Sparse array optimization method and system based on improved arctic sea parrot optimization algorithm

Abstract

The application discloses a sparse array optimization method and system based on an improved arctic tern optimization algorithm, and the method comprises the following steps: according to an array element switch state matrix and an excitation amplitude matrix, an array antenna pattern optimization model is constructed under a preset constraint condition, and minimization of a peak sidelobe level is taken as an objective function; and the array antenna pattern optimization model is solved according to the improved arctic tern optimization algorithm, so that the lowest peak sidelobe level and the array element distribution are obtained. In view of the characteristics of a large number of optimization variables and strong nonlinearity of a traditional sparse array optimization, the algorithm adopts a sparse matrix strategy of joint coding of switches and excitation, and the array element switch matrix and the excitation amplitude matrix are optimized cooperatively, so that the solution space dimension is compressed significantly, and the solving efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the field of array antenna optimization technology, and in particular relates to a sparse array optimization method and system based on an improved puffin optimization algorithm. Background Technology

[0002] Array antennas, with their superior beamforming capabilities, high gain, and precise directional control, are widely used in various fields such as wireless communication, radar detection, mobile communication systems, and radio frequency identification (RFID). The optimization problem of array antennas typically involves the comprehensive optimization of multiple structural parameters, rather than just the geometric design of individual array elements. Therefore, it is considered a complex nonlinear optimization problem, requiring advanced optimization techniques for effective solutions.

[0003] With the rapid development of information technology, researchers use computer technology to model and identify parameters of array antennas, and employ advanced optimization algorithms for global search to effectively find the optimal array antenna layout to achieve the best radiation performance. Existing array antenna optimization methods mainly include swarm intelligence algorithms such as genetic algorithms, particle swarm optimization (PSO), and ant colony optimization (ACO), which have been widely applied in many industrial and engineering optimization fields. However, sparse array antenna design often involves complex nonlinear optimization problems. These traditional optimization algorithms often struggle to converge quickly and are prone to getting trapped in local optima when dealing with the precise positions and excitation amplitudes of array elements. Therefore, designing an efficient optimization algorithm that can guarantee both global search capability and improve local optimization accuracy has become a key issue in array antenna optimization research. Summary of the Invention

[0004] This invention provides a sparse array optimization method and system based on an improved puffin optimization algorithm, which is used to solve the technical problem that it is often difficult to converge quickly and easy to get trapped in local optima when dealing with the precise position and excitation amplitude of array elements.

[0005] In a first aspect, the present invention provides a sparse array optimization method based on an improved Arctic puffin optimization algorithm, comprising:

[0006] Based on the array element switching state matrix and excitation amplitude matrix, an array antenna pattern optimization model is constructed under preset constraints with the objective function of minimizing peak sidelobe level.

[0007] The array antenna pattern optimization model is solved using the improved Arctic Puffin optimization algorithm to obtain the lowest peak sidelobe level and array element distribution, specifically including:

[0008] Calculate the peak sidelobe level for each initial element distribution to obtain the current lowest peak sidelobe level and the corresponding optimal element distribution;

[0009] In the initialization phase, a dynamic back-learning strategy based on the Tent-Logistic-Cosine chaotic mapping is used to generate the initial array element distribution;

[0010] In the middle of the iteration, the positions of the array elements are updated according to the rules of the air flight stage and the rules of the diving foraging stage. A deep fusion strategy based on the nonlinear chaotic perturbation adaptive step size strategy and the piecewise variable-scale convex lens imaging strategy is introduced to adaptively adjust the mutation probability.

[0011] At the end of the iteration, a dynamic weight-driven neighborhood-difference collaborative mutation mechanism is activated to fine-tune the array element positions. The target lowest peak sidelobe level of the updated array element distribution is calculated. If the target lowest peak sidelobe level is better than the current lowest peak sidelobe level, it is replaced with the updated array element distribution.

[0012] Update the globally optimal array element distribution and the corresponding lowest peak sidelobe level;

[0013] Determine if the termination condition is met. If not, update the iteration count and continue iterating. Otherwise, output the globally optimal array element distribution and the lowest peak sidelobe level for each generation.

[0014] Secondly, the present invention provides a sparse array optimization system based on an improved Arctic puffin optimization algorithm, comprising:

[0015] The module is configured to construct an array antenna pattern optimization model with the objective function of minimizing peak sidelobe level under preset constraints, based on the array element switching state matrix and excitation amplitude matrix.

