Weapon-target distribution optimization method based on improved golden sine algorithm

Abstract

The invention discloses a weapon-target allocation optimization method based on an improved golden sine algorithm. The method comprises the following steps: establishing a weapon-target damage probability matrix; aiming at a weapon-target allocation problem, establishing a mathematical model comprising a weapon allocation matrix, a target function and a constraint function; generating an original population satisfying the constraint; and optimizing the population by adopting an improved golden sine algorithm, optimizing the population by updating a golden section coefficient and an individual position and using a dynamic random reverse learning strategy, and searching a better individual until iteration is ended. Compared with the prior art, the method provided by the invention avoids falling into a local optimal solution in the WTA problem optimization process by improving the position updating formula of the golden sine algorithm, and meanwhile, the population diversity is improved by fusing the dynamic random reverse learning strategy, and the algorithm is prevented from premature convergence, so that the algorithm has relatively strong global search capability, and the algorithm is more suitable for being popularized and used. And meanwhile, the method has relatively high capability of jumping out of a local optimal solution.

Description

Technical Field

[0001] The invention relates to the field of optimization algorithms and auxiliary decision making, and in particular to a weapon-target allocation optimization method based on an improved golden sine algorithm. Background Art

[0002] The study of the weapon target assignment (WTA) problem originated from the missile allocation problem (MAP), which was originally a study of the missile defense operations optimization problem, that is, how to allocate interceptor missiles to achieve the optimal interception of enemy incoming missiles; after widespread attention and research in the academic community, it gradually developed into the current WTA problem.

[0003] The WTA problem is essentially an NP-complete problem. At the same time, there are a large number of extreme points in the solution space of the WTA problem. Therefore, there is no algorithm that can achieve the optimal solution to the WTA problem within polynomial time. For the solution of the WTA problem, there are traditional branch and bound method, cutting plane method, Hungarian method and other traditional exact algorithms. This algorithm can find the optimal solution of the WTA problem, but when facing a large-scale problem, it will fall into the dilemma of significantly increasing the solution time. Therefore, the current research on the algorithm for solving the WTA problem is mostly focused on heuristic algorithms, such as genetic algorithms (GAs) and particle swarm optimization algorithms. However, since there are a large number of extreme points in the solution space of the WTA problem, and the solution space will increase exponentially with the increase of the problem scale, these algorithms often have the problem of being easily trapped in the local optimal solution or premature convergence. In order to solve the problem that the genetic algorithm is prone to fall into the local optimal solution, natural selection and genetic operators can be designed to obtain better individuals, but this method has high requirements for the design of genetic operators; by improving the position and velocity update formulas in the particle swarm algorithm, the problem of premature convergence of the particle swarm can be reduced, but this method increases the possibility of it falling into the local optimal solution.

[0004] The golden sine algorithm (GSA) is a new meta-heuristic optimization algorithm that uses the sine function in mathematics for iterative optimization. It has the characteristics of fast convergence speed and good robustness. At the same time, there are few parameters that need to be adjusted in the algorithm, so it is easy to implement. However, since the weapon-target assignment problem is a 0-1 assignment problem, the new position calculated according to the position update formula in the original golden sine algorithm will have an over-constraint problem, that is, too many weapons will be assigned to the target numbered 1 and the target numbered n, which will cause the algorithm to fall into a local optimal solution during the solution process. Summary of the invention

[0005] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art. The present invention provides an improved golden sine algorithm (RGSA) to optimize weapon-target allocation. The method avoids falling into a local optimal solution during the optimization process of the WTA problem by improving the position update formula of the golden sine algorithm. At the same time, a dynamic random reverse learning strategy is integrated to improve the population diversity and prevent the algorithm from converging prematurely, so that the algorithm has a strong global search capability and a strong ability to jump out of the local optimal solution.

[0006] The present invention proposes a weapon-target allocation optimization method based on an improved golden sine algorithm, and its technical solution includes the following steps: S1: establishing a weapon-target damage probability matrix according to a combat scenario;

[0007] S2: For the weapon-target allocation problem, a mathematical model including the weapon allocation matrix, objective function and constraint function is established;

[0008] S3: Generate the original population that satisfies the constraints;

[0009] S4: Use the improved golden sine algorithm to optimize the population, update the golden section coefficient, update the individual position, and use a dynamic random reverse learning strategy to optimize the population, looking for better individuals until the iteration terminates.

