A Multi-Objective Optimization Method for Pixel Antennas Based on BPSO-MLP Algorithm

Abstract

This invention relates to a multi-objective optimization method for pixel antennas based on the BPSO-MLP algorithm, applied in the field of wireless communication antenna technology. An improved binary particle swarm optimization algorithm is used to perform a global search in the high-dimensional discrete coding space of the pixel antenna. A dynamic temperature parameter is introduced to adjust the shape of the sigmoid mapping function, and a probability-driven mutation mechanism is employed to effectively balance exploration and development capabilities. A performance prediction model is established through a designed multilayer perceptron neural network, enabling rapid and accurate prediction of key performance indicators such as bandwidth, gain, and radiation pattern of candidate antenna structures. An intelligent optimization mechanism submits the high-potential solutions selected through prediction to full-wave electromagnetic simulation, and the simulation results are fed back to the optimization algorithm to dynamically update the prediction model. This invention effectively solves the problems of high-dimensional discrete search, high simulation costs, and coordination of multiple performance indicators in multi-objective optimization of pixel antennas, providing an efficient solution for the design of reconfigurable antennas for next-generation communication systems.

Description

Technical Field

[0001] This invention relates to a multi-objective optimization method for pixel antennas based on binary particle swarm optimization and multilayer perceptron (BPSO-MLP) algorithm, which is mainly applied in the field of wireless communication antenna technology and belongs to the field of radio frequency front-end devices. Background Technology

[0002] With the rapid development of 5G mobile communication, low-Earth orbit satellite internet, and integrated sensing and communication systems, unprecedented demands are being placed on antennas for multifunctionality, reconfigurability, wide bandwidth, and high efficiency. While traditional microstrip antennas can achieve beam scanning, they require complex feed networks, phase shifters, and power amplifiers, resulting in large system size, high power consumption, and high cost. Furthermore, mechanically steerable antennas have slow response times, making it difficult to meet the real-time beam switching requirements of modern communication.

[0003] Pixel antennas, as an emerging reconfigurable antenna technology, can achieve flexible reconfiguration of frequency, radiation pattern, and polarization by controlling the switching state of surface radiating elements. Their core advantage lies in the fact that they eliminate the need for complex phase shifter networks, achieving beamforming solely through digital coding to control the surface current distribution. However, the optimized design of pixel antennas faces significant challenges:

[0004] There is a highly nonlinear mapping between the performance of a pixel antenna and the switching states of its surface elements. For a pixel antenna with N switching elements, the possible combinations of switching states reach 2^(N-1). N When N is large, traditional full permutation simulation methods are computationally infeasible due to the "combinatorial explosion" problem. For example, S. Koziel, J. Tan, and others published in IEEE Transactions on Antennas and Propagation that optimization algorithms such as genetic algorithms, simulated annealing algorithms, and traditional particle swarm optimization algorithms can be used to handle such high-dimensional discrete optimization problems, but these methods suffer from slow convergence speed, susceptibility to local optima, and the need for extensive and time-consuming electromagnetic simulations, severely limiting design efficiency.

[0005] Most existing pixel antenna designs only support frequency reconfiguration or one-dimensional pattern scanning, making it difficult to simultaneously achieve synergistic optimization of multiple target performances such as wide bandwidth, two-dimensional large-angle scanning, and high gain. For example, some phased arrays based on pattern-reconfigurable antennas can achieve a scanning range of ±60°, but are limited to one-dimensional scanning; while some two-dimensional scanning arrays suffer from low gain and narrow bandwidth. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing pixel antenna optimization techniques, such as low computational efficiency, susceptibility to local optima, and insufficient multi-objective coordination capabilities, and to provide a multi-objective optimization method for pixel antennas based on the BPSO-MLP algorithm. This method aims to significantly reduce the number of full-wave electromagnetic simulations, greatly improve optimization efficiency while ensuring optimization performance, and achieve simultaneous optimization of bandwidth, gain, and radiation pattern.