[0016] The solution module is configured to solve the array antenna pattern optimization model according to the improved Arctic Puffin optimization algorithm to obtain the lowest peak sidelobe level and array element distribution, specifically including:

[0017] Calculate the peak sidelobe level for each initial element distribution to obtain the current lowest peak sidelobe level and the corresponding optimal element distribution;

[0018] In the initialization phase, a dynamic back-learning strategy based on the Tent-Logistic-Cosine chaotic mapping is used to generate the initial array element distribution;

[0019] In the middle of the iteration, the positions of the array elements are updated according to the rules of the air flight stage and the rules of the diving foraging stage. A deep fusion strategy based on the nonlinear chaotic perturbation adaptive step size strategy and the piecewise variable-scale convex lens imaging strategy is introduced to adaptively adjust the mutation probability.

[0020] At the end of the iteration, a dynamic weight-driven neighborhood-difference collaborative mutation mechanism is activated to fine-tune the array element positions. The target lowest peak sidelobe level of the updated array element distribution is calculated. If the target lowest peak sidelobe level is better than the current lowest peak sidelobe level, it is replaced with the updated array element distribution.

[0021] Update the globally optimal array element distribution and the corresponding lowest peak sidelobe level;

[0022] Determine if the termination condition is met. If not, update the iteration count and continue iterating. Otherwise, output the globally optimal array element distribution and the lowest peak sidelobe level for each generation.

[0023] Thirdly, an electronic device is provided, comprising: at least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the sparse array optimization method based on the improved Arctic Puffin optimization algorithm according to any embodiment of the present invention.

[0024] Fourthly, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the program instructions are executed by a processor, the processor performs the steps of the sparse array optimization method based on the improved Arctic puffin optimization algorithm according to any embodiment of the present invention.

[0025] This application presents a sparse array optimization method and system based on an improved Arctic Puffin Optimization Algorithm (APO). First, it introduces a dynamic back-learning strategy using a Tent-Logistic-Cosine chaotic mapping to construct an initial population with high uniformity and diversity, significantly expanding the early search space and reducing the risk of getting trapped in local optima. Second, it deeply couples an adaptive step-size strategy with a convex lens imaging strategy, forming an adaptive transition mechanism of large-step global exploration in the early iteration and small-step fine mining in the later iteration. Simultaneously, it continuously injects diversity into the population through high-amplitude convex lens perturbations, significantly enhancing the ability to escape local optima. Finally, it proposes a "neighborhood-difference co-mutation" mechanism, integrating the advantages of neighborhood-based fine perturbations and the large escape of random difference mutations. A secondary search is performed on the optimal individual at the end of the iteration, further improving convergence accuracy and speed. Addressing the characteristics of traditional sparse array optimization—numerical complexity and strong nonlinearity—the algorithm employs a sparse matrix strategy of switch-excitation joint encoding, co-optimizing the element switch matrix and excitation amplitude matrix to significantly compress the solution space dimension and accelerate solution efficiency. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 A flowchart illustrating a sparse array optimization method based on an improved puffin optimization algorithm, as provided in an embodiment of the present invention;

[0028] Figure 2 This invention provides a schematic diagram illustrating the performance of different optimization algorithms under four different benchmark functions in a specific embodiment.

[0029] Figure 3 This is a schematic diagram showing the array radiation pattern results obtained by different algorithms in a specific embodiment of the present invention;

[0030] Figure 4 This is a schematic diagram showing the array radiation pattern results with two desired zeros from different algorithms in a specific embodiment of the present invention.

[0031] Figure 5 A structural block diagram of a sparse array optimization system based on an improved puffin optimization algorithm is provided in an embodiment of the present invention.

[0032] Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Please see Figure 1 The diagram shows a flowchart of a sparse array optimization method based on an improved Arctic Puffin optimization algorithm according to this application.

[0035] like Figure 1 As shown, the sparse array optimization method based on the improved Arctic Puffin optimization algorithm specifically includes the following steps:

[0036] Step S101: Based on the array element switching state matrix and the excitation amplitude matrix, construct an array antenna pattern optimization model with the objective function of minimizing the peak sidelobe level under preset constraints.

