A Multi-Objective Antenna Optimization Method Based on Neural Networks and Evolutionary Algorithm Game Theory Model

Abstract

This invention discloses a multi-objective optimization method for antennas based on a game model of neural networks and evolutionary algorithms. It achieves efficient multi-objective optimization of lens antennas through integrated modeling technology, a game algorithm of PSO-GAO (Particle Swarm Optimization) and INN (Inverse Neural Network), and a defined objective function. Compared with existing lens antenna design methods, the proposed method has the following advantages: 1) High degree of automation, strong versatility, and high design efficiency in antenna design; 2) The proposed PSO-GAO and INN game algorithm provides a new solution to the problem of difficulty in determining the training set size; 3) INN can dynamically adjust the total number of optimization generations and the population size of PSO-GAO; 4) INN can assist PSO-GAO gradient descent to converge quickly; 5) The designed lens antenna can achieve good multi-objective characteristics.

Description

Technical Field

[0001] This invention relates to the field of lens antenna technology, specifically to a multi-objective optimization method for antennas based on a game model of neural networks and evolutionary algorithms (PSO-GAO vs INN). Background Technology

[0002] The increasing complexity of the electromagnetic environment and the growing demands of applications necessitate continuous improvements in the performance of systems such as radar, guidance systems, communications, biomedicine, electronic countermeasures, and radio astronomy. This places higher requirements on the performance of radiating antennas within these systems. Antenna design must consider satisfying multiple specific performance indicators, such as impedance bandwidth, aperture efficiency, gain, gain bandwidth, beamforming, and sidelobe level (SLL), thus presenting a significant challenge to modern antenna design. Furthermore, lens antennas offer advantages such as rich morphological variations and excellent electromagnetic characteristics. The development of 3D printing technology has made it possible to develop complex all-dielectric lens antenna structures, making them excellent candidates for meeting the needs of future antenna systems. Therefore, researching multi-objective optimization techniques for lens antennas is crucial.

[0003] Currently, most antenna designs in domestic and international literature are based on traditional trial-and-error methods. This requires continuous simulation (parameter scanning) to obtain the antenna's electrical performance by constantly changing its structural parameters, resulting in inconsistent design outcomes. Therefore, this method is extremely time-consuming, labor-intensive, and inefficient. To improve antenna design efficiency, antenna optimization algorithms based on evolutionary algorithms are gradually emerging. For example, full-wave simulation combined with genetic algorithms can be used to design superlens antenna elements, ensuring that each element meets specific transmission phase requirements. Finally, the elements are arrayed according to phase compensation rules to obtain an ultra-wideband, high-gain superlens antenna. Although this method avoids manual parameter tuning and optimization of lens antenna elements, accelerating the design of superlens antennas, it requires frequent calls to full-wave simulation software for optimization, leading to excessively long optimization times. Furthermore, manual array design of the algorithm-optimized elements is still necessary, a complex process requiring further calls to simulation software. On the other hand, with the further enhancement of computing power and the development of machine learning, machine learning methods (including neural networks, support vector regression, Gaussian process regression, etc.) are increasingly being applied to the electromagnetic field to accelerate design, especially neural network-based methods, which have achieved good results. For example, some literature uses neural networks to predict the S11 of antennas, enabling the design of multi-mode resonant antennas. However, research on lens antenna design based on neural networks, especially multi-target lens antenna design, is still very lacking. Summary of the Invention

[0004] This invention provides a multi-objective optimization method for antennas based on a game model of neural networks and evolutionary algorithms, which can realize the automatic and rapid integrated design of multi-objective lens antennas.

[0005] To solve the above problems, the present invention is achieved through the following technical solution:

[0006] The antenna multi-objective optimization method based on neural network and evolutionary algorithm game model includes the following steps:

[0007] Step 1: First, determine the feed structure based on the given design objectives; then, determine the lens structure based on the determined feed structure and the given design objectives; finally, match and fix the determined lens structure with the feed structure to obtain the lens antenna structure model.