[0007] The present invention adopts the following technical solution:

[0008] A multi-target optimization method for pixel antennas based on the BPSO-MLP algorithm includes the following steps:

[0009] Step 1: Construct the BPSO-MLP collaborative optimization framework, which includes the global searcher BPSO and the pre-filter MLP;

[0010] Step 2: Model the pixel antenna to be optimized as an M×N digitally encoded metasurface, with each pixel unit corresponding to an RF switch; and encode the pixel antenna structure using a binary string of length L, where each bit '0' or '1' corresponds to the "open" or "closed" state of each RF switch; where L = M×N, and M and N are the number of rows and columns of the pixel unit;

[0011] Step 3: Use the global search engine BPSO to optimize the pixel antenna in the binary coding space using the binary particle swarm optimization algorithm to obtain multiple candidate pixel antennas. Use the multilayer perceptron neural network (MLP) to predict the performance of the candidate pixel antennas optimized by BPSO and obtain the predicted values ​​of bandwidth, gain and radiation pattern main lobe position.

[0012] Step 4: Determine whether the predicted value meets the performance requirements. If it does, perform full-wave electromagnetic simulation evaluation, calculate the fitness function, select the optimal candidate pixel antenna, and return to Step 3. If the predicted value does not meet the performance requirements, return directly to Step 3. This process continues until the set number of iterations is reached or the fitness function converges.

[0013] Furthermore, the multilayer perceptron neural network used by the pre-screener MLP includes an input layer, two hidden layers, and an output layer.

[0014] The input layer has L neurons, the first hidden layer has 2L neurons, the second hidden layer has L neurons, and the output layer has 3 neurons, corresponding to the predicted values ​​of bandwidth, gain, and main lobe position of the radiation pattern, respectively. The hidden layers use the Leaky ReLU activation function, and the Adam adaptive moment estimation algorithm is used as the optimizer for network training.

[0015] Furthermore, in step 3, the binary particle swarm optimization algorithm is used with the global searcher BPSO to optimize the pixel antenna in the binary coding space. The specific process is as follows:

[0016] Step 301: Initialize the parameters of the binary particle swarm optimization algorithm, including the upper limit of the number of iterations, the number of particles, the learning factor, and the range of values ​​for the inertia weight; the position of the particle is the encoding result of the pixel antenna structure, and the velocity is the direction and step size of the particle's movement in the search space.

[0017] Step 302, calculate the inertia weight. and learning factors and ;

[0018] ;

[0019] ;

[0020] In the formula, These are the maximum and minimum values ​​of the inertia weight, respectively. This is the upper limit of the number of iterations. This represents the current iteration number; and These are the initial values ​​of the learning factor; and These are the final values ​​of the learning factor when the number of iterations reaches the set maximum number of iterations;

[0021] Step 303, utilizing inertia weights and learning factors and Update the speed of the binary particle swarm optimization algorithm;

[0022]

[0023] In the formula, For the updated speed, At the current speed, and It is a random number within the interval [0, 1]. This represents the optimal fitness position found by the user from the start of the search to the current iteration. This represents the position with the best fitness among all particles in the entire particle swarm. Let be the coordinates of the current position of the i-th particle in the search space at the current iteration number t;

[0024] Step 304, perform location update:

[0025] Dynamic temperature parameters The attenuation formula is:

[0026]

[0027] In the formula, For attenuation rate control parameters, This is the set temperature parameter value when the number of cycles reaches the set maximum number of cycles.

[0028] Location update probability The formula is:

[0029]

[0030] The probability of each bit being '1' is calculated by combining the Sigmoid function with dynamic temperature parameters, and then the new binary position of the particle is determined by random sampling. :

[0031]

[0032] In the formula, rand() represents a random number between 0 and 1;

[0033] Then, an adaptive mutation probability based on particle velocity is introduced. :

[0034]

[0035] In the formula, This is the mutation probability parameter;

[0036] Based on adaptive mutation probability Adjust the binary position of the particles.

[0037] Furthermore, the fitness function in step 4 is:

[0038]

[0039] in, For maximum gain, To meet the return loss S 11 Number of frequency points corresponding to the maximum continuous bandwidth of <-10dB This is the angle index corresponding to the maximum gain. Indicates a directional range.