[0037] In this step, in the design of sparse planar array antennas, it is assumed that there is a rectangular planar array antenna model consisting of M×N array elements in the XOY plane, with the N array elements along the X direction (lateral direction) spaced at intervals of... M array elements are evenly arranged along the Y direction (vertical direction) at intervals of... The elements are evenly arranged. Therefore, (m, n) can be used to represent the position of any element in the array.

[0038] Matrix A represents the switching state of each element in the array:

[0039] ,

[0040] In the formula, express The position of the array element switch state. =1 means The array element at the location is activated. =0 means The array element at the location is turned off.

[0041] Matrix B represents the excitation of each element in the array:

[0042] ,

[0043] In the formula, express The magnitude of the excitation of the array element at the position, and 0 ≤ ≤1.

[0044] Let matrix C be:

[0045] ,

[0046] In the formula, when =0 indicates The array element at the location is closed, when When >0, it means The array element at the location is activated, at this time The value represents the magnitude of the excitation of the array element, and 0 ≤ ≤1.

[0047] Therefore, the expression for the array antenna pattern optimization model is:

[0048] ,

[0049] In the formula, The result is the optimization of the array antenna pattern. Let be the number of array elements in the y-direction of the antenna array. Let be the number of array elements in the z-direction of the antenna array. The excitation magnitude of the array element at position (m,n), 0≤m≤ , 0≤n≤ Let the elevation angle of the incoming wave be... azimuth angle is The antenna elevation angle beam direction is The azimuth beam direction is , The imaginary unit is the phase constant in free space. , λ is the wavelength.

[0050] Step S102: Solve the array antenna pattern optimization model according to the improved Arctic Puffin optimization algorithm to obtain the lowest peak sidelobe level and array element distribution.

[0051] In this step, the process of solving the array antenna pattern optimization model according to the improved Arctic Puffin optimization algorithm specifically includes:

[0052] Calculate the peak sidelobe level for each initial element distribution to obtain the current lowest peak sidelobe level and the corresponding optimal element distribution.

[0053] In the initialization phase, a dynamic back-learning strategy based on the Tent-Logistic-Cosine chaotic mapping is used to generate the initial array element distribution.

[0054] In this embodiment, for array antenna optimization, the Arctic Puffin optimization algorithm balances the global and local search performance well, which is beneficial for the effective search of the global optimum and the improvement of overall execution efficiency. However, the initial population distribution of the Arctic Puffin optimization algorithm is not uniform enough, which affects the convergence speed of the algorithm. In order to address the above-mentioned defects of the Arctic Puffin optimization algorithm, this paper proposes an improved Arctic Puffin optimization algorithm based on a dynamic back-learning strategy of Tent-Logistic-Cosine chaotic mapping.

[0055] As is well known, chaotic maps are widely used in swarm intelligence algorithms due to their good randomness and ergodicity, effectively maintaining population diversity and enhancing global search capabilities. Compared with other maps, the Tent chaotic map, with its simplicity and efficiency, has become one of the commonly used chaotic systems. It possesses good nonlinear behavior and is sensitive to initial conditions, introducing sufficient randomness and diversity into the optimization process. By incorporating the Logistic map and cosine function into the Tent map, a Tent-Logistic-Cosine chaotic strategy is formed. This combined operation not only effectively integrates the dynamic characteristics of the three maps but also increases the complexity of the system through the nonlinear transformation of the cosine function, thereby improving the diversity of the population solution set and avoiding premature convergence of the optimization algorithm.

[0056] The expression for the Tent-Logistic-Cosine chaotic mapping is:

[0057]

[0058] In the formula, This represents the location of the Arctic puffin after chaotic mapping iteration. A random number between 0 and 1 This is the current location information of the Arctic puffin.

[0059] While using the Tent-Logistic-Cosine chaotic mapping to generate initial solutions, a dynamic back-learning strategy is introduced. This expands the search space of the Arctic puffin, thereby improving the quality of the population initialization solutions. The expression for the dynamic back-learning strategy is:

[0060] ,

[0061] In the formula, To initialize the population using random generation, , All are random numbers distributed between 0 and 1. For reverse initial population, This represents the lower bound of the current problem. This represents the upper limit of the current problem.