[0008] Step 2: Use MATLAB-CST co-simulation to perform integrated modeling of the lens antenna structure model from Step 1, and obtain the integrated structure model of the lens antenna.

[0009] Step 3: Define the objective function for the predicted values ​​of the particle swarm genetic algorithm and the inverse neural network according to the design goal; this objective function contains two or more sub-objective functions, each sub-objective function corresponds to a different performance index, and the weights of each sub-objective function are assigned according to the importance of the performance index;

[0010] Step 4: Set the initial total number of optimization generations and the initial population size for the particle swarm genetic algorithm; at the same time, set the key parameters for the particle swarm genetic algorithm and the inverse neural network.

[0011] Step 5: Initialize the position and velocity of particles in the particle swarm genetic algorithm population, individual extreme values, and population extreme values, and let the position of each particle in the population represent a structural parameter vector of a lens antenna;

[0012] Step 6: Based on the integrated structural model of the lens antenna from Step 2 and the objective function from Step 3, execute the particle swarm genetic algorithm; during each iteration of the particle swarm genetic algorithm:

[0013] Step 6.1: Input the position of each particle in the population, i.e. the structural parameter vector of the lens antenna, into the integrated structural model of the lens antenna in Step 2. By writing the corresponding program in MATLAB to call CST to perform parameterized modeling of the lens and feed in the integrated structural model of the lens antenna, the actual values ​​of each performance index of the lens antenna corresponding to the structural parameter vector of each lens antenna are obtained.

[0014] Step 6.2: Substitute the structural parameter vector of each lens antenna from Step 6.1 and the actual values ​​of each performance index of the lens antenna corresponding to the structural parameter vector of the lens antenna into the objective function defined in Step 3, and calculate the objective function corresponding to the structural parameter vector of each lens antenna;

[0015] Step 6.3: Update the individual extreme value and the population extreme value based on the objective function calculated in Step 6.2, where the individual extreme value is the best position found so far by each particle in the population, and the population extreme value is the best position found so far by all particles in the population.

[0016] Step 7: Iteratively execute the particle swarm genetic algorithm from step 6 until the number of iterations of the particle swarm genetic algorithm reaches the current total number of optimization generations. Then, determine whether each sub-objective function corresponding to the population extremum is within the set limit range.

[0017] If so, the current group extremum is output as the structural parameter vector of the final optimized lens antenna;

[0018] Otherwise, the positions of all particles in the current population, i.e., the structural parameter vectors of all lens antennas and the actual values ​​of each performance index of the corresponding lens antennas, are used to form a training set, which is then passed to the inverse neural network for training to obtain the currently trained inverse neural network.

[0019] Step 8: Input the target values ​​of each performance index of the lens antenna into the inverse neural network trained in Step 7 to obtain the predicted structural parameter vector of the lens antenna; at the same time, input the predicted structural parameter vector of the lens antenna into the integrated structural model of the lens antenna in Step 2. By writing the corresponding program in MATLAB to call CST to perform parametric modeling of the lens and feed in the integrated structural model of the lens antenna, the simulated values ​​of each performance index of the lens antenna corresponding to the predicted structural parameter vector of the lens antenna are obtained.

[0020] Step 9: Using the predicted structural parameter vector of the lens antenna obtained in Step 8 and the simulated values ​​of various performance indicators of the lens antenna, substitute them into the objective function defined in Step 3 to calculate the objective function corresponding to the structural parameter vector of the lens antenna at this time, and determine whether the calculated objective function has converged:

[0021] If convergence is achieved, the currently predicted structural parameter vector of the lens antenna is output as the final optimized structural parameter vector of the lens antenna.

[0022] Otherwise, first compare the currently predicted structural parameter vector of the lens antenna with the current worst individual extreme value in the particle swarm genetic algorithm: if the currently predicted structural parameter vector of the lens antenna is better than the current worst individual extreme value, then replace the current worst individual extreme value with the currently predicted structural parameter vector of the lens antenna; otherwise, do nothing; then increase the total number of optimization generations and the initial population size at the same time, and return to step 5.