[0040] Compared with the prior art, the present invention has the following significant advantages:

[0041] a) Extremely high optimization efficiency: By pre-screening the massive number of candidate solutions generated by BPSO through MLP, approximately 93% of invalid electromagnetic simulations of low-fitness solutions are avoided, reducing the total optimization time to less than 10% of the traditional BPSO algorithm. For example, for the optimization of a 5×5 pixel antenna, traditional BPSO requires 1280 simulations (approximately 64 hours), while BPSO-MLP only requires 92 effective simulations (approximately 5 hours).

[0042] b) Excellent overall performance: The method of this invention can effectively coordinate the optimization of multiple objectives such as bandwidth, gain, and radiation pattern. Experiments have shown that the optimized antenna can achieve a relative bandwidth of over 25% in the Ku band (15 GHz center frequency), a gain of over 9 dBi in the 0° direction, and beam reconfiguration within the range of -65° to +65° while maintaining excellent gain flatness.

[0043] c) Powerful global search capability: The improved BPSO algorithm effectively balances the algorithm's exploration and development capabilities through dynamic temperature parameters and probability-driven mutation mechanisms, avoiding premature convergence and finding the global optimum or satisfactory solution more reliably in high-dimensional discrete space.

[0044] d) Good versatility and scalability: The method of this invention demonstrates good optimization effects and efficiency improvements for pixel antenna arrays of different sizes (such as 7×7, 9×9, 15×15), proving its versatility. This method can be extended to the design of antennas in the millimeter-wave band and larger-scale arrays.

[0045] e) High degree of automation: The entire “prediction-simulation-feedback” process is carried out automatically, reducing manual intervention and providing convenient and efficient automated design tools for engineering applications. Attached Figure Description

[0046] Figure 1 This is the overall architecture diagram of the BPSO-MLP collaborative optimization method provided in the embodiments of the present invention.

[0047] Figure 2 This is a schematic diagram of the MLP neural network structure used in this embodiment of the invention (input layer - hidden layer - output layer, with the number of neurons and residual connections labeled).

[0048] Figure 3 This is a schematic diagram of a 5×5 planar pixel antenna model used for optimization in an embodiment of the present invention.

[0049] Figure 4 This is a schematic diagram showing the gain prediction results and errors of the MLP network on the test set in an embodiment of the present invention.

[0050] Figure 5This is a schematic diagram showing the bandwidth prediction results and errors of the MLP network on the test set in an embodiment of the present invention.

[0051] Figure 6 This is a comparison chart of the S11 parameters of the pixel antenna optimized by the BPSO-MLP algorithm and the traditional BPSO algorithm in the embodiments of the present invention under 0° beam pointing.

[0052] Figure 7 This is a comparison of the main lobe gain of the pixel antenna optimized by the BPSO-MLP algorithm and the traditional BPSO algorithm in this embodiment of the invention under 0° beam pointing.

[0053] Figure 8 This is a comparison chart of the S11 parameters of the pixel antenna optimized by the BPSO-MLP algorithm and the traditional BPSO algorithm in this embodiment of the invention under a -45° beam pointing.

[0054] Figure 9 This is a comparison of the main lobe gain of the pixel antenna optimized by the BPSO-MLP algorithm and the traditional BPSO algorithm in this embodiment of the invention under a -45° beam pointing.

[0055] Figure 10 This is the optimized radiation pattern of the pixel antenna in the 15 GHz band, within the scanning range of -65° to +65°, obtained by using the BPSO-MLP algorithm in this embodiment of the invention. Detailed Implementation

[0056] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0057] A multi-target optimization method for pixel antennas based on the BPSO-MLP algorithm, the specific steps of which are as follows:

[0058] Step 1: Construct the BPSO-MLP collaborative optimization framework, the architecture of which is shown in the figure below. Figure 1 As shown, it includes the global searcher BPSO and the pre-filter MLP;

[0059] The pre-screener MLP uses a multilayer perceptron neural network consisting of one input layer, two hidden layers, and one output layer.