[0062] First, the algorithm generates the initial population. Reverse initial population Then the two populations were merged into a new population. ={ ∪ The fitness values ​​of the new population are calculated, and a greedy strategy is used to ensure sufficient competition within the population, selecting the best N individuals as the initial population. This method allows the population to approach the optimal solution more quickly, thereby improving the convergence speed of the algorithm.

[0063] In the middle of the iteration, the positions of the array elements are updated according to the rules of the air flight stage and the diving foraging stage. A deep fusion strategy based on the nonlinear chaotic perturbation adaptive step size strategy and the piecewise variable-scale convex lens imaging strategy is introduced to adaptively adjust the mutation probability.

[0064] In this embodiment, an improved framework is proposed that deeply couples the adaptive step size strategy with the convex lens imaging strategy. Without altering the original two-stage structure of the APO (Aerial Probe Animal) system ("aerial flight - diving forage"), this method systematically reshapes the step size factor and mutation mechanism, enabling an adaptive transition from early wide-area exploration to later fine-grained mining. Furthermore, high-amplitude convex lens imaging perturbations are introduced at key iteration nodes to continuously inject diversity into the population.

[0065] In the initial iteration phase, introducing significant migration behavior enhances the long-distance search capability of individual puffins, expands the global exploration range, helps the algorithm quickly approach potential high-quality solutions, and accelerates convergence. As iterations progress, gradually reducing the movement range facilitates finer searching of local areas, improving solution accuracy. To achieve a dynamic transition from global search to local exploration, an adaptive step size factor is introduced to adjust the search intensity in segments, as shown in the following expression:

[0066] ,

[0067] ,

[0068] In the formula, These are the weight coefficients in the Logistic-Sine chaotic mapping. These are the control parameters for chaotic mapping. and Let be the chaotic variables in the t-th and t+1-th iterations, respectively. and These are the minimum and maximum step size factors, respectively. For nonlinear attenuation coefficient, is the perturbation amplitude coefficient, rand() is a standard normal random number, t is the current iteration number, and T is the maximum iteration number.

[0069] Simultaneously, a convex lens imaging learning strategy is introduced to perturb the Arctic puffin population that intensifies its search during the diving foraging phase, thereby enhancing population diversity and increasing the algorithm's likelihood of escaping local optima. The mathematical expression for this is as follows:

[0070] ,

[0071] ,

[0072] The Arctic puffin's target location update strategy for enhanced searching during the diving foraging phase is based on selection probability. Decide:

[0073] ,

[0074] When random value When the value is less than 0.5, the original algorithm strategy is used for position updating; otherwise, the convex lens imaging learning strategy is used for position updating, and its mathematical expression is as follows:

[0075] ,

[0076] in, For the first The dynamic scaling factor for each stage, , Let j be the scaling adjustment factor for the j-th stage. and These are the disturbance amplitude coefficients for stages 1 and 2. and Let θ be a uniformly random number in the interval [0,1], and let θ be the phase switching ratio. This represents the lower bound of the current problem. The upper limit of the current problem, This represents the current iteration number. The maximum number of iterations, To select the probability, For the first The individual in the first t+1 Position after the next iteration For the first The individual in the first t+1 The location after the next foraging gathering iteration. For the first The updated position of each individual Let be a uniformly random number within the interval [0,1] generated in the t-th iteration. To adjust the adaptive factor for the Arctic puffin's position in the water, For the first The current location of an individual.

[0077] At the end of the iteration, a dynamic weight-driven neighborhood-difference co-mutation mechanism is activated to fine-tune the array element positions. The target lowest peak sidelobe level of the updated array element distribution is calculated. If the target lowest peak sidelobe level is better than the current lowest peak sidelobe level, the updated array element distribution is used instead.

[0078] In this embodiment, a neighborhood-based mutation strategy and a random differential mutation strategy are deeply integrated to form a "neighborhood-differential co-mutation" mechanism to update the position of the Arctic puffin, enhancing the local exploration capability of the optimization algorithm and ensuring population diversity. To enable individuals to escape local optima, a random differential mutation strategy is applied to the currently optimal individual. This generates a larger step size, allowing the algorithm to escape local optima. In the later stages of the algorithm, the neighborhood-based mutation strategy has good local search capabilities, performing directional small perturbations within the neighborhood of the current solution, effectively improving convergence efficiency and accuracy. Combining the neighborhood-based mutation strategy and the random differential mutation strategy, a neighborhood-differential co-mutation mechanism is proposed, expressed as:

[0079] ,

[0080] ,

[0081] ,

[0082] ,

[0083] In the formula, and These are the maximum and minimum values ​​of the difference scaling factor, respectively. and These are the minimum and maximum values ​​of the neighborhood scaling factor. Neighborhood-difference fusion weights The neighborhood scaling factor. This represents the cumulative number of successes of the neighborhood mutation strategy up to iteration t. This represents the cumulative number of successes of the random differential mutation strategy at iteration t. Let be the optimal position in the neighborhood of an individual in generation t. Let be the position vector of the i-th individual in generation t. , These are the positions of two distinct individuals randomly selected from the population. To prevent small constants with a denominator of zero, To integrate the nonlinear decay coefficient of the weights, The amplitude of the chaotic disturbance. This is the difference scaling factor.

[0084] Update the globally optimal array element distribution and the corresponding lowest peak sidelobe level;

[0085] Determine if the termination condition is met. If not, update the iteration count and continue iterating. Otherwise, output the globally optimal array element distribution and the lowest peak sidelobe level for each generation.

[0086] In summary, the method in this application solves multi-objective optimization problems by improving the CEAM-APO algorithm. First, a dynamic back-learning strategy using the Tent-Logistic-Cosine chaotic map is adopted to replace the traditional random method for generating the initial population, improving initialization efficiency. Second, an adaptive step-size strategy and a convex lens imaging strategy are introduced to enhance global exploration capabilities and avoid getting trapped in local optima. Finally, at the end of the algorithm, a tail mutation operation is performed by deeply fusing a neighborhood-based mutation strategy and a random differential mutation strategy to ensure continuous optimization of the solution quality. The algorithm implementation process is as follows:

[0087] Initialization: Initialize the parameters of the CEAM-APO algorithm, randomly initialize the population, generate an initial value set using the dynamic back learning strategy of Tent-Logistic-Cosine chaotic mapping, calculate the corresponding fitness value, and select the current optimal fitness value.

[0088] Execute either the aerial flight phase or the underwater foraging phase: Based on the algorithm's current state, choose whether to enter either the aerial flight phase or the underwater foraging phase. In the underwater foraging enhanced search phase, an adaptive step-size strategy and a convex lens imaging strategy are applied to update individual positions to improve population diversity and ensure the population's broad exploration capabilities, thereby meeting the algorithm's requirements for diversity and global search during optimization. In this way, premature convergence to local optima is avoided, maintaining stronger exploratory power and stability.

[0089] A deep fusion strategy of neighborhood-based mutation and random differential mutation is implemented: During the optimization process, the population is further optimized by applying a deep fusion strategy of neighborhood-based mutation and random differential mutation, thereby breaking the constraints of local optima, enhancing the global exploration ability of the population, promoting the algorithm to explore in a wider solution space, and improving optimization performance.

[0090] Update population location and fitness values: Update the population location and fitness values ​​to accurately reflect the latest optimization results.

[0091] Check maximum iterations: Check if the maximum number of iterations has been reached. If the maximum number of iterations has been reached, output the optimal fitness value and terminate the algorithm. If the maximum number of iterations has not been reached, return to continue the optimization process.

[0092] Unlike deep learning methods, this approach does not require iterative gradient learning based on massive amounts of data. Instead, it adaptively finds the optimal array element arrangement through swarm intelligence, avoiding time-consuming iterative training computations. Furthermore, this method utilizes a dynamic back-learning strategy based on the Tent-Logistic-Cosine chaotic map to improve the initial population distribution, thereby enhancing the initial population quality and global search capability. It integrates adaptive step-size and convex lens imaging strategies, increasing the probability of population mutation and the likelihood of escaping local optima. By designing a fusion of neighborhood-based and random differential mutation strategies to dynamically adjust the position of the Arctic Puffin during the enhanced search phase, it balances the global and local search capabilities of the algorithm during iteration. This not only improves the algorithm's solution accuracy but also prevents it from prematurely falling into local optima. It can adapt to complex nonlinear problems in array antennas, thus achieving the goal of rapidly adjusting the excitation current, array element arrangement, and effectively optimizing peak sidelobe levels and sidelobe widths.