[0023] In step 4 above, the key parameters of the particle swarm genetic algorithm include mutation probability and crossover probability; the key parameters of the inverse neural network include the dimensions of the input layer, hidden layer and output layer, the number of training iterations, and the loss function.

[0024] In step 3 above, the objective function is defined as follows:

[0025]

[0026] In the formula, The objective function is... Let w be the i-th sub-objective function. i Let m be the weighting factor of the i-th sub-objective function, and m be the number of performance indicators of the lens antenna to be satisfied. Let be the target value of the i-th performance index of the lens antenna at the operating frequency freq. Let be the actual value of the i-th performance index of the lens antenna at the operating frequency freq, where maxfreq is the maximum operating frequency of the lens antenna and minfreq is the minimum operating frequency of the lens antenna. Let be an n-dimensional normalized structural parameter vector, where n is the number of structural parameters of the lens antenna to be optimized.

[0027] This invention utilizes a game-theoretic algorithm combining PSO-GAO (Particle Swarm Optimization) and INN (Inverse Neural Network), integrated modeling techniques, and objective function definition methods to construct a highly efficient multi-objective optimization algorithm for lens antennas. Examples verify its efficiency in multi-objective lens antenna design. Compared to existing lens antenna design methods, the proposed method has the following advantages: 1) High degree of automation, strong versatility, and high design efficiency in antenna design; 2) The proposed PSO-GAO and INN game-theoretic algorithm provides a new solution to the problem of difficulty in determining the training set size; 3) INN can dynamically adjust the total number of optimization generations and population size of PSO-GAO; 4) INN can assist PSO-GAO gradient descent to converge quickly; 5) The designed lens antenna can achieve good multi-objective characteristics. Attached Figure Description

[0028] Figure 1 This is a flowchart of a multi-objective optimization method for antennas based on a game model using neural networks and evolutionary algorithms.

[0029] Figure 2 This is a flowchart of the Particle Swarm Optimization Genetic Algorithm (PSO-GAO).

[0030] Figure 3 This is a flowchart of an inverse neural network (INN).

[0031] Figure 4 The following is a model of a lens antenna for an embodiment. (a) is a side view and (b) is a top view.

[0032] Figure 5 The gain curve of the lens antenna is shown in the example.

[0033] Figure 6 The aperture efficiency curve of the lens antenna is shown in the example.

[0034] Figure 7 The sidelobe level curve of the lens antenna is shown in the example.

[0035] Figure 8 The radiation pattern of the lens antenna at 66 GHz is shown in the example.

[0036] Figure 9 The radiation pattern of the lens antenna at 71 GHz is shown in the example.

[0037] Figure 10 The radiation pattern of the lens antenna at 76 GHz is shown in the example. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0039] See Figure 1 A multi-objective optimization method for antennas based on a neural network and evolutionary algorithm game model includes the following steps:

[0040] Step 1: First, determine the feed structure based on the given design objectives; then, determine the lens structure based on the determined feed structure and the given design objectives; finally, match and fix the determined lens structure with the feed structure to obtain the lens antenna structure model.

[0041] Before optimization, the design goals of the lens antenna must first be determined, such as antenna gain, aperture efficiency, and sidelobe level (SLL), and these design goals should be specified into numerical values. In a preferred embodiment of the present invention, the relationship between the design objective and the lens antenna structure is analyzed by exploring the scattering characteristics of the basic medium model, and then the structure of the feed source and lens is finally determined.

[0042] Step 2: Use MATLAB-CST co-simulation to perform integrated modeling of the lens antenna structure model from Step 1, and obtain the integrated structure model of the lens antenna.

[0043] This invention integrates the modeling of the lens antenna and the feed source, allowing for direct utilization of this integrated structural model during subsequent Particle Swarm Optimization (PSO) and Inverse Neural Network (INST) algorithms. By writing a corresponding program in MATLAB to call CST for parametric modeling of the lens and feed source within the lens antenna structural model, various performance indicators (i.e., electromagnetic response, including radiation pattern, gain, aperture efficiency, sidelobe level, etc.) of the lens antenna to be optimized can be directly obtained for subsequent algorithm optimization. This integrated modeling makes integrated optimization of the lens antenna feasible, eliminating the need for a series of operations such as designing lens elements, calculating compensation phases, and array arrangement. This simplifies and streamlines lens optimization, achieving automation and improving optimization efficiency. Furthermore, it allows for flexible application in antenna optimization, suitable for various optimization scenarios and objectives.