[0060] The input layer has n neurons, hidden layer 1 has 2n neurons, hidden layer 2 has n neurons, and the output layer has m neurons, where m is 3, corresponding to the bandwidth BW, gain Gain, and the predicted value Di of the main lobe position in the radiation pattern, respectively. The hidden layers use the Leaky ReLU activation function, and the Adam adaptive moment estimation algorithm is used as the optimizer for network training. The network architecture diagram is shown below. Figure 2 As shown.

[0061] Step 2: Model the pixel antenna to be optimized as an M×N digitally encoded metasurface, with each pixel unit corresponding to an RF switch; and encode the pixel antenna structure using a binary string of length L, where each bit '0' or '1' corresponds to the "open" or "closed" state of each RF switch; where L = M×N, and M and N are the number of rows and columns of the pixel unit.

[0062] Step 3: Using the global search engine BPSO, the binary particle swarm optimization algorithm is used to optimize the pixel antenna in the binary coding space to obtain multiple candidate pixel antennas. Then, the multilayer perceptron neural network is used to predict the performance of the candidate pixel antennas optimized by BPSO, and the predicted values ​​of bandwidth, gain and radiation pattern main lobe position are obtained.

[0063] Specifically, the binary particle swarm optimization algorithm is used to optimize the pixel antenna in the binary coding space using the global searcher BPSO. The specific process is as follows:

[0064] Step 301: Initialize the parameters of the binary particle swarm optimization algorithm, including the upper limit of the number of iterations, the number of particles, the learning factor, and the range of values ​​for the inertia weight; the position of the particle is the encoding result of the pixel antenna structure, and the velocity is the direction and step size of the particle's movement in the search space.

[0065] Step 302, calculate the inertia weight. and learning factors and ;

[0066] In particle swarm optimization (PSO) algorithms, the setting of inertia weights significantly impacts the algorithm's search performance. Larger inertia weights enhance global search capabilities, while smaller inertia weights are more beneficial for refined local searches. However, the linear inertia weight function used in traditional PSO algorithms often causes particles to prematurely fall into local optima, increasing the number of iterations and reducing optimization efficiency. To address this issue, this invention proposes a nonlinear inertia weight function that effectively balances the algorithm's global search capability in the early stages with its local search capability in the later stages. The specific expression is as follows:

[0067]

[0068] Learning factor in particle swarm optimization and These factors determine the influence of individual particle experience information and other particle experience information on the optimization trajectory, thereby regulating the algorithm's search behavior. In the early stages of algorithm optimization, to prevent particles from prematurely getting trapped in local optima, a larger [value] is typically used. Values ​​and smaller ones The value is adjusted to enhance the particle's reliance on individual experience, thereby expanding the search range. As the number of iterations increases, the value is gradually decreased. and increase To promote particle convergence towards the swarm optimum, this invention proposes a nonlinear asymmetric learning factor function. This function dynamically adjusts the trend of the learning factor, thereby enhancing the particle's ability and range to converge towards the global optimum in the early stages of optimization. The specific expression is as follows:

[0069]

[0070] In the formula, These are the maximum and minimum values ​​of the inertia weight, respectively. This is the upper limit of the number of iterations. This represents the current iteration number; and These are the initial values ​​of the learning factor; and These are the final values ​​of the learning factor when the number of iterations reaches the set maximum number of iterations;

[0071] Step 303, utilizing inertia weights and learning factors and Update the speed of the binary particle swarm optimization algorithm;

[0072]

[0073] In the formula, For the updated speed, At the current speed, and It is a random number within the interval [0, 1]. This represents the optimal fitness position found by the user from the start of the search to the current iteration. This represents the position with the best fitness among all particles in the entire particle swarm. Let be the coordinates of the current position of the i-th particle in the search space at the current iteration number t;

[0074] Step 304, perform location update:

[0075] This invention uses binary encoding to represent switch on and off states, with 1 representing a closed switch and 0 representing an open switch. Therefore, traditional particle swarm optimization needs to be improved to use binary output to achieve reconfigurable optimization. Commonly used mapping functions are prone to getting trapped in local optima; this invention introduces a dynamic temperature parameter. The value of , which varies with the iteration number t or decays, controls the steepness of the sigmoid function in the particle swarm optimization (PSO) algorithm. Its core function is to regulate the balance between exploration and development in the early stages of the algorithm, making the algorithm tend to converge quickly to the current optimal region in the initial stage, while gradually increasing the randomness in the later stages to avoid premature convergence.

