following steps: S1: Establish a weapon-target damage probability matrix for combat scenarios; S2: For the weapon-target allocation problem, establish a mathematical model that includes a weapon allocation matrix, objective function, and constraint function; The specific steps of S2 are as follows: S201: Establish a weapon allocation matrix; S202: The objective function is established with the goal of maximizing the overall damage probability of the weapon to the target under the current allocation scheme. S203: Establish a constraint function, with the constraints being "at least one weapon is assigned to each target for attack" and "all weapons must be used"; S3: Generate the original population that satisfies the constraints; S4: The population is optimized by using an improved golden sine algorithm. The population is optimized by updating the golden ratio, updating the individual position, and using a dynamic random back-learning strategy to find better individuals until the iteration terminates. The specific steps in S4 are as follows: S401: Calculate the initial golden ratio; S402: Calculate the objective function value for each individual and obtain the current optimal objective function value and the corresponding individual; S403: The individual position is updated using the improved golden sine algorithm position update formula; Calculate the objective function value for each individual after the golden sine position update, and update the current optimal objective function value and the corresponding individual; In S403, the formula for updating individual positions is as follows: ， in, Indicates the first The second iteration The location of an individual, using Indicates the first The position of the optimal individual in the next iteration. The distance is a random number. For direction random numbers, To scale random numbers, The golden ratio; After the position update, add a boundary check step: set the value to 1 for elements exceeding the lower bound of 1, and set the value to 1 for elements exceeding the upper bound of 1. The element values ​​are For non-integer cases that occur in each element during the position update process, the elements in the individual are rounded down. S404: Update individual positions using a dynamic stochastic back-learning strategy; calculate the objective function value for each individual after back-learning, and update the current optimal objective function value and the corresponding individual; S405, Update the golden ratio; S406: Determine if the iteration has ended. If not, repeat S403 and enter the iteration calculation again. If the iteration has ended, output the final objective function value and allocation scheme.

2. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 1, characterized in that, The objective function formula in S2 is: ； In the formula: Let be the objective function. For the number of weapons, The target number; Representing the weapon against the first Probability of damage to a target ;element Assign elements from the matrix to the weapons.

3. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 2, characterized in that, In S203, the constraint function is established as follows: 。 4. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 1, characterized in that, The specific steps for generating the original population in S3 are as follows: S301: For ease of calculation during the iteration process, the weapon allocation matrix is... A coding method is used: weapon allocation matrix Encoded as a vector The vector size is the number of weapons. The vector contains elements 1 to 1. Any integer between the ranges, and the weapon allocation matrix. The correspondence is: vector The Middle Elements and their values , indicating the first weapon against the first Targets are engaged, corresponding weapon allocation matrix. Middle elements The value is 1; S302: First, generate an initial individual. Randomly assign 1 to each element within the original individual. Given any integer between 1 and 2, then copy the original individual vectors to the number of individuals in the population, and reorder the elements in each individual to form the population.

5. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 1, characterized in that, In S402, the updated objective function is as follows: ， in, For the first The individual's objective function value, where The first in the population Individual, Let S1 be the damage probability matrix. For the first Among the individuals, the first One weapon strikes the first The probability of damage to a target.

6. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 1, characterized in that, S404 includes: (1) A dynamic random backward learning strategy is used for each individual to update the individual's position; (2) Calculate the objective function value of each individual after reverse learning, and update the current optimal objective function value and the corresponding individual.

7. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 6, characterized in that, The dynamic stochastic back-learning strategy is as follows: ， in, To learn random numbers in reverse, For the first In the nth iteration The position after backward learning for each individual The upper and lower bounds of the solution, The value is 1 and , For dynamic reverse learning probability; For the maximum number of iterations is The The formula for the next iteration is: .

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