[0044] Step 3: Define the objective function for the predicted values ​​of the particle swarm genetic algorithm and the inverse neural network according to the design objectives.

[0045] To accommodate multi-objective requirements, the defined objective function will include multiple sub-objectives, each corresponding to different performance metrics, such as gain, aperture efficiency, sidelobe level, and radiation pattern. Furthermore, a sub-objective weighting method will be introduced to assign weights to each sub-objective based on its importance; that is, each sub-objective will be multiplied by a coefficient, with more important sub-objectives having larger coefficients and vice versa, making optimization more targeted. In addition, to make the objective function more accurately describe the design requirements, a worst-case performance index extraction method will be introduced. This method further customizes each sub-objective function according to the characteristics of each sub-objective, that is, it extracts the worst electromagnetic response in the entire frequency band for optimization, while retaining values ​​that are better than the target electromagnetic response. This invention uses an efficient and convenient objective function definition method, namely, defining the objective function using a sub-objective superposition method, and further refining the objective function using the sub-objective weighting method and the worst-case performance index extraction method. The designed objective function is as follows:

[0046]

[0047] In the formula, The objective function is... Let be an n-dimensional normalized structural parameter vector, where n is the number of structural parameters of the lens antenna to be optimized, i.e., the number of variables; min(*) denotes the minimum function. w is the i-th sub-objective function; iis the weighting factor for the i-th sub-objective function; m is the number of performance indicators of the lens antenna to be satisfied. Let be the target value of the i-th performance index of the lens antenna at the operating frequency freq; represents the actual value of the i-th performance index of the lens antenna at the operating frequency freq; maxfreq is the maximum operating frequency of the lens antenna; minfreq is the minimum operating frequency of the lens antenna; max(*) represents the maximum function.

[0048] In particle swarm optimization (PSO-GAO), the objective function measures the difference between the electromagnetic response parameters corresponding to the current structural parameters and the design target (performance index), thereby guiding PSO-GAO to perform efficient and directional optimization. The objective function of the PSO-GAO defined in this invention is:

[0049]

[0050] In inverse neural networks, the objective function measures the difference between the predicted values ​​and the design objective (performance metric), thereby preventing the INN from predicting spurious values. The objective function for the inverse neural network defined in this invention is:

[0051]

[0052] Step 4: Set the initial total number of optimization generations and the initial population size for the particle swarm genetic algorithm; at the same time, set other key parameters for the particle swarm genetic algorithm and the inverse neural network.

[0053] In this invention, due to the intervention of the INN, the total number of optimization generations and the population size of the particle swarm genetic algorithm will change with the iteration process of the INN. Similarly, the number of training data in the inverse neural network will also change with the iteration process of the INN. Therefore, the total number of optimization generations and the population size set at this time are only initial values. In this embodiment, the initial total number of optimization generations and the initial population size are set to be equal, that is, both are set to N=40.

[0054] In addition to the above, similar to existing particle swarm optimization (PSO) and inverse neural networks, key parameters for both algorithms need to be set before starting. Key parameters for PSO include mutation probability and crossover probability; for example, mutation probability is typically set to 0.6, and crossover probability to 0.8. Key parameters for inverse neural networks include the dimensions of the input layer, hidden layers, and output layer, the number of training iterations, and the loss function.

[0055] Step 5: Initialize the positions and velocities of particles in the particle swarm genetic algorithm population, individual extreme values, and population extreme values, and let the position of each particle in the population represent a structural parameter vector of a lens antenna.