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

[0011] S201: Establish weapons allocation matrix;

[0012] S202: Taking the highest comprehensive probability of damage to the target by the weapon under the current allocation scheme as the optimization goal, an objective function is established;

[0013] S203: Establish a constraint function.

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

[0015]

[0016] Where: E is the objective function, m is the number of weapons, n is the number of targets; d ij represents the probability of damage of the i-th weapon to the j-th target i∈m,j∈n; the element x ij Assign elements of the matrix to the weapons.

[0017] Furthermore, in S2, the constraint function is established based on the constraints of "at least one weapon is assigned to each target to attack it" and "all weapons need to be used":

[0018]

[0019] Furthermore, the specific steps for generating the original population in S3 are as follows:

[0020] S301: To facilitate calculations during the iteration process, a coding method is used for the weapon allocation matrix X: the weapon allocation matrix X is encoded as a vector P, the vector size is the number of weapons m, 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], indicating that the i-th weapon strikes the P[i]-th target, corresponds to the element x in the weapon allocation matrix X i,P[i] The value is 1;

[0021] S302: First generate an original individual P I , randomly assign any integer between 1 and n (target number) to the internal elements of the original individual, then copy the original individual vector with the number of individuals in the population (popsize), reorder the elements in each individual, and form a population.

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

[0023] S401: Calculate the initial golden ratio;

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

[0025] S403: using the improved golden sine algorithm position update formula to update the individual position; calculating the objective function value of each individual after the golden sine position update, and updating the current optimal objective function value and the corresponding individual;

[0026] S404: Adopting a dynamic random reverse learning strategy to update individual positions; calculating the objective function value of each individual after reverse learning, and updating the current optimal objective function value and the corresponding individual;

[0027] S405, updating the golden section coefficient;

[0028] S406: Determine whether the iteration is finished. If not, repeat S403 and enter the iterative calculation again. If the iteration is finished, output the final objective function value and the allocation plan.

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

[0030]

[0031] Among them, F I is the objective function value of the Ith individual, where I is the Ith individual in the population, D is the damage probability matrix in S1, D(i,P I[i]) is the number of weapons in the Ith individual that strike the Pth individual. I [i] The probability of damaging a target.

[0032] Furthermore, 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] Among them, P I (t) represents the position of the Ith individual in the tth iteration, and P B (t) represents the position of the optimal individual in the tth iteration, R1 is the distance random number, R2 is the direction random number, and R3 is the scaling random number.

[0035] Further, S404 includes:

[0036] (1) Adopt 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] Furthermore, the dynamic reverse learning strategy is as follows:

[0039]

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

[0041] For the maximum number of iterations t max The tth iteration of is calculated as:

[0042] p=t / t max .

[0043] The beneficial effects of the present invention are as follows: in view of the problems existing in the current weapon-target allocation problem, a weapon-target allocation optimization method based on an improved golden sine algorithm is proposed, firstly, the population is initialized, and then the improved golden sine algorithm is used to optimize the population. During the optimization process, the over-constraint problem of the original golden sine algorithm in the weapon-target allocation problem is solved by using the improved golden sine algorithm position update formula; at the same time, a dynamic random reverse learning strategy is proposed, so that individuals that meet the dynamic reverse learning requirements randomly adopt global dynamic reverse learning or elite reverse learning, further increasing the algorithm's ability to explore the solution space. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0046] Figure 3 It is the over-constraint phenomenon of the golden sine algorithm optimizing the WTA problem, the objective function curve that does not meet the minimum allocation number, and the corresponding weapon allocation situation. DETAILED DESCRIPTION

[0047] See also Figure 1 As shown in the flowchart, the present invention provides a weapon-target allocation optimization method based on an improved golden sine algorithm. To achieve the above purpose, the present invention provides the following technical solution including the following steps:

[0048] S1. For the WTA scenario of m weapons attacking n targets, establish the weapon-target damage probability matrix D;

[0049]

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

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

[0052] S201: Establish weapon allocation matrix X: element x in weapon allocation matrix X ij is a Boolean number (x ij ={0,1}), x ij=1 means the i-th weapon hits the j-th target, x ij =0 means that the i-th weapon did not hit the j-th target; where i∈m,j∈n;

[0053]

[0054] S202: Taking the highest comprehensive probability of damage to the target by the weapon under the current allocation scheme as the optimization goal, establish the objective function E:

[0055]

[0056] S203: Establish constraint functions for the constraints "each target must be assigned at least one weapon to attack it" and "all weapons must be used":

[0057]

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

[0059] S301: To facilitate calculations during the iteration process, a coding method is used for the weapon allocation matrix X: the weapon allocation matrix X is encoded as a vector P, the vector size is the number of weapons m, 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], indicating that the i-th weapon strikes the P[i]-th target, corresponds to the element x in the weapon allocation matrix X i,P[i] The value is 1.