[0076] Dynamic temperature parameters The attenuation formula is:

[0077]

[0078] In the formula, For attenuation rate control parameters, This is the set temperature parameter value when the number of cycles reaches the set maximum number of cycles.

[0079] Location update probability The formula is:

[0080]

[0081] The probability of each bit being '1' is calculated by combining the Sigmoid function with dynamic temperature parameters, and then the new binary position of the particle is determined by random sampling. :

[0082]

[0083] In the formula, rand() represents a random number between 0 and 1;

[0084] Then, an adaptive mutation probability based on particle velocity is introduced. :

[0085]

[0086] In the formula, This is the mutation probability parameter;

[0087] Based on adaptive mutation probability Adjust the binary position of the particles.

[0088] Step 4: Determine whether the predicted value meets the performance requirements. If it does, perform full-wave electromagnetic simulation evaluation, calculate the fitness function, select the optimal candidate pixel antenna, and return to Step 3. If the predicted value does not meet the performance requirements, return directly to Step 3. This process continues until the set number of iterations is reached or the fitness function converges.

[0089] The fitness function is:

[0090]

[0091] in, For maximum gain, To meet the return loss S 11 Number of frequency points corresponding to the maximum continuous bandwidth of <-10dB This is the angle index corresponding to the maximum gain. Indicates a directional range.

[0092] This embodiment uses a 5×5 digitally coded metasurface pixel antenna operating in the Ku band with a center frequency of 15 GHz as an example. Its structural schematic diagram is shown below. Figure 3 As shown, the goal is to achieve multi-objective optimization with a bandwidth greater than 25%, a scanning range covering ±65°, and a gain attenuation of less than 3dB during scanning.

[0093] In this embodiment of the invention, a phased array structure based on a pattern-reconfigurable antenna is described using a specific size combination (the data below are in millimeters):

[0094] Figure 3 In the diagram, 1-45 represent the RF pin switches between pixel metal blocks, with dimensions of 1.25×1.25. S1-S25 represent pixel metal blocks, with dimensions of 5×5. t1 and t2 form a T-shaped power divider network to achieve efficient coupling of electromagnetic energy. t1 has dimensions of 35×1.25, and t2 has dimensions of 1.25×5. The dielectric substrate uses Rogers RT / duroid 5880 high-frequency board material, which has a stable dielectric constant of 2.2 and extremely low dielectric loss tangent (tanδ<0.0009). Its dimensions are 45×50, and its wideband characteristics ensure stable electrical performance within the Ku band. In the diagram, the yellow part represents the pixel copper sheet of the antenna, the white part represents the switch, and the green part represents the pixel FR4 material substrate.

[0095] Example 1: BPSO-MLP optimization for a 5×5 pixel antenna.

[0096] 1. Optimize system configuration:

[0097] Software platform: ANSYS HFSS is used for full-wave electromagnetic simulation. The optimization process and algorithm execution are controlled by MATLAB scripts to achieve MATLAB-HFSS joint automated simulation.

[0098] Hardware platform: High-performance computing workstation.

[0099] 2. Parameter settings:

[0100] BPSO parameters:

[0101] Population size: 5 particles; Maximum number of iterations: 256; Inertia weight w: linearly decreasing, from 0.9 to 0.4; Learning factor and All values ​​are 1.5; Dynamic temperature parameters: =1, Attenuation rate control parameter =4.6; Probability of mutation parameter :4.6.

[0102] MLP parameters:

[0103] Network structure: 45 neurons in the input layer, 90 neurons in the first hidden layer, 45 neurons in the first hidden layer, and 3 neurons in the output layer (corresponding to bandwidth, gain, and main lobe direction).

[0104] Activation function: Leaky ReLU;

[0105] Optimizer: Adam (learning rate η=0.001);

[0106] Training set: Initially 920 sets of historical simulation data, which will be dynamically updated later.

[0107] Update strategy: Trigger MLP retraining every 50 new simulation data points, using early stopping (patience value 20 rounds).