[0056] In this invention, the position of each particle in the population represents a structural parameter vector of a lens antenna. Each lens antenna's structural parameter vector is an n-dimensional vector, comprising n structural parameters of the lens antenna to be optimized. Before running the particle swarm genetic algorithm, the particle velocities need to be initialized. Location Individual extreme values Population extreme values N is the population size, and all four terms are n-dimensional vectors. The particle's position represents the variable to be optimized (i.e., the lens structure parameters), the particle's velocity is used to update the position, the initial particle position is the initial individual extreme value, and the optimal position among all particles is the initial population extreme value.

[0057] Step 6: Execute the particle swarm genetic algorithm based on the integrated structural model of the lens antenna in Step 2 and the objective function in Step 3.

[0058] Particle Swarm Optimization (PSO) and Genetic Algorithm (GAO) are fusion algorithms. In this algorithm, PSO is the primary algorithm, and GAO is the auxiliary algorithm. The fusion is manifested as follows: in the PSO algorithm, the particle positions are updated using the PSO update mechanism; then, these particles are used as chromosomes in the genetic algorithm, and the crossover and mutation mechanisms of the genetic algorithm are used to update the chromosomes. The operation process of the PSO-GAO algorithm is as follows: Figure 2 As shown.

[0059] During each iteration of the particle swarm genetic algorithm:

[0060] First, the positions of the particles in the population are fed into the integrated structural model of the lens antenna in step 2. By writing the corresponding program in MATLAB to call CST to perform parameterized modeling of the lens and feed in the integrated structural model of the lens antenna, the actual values ​​of each performance index of the lens antenna corresponding to the structural parameter vector of each lens antenna are obtained.

[0061] Then, the structural parameter vector of the lens antenna is used as the objective function defined in step 3. The actual values ​​of each performance index of the lens antenna corresponding to the structural parameter vector of the lens antenna are used as the objective function defined in step 3. Calculate the objective function corresponding to the structural parameter vector of the lens antenna.

[0062] Finally, the individual and population extreme values ​​are updated based on the calculated objective function, where the individual extreme value is the best position found so far by each particle in the population, and the population extreme value is the best position found so far by all particles in the population.

[0063] Step 7: Iteratively execute the particle swarm optimization (PSO) algorithm from Step 6 until the total number of iterations reaches the current total number of generations. Then, determine whether each sub-objective function corresponding to the population extremum is within a predefined range. The range of the sub-objective functions refers to the pre-defined upper and lower limits of each performance indicator.

[0064] If so, the algorithm ends, and the current population extremum is output as the final optimized structural parameter vector of the lens antenna;

[0065] Otherwise, the particle swarm genetic algorithm enters a frozen state, and the positions of all particles in the current population (the structural parameter vectors of all lens antennas and the actual values ​​of the corresponding lens antennas at each operating frequency) are formed into a training set and passed to the INN for training, thus obtaining the currently trained inverse neural network.

[0066] Collect N training data using PSO-GAO Where j = 1, 2, ..., N, and N is the number of training data points; in this embodiment, since the population size is N, the number of training data points in the training set is also N. Let n be an n-dimensional normalized structural parameter vector, where n is the number of structural parameters of the lens antenna to be optimized. Let be an m-dimensional electromagnetic response parameter vector, where m is the number of performance parameters to be satisfied by the lens antenna. In, for example... Figure 4 In the embodiment shown, the structural parameters include the outer diameters R1-R5 of different regions of the lens, the heights h1-h5 of different regions of the lens, and the focal length F, where n = 11; the electromagnetic response includes the sidelobe level (SLL), gain, and aperture efficiency, where m = 3.

[0067] INN is a key step in assisting gradient descent in PSO-GAO. It is crucial when the number of PSO-GAO iterations reaches the total number of optimization generations, and the current objective function... If convergence is not achieved, PSO-GAO pauses, and INN temporarily takes over. At this point, the positions of all particles in the current population, i.e., the structural parameter vectors of all lens antennas and the actual values ​​of their respective performance indicators at each operating frequency—that is, N sets of training data—are generated and passed to INN. During the training of the inverse neural network, training stops when the loss function corresponding to INN converges (e.g., when the loss function falls below the target loss function value of 0.0025) or the maximum number of training iterations is reached (e.g., 50,000 iterations), indicating that INN has been trained successfully and possesses a certain predictive ability. The training process of the inverse neural network follows the existing inverse neural network training methods, as follows: Figure 3 As shown.