[0060] S302: First generate an original individual P I , randomly assign any integer between 1 and n (target number) to the internal elements of the original individual, then copy the original individual vector with the number of individuals in the population (popsize), reorder the elements in each individual, and form a population.

[0061] S4: Use the improved golden sine algorithm to optimize the population, update the golden section coefficient, update the individual position, and use a dynamic random reverse learning strategy to optimize the population, looking for better individuals until the iteration terminates.

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

[0063]

[0064] Where a and b are the golden ratio search values, τ is the golden ratio, and c1 and c2 are the golden ratio coefficients.

[0065] S402: Calculate the objective function value of each individual to obtain the current optimal objective function value and the corresponding individual; Calculate the objective function value F of each individual I , find the objective function value F with the highest value B And the corresponding weapon allocation plan P B , for the encoding method adopted in S301, the updated objective function is as follows:

[0066]

[0067] Among them, 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 number of weapons in the Ith individual that strike the Pth individual. I [i] The probability of damaging a target.

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

[0069] (1) Iteration starts. For each iteration, the position of each individual is updated according to the position update formula of the improved golden sine algorithm. 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 in the tth iteration, and P B (t) represents the position of the optimal individual in the tth iteration, R1 is a distance random number in the range of [0,2π], R2 is a direction random number in the range of [0,π], and R3 is a scaling random number in the range of [0,1].

[0072] In order to avoid the situation where some elements in an individual exceed the bounds after the position update, a boundary check step is added after the position update. The elements exceeding the lower bound 1 are set to 1, and the elements exceeding the upper bound n are set to n. For non-integer situations of each element in the position update process, each element in the individual is rounded.

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

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

[0075] S404: Adopting a dynamic random reverse learning strategy to update individual positions; calculating the objective function value of each individual after reverse learning, and updating the current optimal objective function value and the corresponding individual;

[0076] (1) Adopt a dynamic random reverse learning strategy for each individual to update the individual position;

[0077] By introducing the dynamic reverse learning probability, there is a higher probability of generating reverse individuals in the early iteration to explore the unknown areas in the solution space, which enhances the global search ability of the algorithm while reducing the number of reverse learning in the later iteration to reduce the amount of calculation of the algorithm; at the same time, by introducing the random reverse learning probability, global reverse learning is combined with elite reverse learning. When individuals perform reverse learning, global reverse learning or elite reverse learning is performed randomly, further increasing the algorithm's ability to explore the solution space. The dynamic reverse learning strategy is as follows:

[0078]

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

[0080] p=t / t max .

[0081] (2) Calculate the objective function value of each individual after reverse learning, and update the current optimal objective function value and the corresponding individual;

[0082] After the dynamic random reverse learning is completed, the objective function value of each individual is calculated according to the updated objective function in S402, and the current optimal individual and the optimal objective 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 golden section coefficient update function 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 reaches c1(t+1)=c2(t+1), it is updated using the following formula:

[0090]

[0091] Among them, r1 and r2 are the golden ratio coefficients in the range of [0,1] to update the random numbers.

[0092] S406: Determine whether the iteration is finished. If not, repeat S403, S404, and S405. If the iteration is finished, output the final objective function value and the allocation plan.

[0093] Example

[0094] The weapon-target assignment method of the improved golden sine algorithm of the invention is further described below 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), the original golden sine algorithm (GSA) and the genetic algorithm (GA) proposed in the present invention are used to solve them respectively, and the simulation results are compared and analyzed.

[0095] Table 1 Simulation scenario settings

[0096]

[0097] Table 2 Comparison of simulation results

[0098]

[0099] from Figure 2 As can be seen from Table 2, the improved golden sine algorithm (RGSA) proposed in the present invention has a higher optimal fitness value than other algorithms. Although the average number of iterations of the GA algorithm is less, its optimal value, worst value and average value of fitness are all lower than those of the GSA algorithm and the RGSA algorithm. The optimal value, worst value and average value of fitness 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 the following problems during the solution process: Figure 3 The problem of over-constraint and failure to meet the single target weapon allocation number constraint is shown in the figure. Analysis shows that: although the convergence speed of the method of the present invention is slow, the improved position update algorithm and dynamic random reverse learning strategy enhance the algorithm's ability to find the global optimal solution and jump out of the local optimal solution, while solving the problem of over-constraint and failure to meet the single target weapon allocation number constraint in the GSA algorithm during the solution process, making the algorithm significantly improved in solution accuracy.