[0108] 3. Optimization process:

[0109] Initialization: BPSO randomly initializes 5 particles (each particle is a 45-bit binary string). MLP is pre-trained using the initial 920 sets of data.

[0110] Iterative loop:

[0111] Based on the current velocity and position, BPSO generates five new candidate antenna structures (binary encoding).

[0112] The MLP reads these 5 codes and predicts their bandwidth, gain, and main lobe orientation.

[0113] A pre-screening threshold is set: prediction gain > 8.5 dBi and prediction bandwidth > 2.7 GHz. Only candidate solutions that meet the conditions are sent to HFSS simulation.

[0114] Assume two candidate solutions are selected for simulation in this round. After HFSS completes the simulation, it returns the S11 curve and radiation pattern data, and the gain prediction results are as follows. Figure 4 As shown, the blue line represents the true value of the data, and the red line represents the estimated data predicted by the MLP algorithm; the bandwidth prediction results are as follows. Figure 5 As shown, the blue line represents the true value, the red line represents the estimated value predicted by the MLP algorithm, and the vertical axis represents the frequency points, with each point representing 10MHz.

[0115] Calculate the true fitness values ​​of these two solutions (using the fitness function F). a The main lobe constraint direction interval Γ is set according to the target scanning direction.

[0116] Update the individual optimality of each particle in BPSO and population global optimum .

[0117] Add these two new (encoding and performance) data pairs to the MLP training pool. Check the training pool data volume; if the increment reaches 50, retrain the MLP.

[0118] Termination judgment: Repeat the above loop until 256 iterations are completed.

[0119] 4. Optimization Results and Analysis:

[0120] Efficiency Improvement: Throughout the 256 iterations, BPSO generated 1280 candidate solutions. After MLP pre-screening, only 92 solutions were used for actual HFSS simulation, eliminating 1188 (approximately 93%) low-potential solutions. The total optimization time was significantly reduced from approximately 64 hours required by traditional BPSO to approximately 5 hours, representing an efficiency improvement of over 90%. The bandwidth curve for 0° reconstruction is shown below. Figure 6 The gain optimization curve is shown in the figure. Figure 7 The bandwidth curve for reconstruction in the -45° direction is shown in the figure. Figure 8 The gain optimization curve is shown in the figure. Figure 9 .

[0121] Performance metrics: The optimized pixel antenna structure performs as follows at a center frequency of 15 GHz:

[0122] Bandwidth: The impedance bandwidth reaches 3.75 GHz with a return loss S11 < -10 dB, and the relative bandwidth is 25%.

[0123] Gain: The gain reaches 10.1 dBi when the beam is pointed at 0°.

[0124] Pattern Reconstruction: When the beam scans within the range of -65° to +65°, the gain fluctuation is less than 3 dB, the sidelobe level is less than -10 dB, and the reconstructed pattern within the range of -65° to +65° is as follows. Figure 10 Figures (a) to (h) are directional patterns reconstructed from representative angles within the scanning range of -65° to +65°.

[0125] Algorithm convergence: The fitness value of the BPSO-MLP algorithm tends to stabilize and approach the optimum after about 17 effective simulations, while the traditional BPSO is still searching after 182 simulations, which proves that BPSO-MLP has a faster convergence speed.

[0126] Example 2: Verification of algorithm universality (taking a 7×7 array as an example).

[0127] To verify the versatility of the method of the present invention, it was applied to the optimization of a 7×7 pixel antenna (91 switches).

[0128] Parameter adjustments: The MLP network structure was adjusted to have 91 neurons in the input layer, 182 neurons in hidden layer 1, 91 neurons in hidden layer 2, and 3 neurons in the output layer. The BPSO particle dimension was adjusted to 91.

[0129] Results: Using the same training set (920 initial samples), although the prediction accuracy of MLP decreased compared to the 5×5 array, it could still effectively filter out about 82% of low-potential solutions, reducing the total optimization time to 16.5% of the traditional method. The optimized antenna performance still met the preset target, demonstrating the algorithm's adaptability to problems of different scales.

[0130] As can be seen, a pattern reconfigurable antenna element with dual-port input can achieve large-angle scanning in two dimensions.