[0068] Step 8: Input the target values ​​of each performance index of the lens antenna into the inverse neural network trained in Step 7 to obtain the predicted structural parameter vector of the lens antenna. Simultaneously, the predicted structural parameter vector of the lens antenna is input into the integrated structural model of the lens antenna from Step 2. By writing a corresponding program in MATLAB to call CST to perform parametric modeling of the lens and feed source in the integrated structural model of the lens antenna, the simulated values ​​of each performance index of the lens antenna corresponding to the predicted structural parameter vector are obtained.

[0069] Step 9: First, use the predicted structural parameter vector of the lens antenna obtained in Step 8 and the simulated values ​​of various performance indicators of the lens antenna to calculate the objective function of Step 3. That is, use the predicted structural parameter vector of the lens antenna as the objective function defined in Step 3. The simulated values ​​of various performance indicators of the lens antenna are used as the objective function defined in step 3. Calculate the objective function corresponding to the structural parameter vector of the lens antenna at this time. Next, determine whether the calculated objective function converges:

[0070] If convergence is achieved, the INN game is successful, and the currently predicted structural parameter vector of the lens antenna is output as the final optimized structural parameter vector of the lens antenna.

[0071] Otherwise, first compare the currently predicted structural parameter vector of the lens antenna with the current worst individual extreme value in the particle swarm genetic algorithm: if the currently predicted structural parameter vector of the lens antenna is better than the current worst individual extreme value, then replace the current worst individual extreme value with the currently predicted structural parameter vector of the lens antenna; otherwise, do not process it. The judgment of the superiority of the currently predicted structural parameter vector of the lens antenna with the current worst individual extreme value is based on the objective function in step 3. The objective function of the currently predicted lens antenna... Objective function of the current worst individual extreme value Comparison calculation: the objective function of the currently predicted lens antenna Objective function less than or equal to the current worst individual extreme value At that time, the currently predicted structural parameter vector of the lens antenna is better than the current worst individual extreme value.

[0072] Next, increase both the total number of generations and the initial population size simultaneously, and return to step 5. The method and specific value of increasing the total number of generations and the initial population size can be manually set, such as by setting different increment steps, as long as the requirement of simultaneous increase in both the total number of generations and the initial population size is met. In this embodiment, the total number of generations and the population size are doubled from their current values. That is, when the current total number of generations and population size are N, both are changed to 2N before returning to step 5.

[0073] As is well known, the most difficult aspects of Particle Swarm Optimization (PSO) genetic algorithms are determining the total number of generations and the population size. Too many generations and a large population size slow down the optimization process and reduce efficiency; while too few generations and a small population size can improve efficiency, they may prevent finding the optimal result. To address this issue, this invention introduces an INN to assist PSO-GAO optimization. The INN can dynamically adjust the total number of generations and the initial population size, allowing them to increase to a reasonable level with a certain gradient. Furthermore, the INN can assist in the rapid convergence of the PSO-GAO objective function. By engaging in a convergence game between PSO-GAO and the INN, the algorithm can escape the excessive simulation optimization of PSO-GAO at any time.

[0074] This embodiment is based on Figure 4 The lens antenna model, design objectives, and INN input column values ​​are shown in Table 1. Since the training data for the INN is normalized, the input target electromagnetic response of the INN also needs to be normalized. The specific input target electromagnetic response values ​​are set by comprehensively considering the design objectives, the electromagnetic response of the INN, and the characteristics of the lens antenna itself. For the INN, a set of input electromagnetic response parameters results in a unique output. However, for a specific design objective, there are usually many sets of input electromagnetic response parameters that meet the requirements. For the designer, only one set of output parameters is needed. Based on the input electromagnetic responses in Table 1, the obtained output structural parameters are...