Claims

1. A weapon-target allocation optimization method based on an improved golden sine algorithm, characterized in that: The following steps are involved: S1: Establish a weapon-target damage probability matrix for combat scenarios; S2: For the weapon-target allocation problem, a mathematical model including the weapon allocation matrix, objective function and constraint function is established; S3: Generate the original population that satisfies the constraints; S4: Use the improved golden sine algorithm to optimize the population, update the golden section coefficient, update the individual position, and use a dynamic random reverse learning strategy to optimize the population, looking for better individuals until the iteration terminates.

2. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 1 is characterized in that: The specific steps of S2 are as follows: S201: Establish weapons allocation matrix; S202: Taking the highest comprehensive probability of damage to the target by the weapon under the current allocation scheme as the optimization goal, an objective function is established; S203: Establish a constraint function.

3. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 2 is characterized in that: The objective function formula in S2 is: Where: E is the objective function, m is the number of weapons, n is the number of targets; d ij represents the probability of damage of the i-th weapon to the j-th target i∈m,j∈n; the element x ij Assign elements of the matrix to the weapons.

4. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 3 is characterized in that: In S2, the constraint function is established based on the constraints of "each target must be assigned at least one weapon to attack it" and "all weapons must be used":

5. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 1 is characterized in that: The specific steps for generating the original population in S3 are as follows: S301: To facilitate calculation in the iterative process, a coding method is used for the weapon allocation matrix X: the weapon allocation matrix X is encoded into a vector P, the vector size is the number of weapons m, the internal elements of the vector are any integers between 1 and n, and the corresponding relationship with the weapon allocation matrix X is: the i-th element in the vector P and its value P[i], indicating that the i-th weapon strikes the P[i]-th target, corresponding to the element x in the weapon allocation matrix X i,P[i] The value is 1; S302: First generate an original individual P I , randomly assign any integer between 1 and n to the internal elements of the original individual, then copy the original individual vector the number of individuals in the population, reorder the elements in each individual, and form a population.

6. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 1 is characterized in that: The specific steps in S4 are as follows: S401: Calculate the initial golden ratio; S402: Calculate the objective function value of each individual to obtain the current optimal objective function value and the corresponding individual; S403: using the improved golden sine algorithm position update formula to update the individual position; Calculate the objective function value of each individual after the golden sine position is updated, and update the current optimal objective function value and the corresponding individual; S404: Update individual positions using a dynamic random reverse learning strategy; Calculate the objective function value of each individual after reverse learning, and update the current optimal objective function value and the corresponding individual; S405, updating the golden section coefficient; S406: Determine whether the iteration is finished. If not, repeat S403 and enter the iterative calculation again. If the iteration is completed, the final objective function value and allocation plan are output.

7. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 6 is characterized in that: In S402, the updated objective function is as follows: Among them, F I is the objective function value of the Ith individual, where I is the Ith individual in the population, D is the damage probability matrix in S1, D(i,P I [i]) is the number of weapons in the Ith individual that strike the Pth individual. I [i] The probability of damaging a target.

8. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 6 is characterized in that: In S403, the individual position update formula is as follows: P I (t+1)=P I (t)|sin(R1)|+R3R2sin(R1)|x1P B (t)-x2P I (t)|, Among them, P I (t) represents the position of the Ith individual in the tth iteration, and P B (t) represents the position of the optimal individual in the tth iteration, R1 is the distance random number, R2 is the direction random number, and R3 is the scaling random number.

9. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 8, characterized in that: S404 includes: (1) Adopt a dynamic random reverse learning strategy for each individual to update the individual 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.

10. The weapon-target allocation optimization method based on the improved golden sine algorithm according to claim 9, characterized in that: The dynamic reverse learning strategy is as follows: Among them, r is the reverse learning random number, P NEWI (t) is the position of the I-th individual after reverse learning in 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 the dynamic reverse learning probability; For the maximum number of iterations t max The tth iteration of is calculated as: p=t / t max 。

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