[0131] The method provided by this invention successfully solves the efficiency and performance bottlenecks in multi-objective optimization of pixel antennas, and provides an effective solution for the efficient and automated design of complex electromagnetic structures.

Claims

1. A pixel antenna multi-objective optimization method based on a BPSO-MLP algorithm, characterized in that, Includes the following steps: Step 1: Construct the BPSO-MLP collaborative optimization framework, which includes the global searcher BPSO and the pre-filter MLP; Step 2: Model the pixel antenna to be optimized as an M×N digitally encoded metasurface, with each pixel unit corresponding to an RF switch; The pixel antenna structure is encoded using a binary string of length L, where each bit '0' or '1' corresponds to the 'open' or 'closed' state of each RF switch; where L = M×N, and M and N are the number of rows and columns of the pixel unit; Step 3: Use the global search engine BPSO to optimize the pixel antenna in the binary coding space using the binary particle swarm optimization algorithm to obtain multiple candidate pixel antennas. Use the multilayer perceptron neural network (MLP) to predict the performance of the candidate pixel antennas optimized by BPSO and obtain the predicted values ​​of bandwidth, gain and radiation pattern main lobe position. Step 4: Determine if the predicted value meets the performance requirements. If it does, perform full-wave electromagnetic simulation evaluation, calculate the fitness function, select the optimal candidate pixel antenna, and return to Step 3. If the predicted value does not meet the performance requirements, return directly to Step 3. This process continues until the set number of iterations is reached or the fitness function converges. The pre-screener MLP uses a multilayer perceptron neural network consisting of one input layer, two hidden layers, and one output layer. The input layer has L neurons, the first hidden layer has 2L neurons, the second hidden layer has L neurons, and the output layer has 3 neurons, corresponding to the predicted values ​​of bandwidth, gain, and main lobe position of the radiation pattern, respectively. The hidden layers use the LeakyReLU activation function, and the Adam adaptive moment estimation algorithm is used as the optimizer for network training. In step 3, the global searcher BPSO is used to optimize the pixel antenna in the binary coding space using the binary particle swarm optimization algorithm. The specific process is as follows: Step 301: Initialize the parameters of the binary particle swarm optimization algorithm, including the upper limit of the number of iterations, the number of particles, the learning factor, and the range of values ​​for the inertia weight; the position of the particle is the encoding result of the pixel antenna structure, and the velocity is the direction and step size of the particle's movement in the search space. Step 302, compute inertia weight and learning factor and ; ； ； wherein are the maximum and minimum inertia weight, respectively, is the upper limit of the number of iterations, is the current iteration number; and are the initial values of the learning factor, respectively; and are the final values of the learning factor when the iteration number reaches the set upper limit of the number of iterations, respectively. Step 303, utilizing inertia weights and learning factors and Update the speed of the binary particle swarm optimization algorithm; ； In the formula, For the updated speed, At the current speed, and It is a random number within the interval [0, 1]. This represents the optimal fitness position found by the user from the start of the search to the current iteration. This represents the position with the best fitness among all particles in the entire particle swarm. Let be the coordinates of the current position of the i-th particle in the search space at the current iteration number t; Step 304, perform location update: Dynamic temperature parameters The attenuation formula is: ； In the formula, For attenuation rate control parameters, This is the set temperature parameter value when the number of cycles reaches the set maximum number of cycles. Location update probability The formula is: ； The probability of each bit being '1' is calculated by combining the Sigmoid function with dynamic temperature parameters, and then the new binary position of the particle is determined by random sampling. : ； In the formula, rand() represents a random number between 0 and 1; Then, an adaptive mutation probability based on particle velocity is introduced. : ； In the formula, This is the mutation probability parameter; Based on adaptive mutation probability Adjust the binary position of the particles.

2. The multi-target optimization method for pixel antennas based on the BPSO-MLP algorithm according to claim 1, characterized in that, The fitness function in step 4 is: ； in, For maximum gain, To meet the return loss S 11 Number of frequency points corresponding to the maximum continuous bandwidth of <-10dB This is the angle index corresponding to the maximum gain. Indicates a directional range.

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