[0075] Table 1 Design Objectives, INN Input Electromagnetic Values, and CST Simulation Results

[0076]

[0077]

[0078] The structural parameters obtained by the method of this invention were simulated in CST using full-wave simulation to demonstrate the effectiveness of this method.

[0079] Figure 5 The image shows the gain curves of the lens antenna in this embodiment. It can be seen that the gain is consistently above 24 dBi, indicating that the lens antenna possesses good gain in the 60-90 GHz range.

[0080] Figure 6 The aperture efficiency curve of the lens antenna in this example shows that the aperture ratio is greater than 65% in the 60-90 GHz range, indicating that the lens antenna has a very good aperture utilization rate.

[0081] Figure 7 The image shows the sidelobe level curve of the lens antenna in the example. It can be seen that the sidelobe level (SLL) is below -15dB in the 60-90GHz range, indicating that the lens antenna has good sidelobe suppression performance.

[0082] Figure 8-10 The radiation patterns of the lens antenna designed for this embodiment at different frequencies show that the antenna has good directivity.

[0083] This invention discloses a multi-objective optimization method for lens antennas based on a game theory approach using inverse neural networks and particle swarm genetic algorithms. First, an initial training set is obtained through a PSO-GAO fusion algorithm, eliminating the tedious manual acquisition of the INN training set. Then, using integrated modeling technology, various performance indicators of the antenna to be optimized are directly obtained for algorithm optimization, improving optimization efficiency. Simultaneously, a sub-objective superposition method is used to define the objective function to achieve multi-objective optimization of the lens antenna (including aperture efficiency, gain, sidelobe level (SLL), etc.). Next, through the game theory mechanism between PSO-GAO and INN, INN intervenes to assist PSO-GAO in optimization and provides a corresponding predicted value for the desired electromagnetic response. This value is then fed into the CST (Computer-Surveyed Array) to verify convergence, thereby guiding INN to achieve a more accurate and efficient gradient descent of the objective function of PSO-GAO. By continuously increasing the iteration count of PSO-GAO and the size of the INN training set, the problem of insufficient or excessive INN training set size is solved. Simultaneously, INN can also dynamically adjust the population size of PSO-GAO to achieve a reasonable value. Finally, the objective functions of PSO-GAO and INN are defined using the minimum optimization after the superposition of various objectives. These functions are used to achieve multi-objective optimization of the lens antenna (including impedance characteristics, gain, aperture efficiency, sidelobe level, etc.). By applying different weights to each objective, the objective functions are dynamically modified, thereby guiding PSO-GAO and INN to achieve more accurate and efficient optimization. This invention utilizes the PSO-GAO vs INN algorithm, integrated modeling technology, and a precise objective function definition method to construct a set of efficient multi-objective optimization algorithms for lens antennas. Examples verify its efficiency in multi-objective lens antenna design.

[0084] It should be noted that although the embodiments described above are illustrative, they are not intended to limit the invention. Therefore, the invention is not limited to the specific embodiments described above. Any other embodiments obtained by those skilled in the art under the guidance of this invention without departing from its principles are considered to be within the protection scope of this invention.

Claims

1. A multi-objective optimization method for antennas based on a game theory model using neural networks and evolutionary algorithms, characterized by: The steps include the following: Step 1: First, determine the feed structure based on the given design objectives; then, determine the lens structure based on the determined feed structure and the given design objectives; finally, match and fix the determined lens structure with the feed structure to obtain the lens antenna structure model. Step 2: Use MATLAB-CST co-simulation to perform integrated modeling of the lens antenna structure model from Step 1, and obtain the integrated structure model of the lens antenna. Step 3: Define the objective function for the predicted values ​​of the particle swarm genetic algorithm and the inverse neural network according to the design goal; this objective function contains two or more sub-objective functions, each sub-objective function corresponds to a different performance index, and the weights of each sub-objective function are assigned according to the importance of the performance index; Step 4: Set the initial total number of optimization generations and the initial population size for the Particle Swarm Optimization (PSO) genetic algorithm; at the same time, set the key parameters for the PSO genetic algorithm and the inverse neural network; the key parameters for the PSO genetic algorithm include mutation probability and crossover probability; the key parameters for the inverse neural network include the dimensions of the input layer, hidden layer, and output layer, the number of training iterations, and the loss function. Step 5: Initialize the position and velocity of particles in the particle swarm genetic algorithm population, individual extreme values, and population extreme values, and let the position of each particle in the population represent a structural parameter vector of a lens antenna; Step 6: Based on the integrated structural model of the lens antenna from Step 2 and the objective function from Step 3, execute the particle swarm genetic algorithm; during each iteration of the particle swarm genetic algorithm: Step 6.1: Input the position of each particle in the population, i.e. the structural parameter vector of the lens antenna, into the integrated structural model of the lens antenna in Step 2. By writing the corresponding program in MATLAB to call CST to perform parameterized modeling of the lens and feed in the integrated structural model of the lens antenna, the actual values ​​of each performance index of the lens antenna corresponding to the structural parameter vector of each lens antenna are obtained. Step 6.2: Substitute the structural parameter vector of each lens antenna from Step 6.1 and the actual values ​​of each performance index of the lens antenna corresponding to the structural parameter vector of the lens antenna into the objective function defined in Step 3, and calculate the objective function corresponding to the structural parameter vector of each lens antenna; Step 6.3: Update the individual extreme value and the population extreme value based on the objective function calculated in Step 6.2, where the individual extreme value is the best position found so far by each particle in the population, and the population extreme value is the best position found so far by all particles in the population. Step 7: Iteratively execute the particle swarm genetic algorithm from step 6 until the number of iterations of the particle swarm genetic algorithm reaches the current total number of optimization generations. Then, determine whether each sub-objective function corresponding to the population extremum is within the set limit range. If so, the current group extremum is output as the structural parameter vector of the final optimized lens antenna; Otherwise, the positions of all particles in the current population, i.e., the structural parameter vectors of all lens antennas and the actual values ​​of each performance index of the corresponding lens antennas, are used to form a training set, which is then passed to the inverse neural network for training to obtain the currently trained inverse neural network. Step 8: Input the target values ​​of each performance index of the lens antenna into the inverse neural network trained in Step 7 to obtain the predicted structural parameter vector of the lens antenna; at the same time, input the predicted structural parameter vector of the lens antenna into the integrated structural model of the lens antenna in Step 2. By writing the corresponding program in MATLAB to call CST to perform parametric modeling of the lens and feed in the integrated structural model of the lens antenna, the simulated values ​​of each performance index of the lens antenna corresponding to the predicted structural parameter vector of the lens antenna are obtained. Step 9: Using the predicted structural parameter vector of the lens antenna obtained in Step 8 and the simulated values ​​of various performance indicators of the lens antenna, substitute them into the objective function defined in Step 3 to calculate the objective function corresponding to the structural parameter vector of the lens antenna at this time, and determine whether the calculated objective function has converged: If convergence is achieved, the currently predicted structural parameter vector of the lens antenna is output as the final optimized structural parameter vector of the lens antenna. Otherwise, first compare the currently predicted structural parameter vector of the lens antenna with the current worst individual extreme value in the particle swarm genetic algorithm: if the currently predicted structural parameter vector of the lens antenna is better than the current worst individual extreme value, then replace the current worst individual extreme value with the currently predicted structural parameter vector of the lens antenna. Otherwise, no action will be taken; Then increase both the total number of optimization generations and the initial population size, and return to step 5.

2. The antenna multi-objective optimization method based on neural network and evolutionary algorithm game model according to claim 1, characterized in that, In step 3, the objective function is defined as follows: In the formula, The objective function is... Let i be the sub-objective function. Let be the weight factor of the i-th sub-objective function. The number of performance indicators for the lens antenna to be met; The lens antenna is set at the operating frequency The target value of the i-th performance metric is given below. For lens antenna at operating frequency The actual value of the i-th performance metric. This is the maximum operating frequency of the lens antenna; This is the minimum operating frequency of the lens antenna; for A normalized structure parameter vector of dimension 1. The number of structural parameters of the lens antenna to be optimized.

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