[0093] In a specific embodiment, array antenna synthesis typically involves numerous variables and is often defined as a multi-objective optimization problem. Therefore, before delving into array antenna optimization, it is necessary to conduct a reliability performance analysis of the proposed CEAM-APO algorithm to demonstrate its statistical performance and overall performance in handling high-dimensional problems.

[0094] To verify the performance of the proposed algorithm, several classic benchmark functions were used for testing, as shown in Table 1. In all algorithm tests, the number of iterations and the population size were set to 1000 and 100, respectively. The performance of the CEAM-APO algorithm was compared with the basic APO algorithm and some popular evolutionary algorithms (PSO, JS, GWO, and SA). Table 2 reports the statistical results of 50 independent runs, including best and worst cost values, mean, standard deviation, and success rate (error less than 1 e^(-1 / 2)). -6 The results show that the performance of APO, PSO, JS, GWO, and SA decreases significantly with increasing dimensionality. Figure 2 The performance of different optimization algorithms is demonstrated under four different benchmark functions. The CEAMA-APO algorithm exhibits superior optimization capability and convergence speed under these four benchmark functions. In particular, its convergence speed to the optimal solution is significantly faster than other traditional algorithms, indicating that the proposed algorithm is exceptionally computationally efficient. The experimental results show that the CEAM-APO algorithm is a reliable choice for high-dimensional problem optimization.

[0095] Table 1. Benchmark Functions

[0096] ,

[0097] Table 2 Comparison of results from 50 independent runs

[0098] ,

[0099] Based on the above comparison and analysis results, the characteristics of the proposed CEAM-APO algorithm can be described as follows:

[0100] First, a significant difference between the CEAM-APO algorithm and the original APO algorithm is the optimization of the search strategy through dynamic parameter adjustment. For example, in the original APO, the foraging factor and weight factor are dynamically adjusted according to the current iteration progress. This adaptability allows the algorithm to flexibly adjust the search strategy according to the characteristics of different problems, thus maintaining good performance on various optimization problems. However, APO may get trapped in local optima in some cases, mainly because its direct generation of puffin locations may lead to insufficient search capability. In contrast, the CEAM-APO algorithm introduces a dynamic back-learning strategy using the Tent-Logistic-Cosine chaotic map to increase the diversity of the initial population. This improvement helps the algorithm escape local optima and increases the probability of finding the global optimum.

[0101] Furthermore, the CEAM-APO algorithm introduces a t-distribution perturbation mutation strategy during iteration, enhancing its global search capability and preventing premature convergence. This strategy is similar to Gaussian mutation in APO, but the CEAM-APO algorithm improves performance through a complex dynamic adjustment mechanism. When the search gets stuck in a local optimum, the t-distribution perturbation mutation strategy breaks the limitation by adding perturbations, enhancing the global exploration capability. Compared with Gaussian mutation, the t-distribution is more volatile, allowing for a broader exploration of the search space and increasing the probability of finding the global optimum. Moreover, the strength and frequency of the t-distribution perturbation can be dynamically adjusted to avoid premature convergence, enhancing the algorithm's applicability and effectiveness in complex optimization problems. This improvement optimizes the search strategy and enhances the performance of the CEAM-APO algorithm in diverse and high-dimensional problems, strengthening its competitiveness.

[0102] Finally, the superiority of the CEAM-APO algorithm is also reflected in its improved convergence speed. By employing a tail mutation strategy, the CEAM-APO algorithm can adjust the individuals in the population at the end of the iteration, thereby significantly improving the convergence speed and approaching the optimal solution of the problem more quickly. This improvement makes CEAM-APO particularly outstanding when dealing with high-dimensional problems, further enhancing its applicability and competitiveness in complex optimization problems.

[0103] The CEAM-APO algorithm is used to handle two different types of linear array antenna synthesis problems: sidelobe suppression and null control.

[0104] In the sidelobe suppression problem, a 20-element linear array antenna model is designed. The problem is to find the optimal excitation current for the array elements to obtain a radiation pattern that minimizes the maximum sidelobe level (SLL). The improved Puffin optimization algorithm uses a population size of 20 in each run, with a maximum of 50 iterations. Assuming uniform element distribution, the optimization process is initiated with the following objective function:

[0105] ,

[0106] In the formula, For fitness value, Array factor;

[0107] In this experiment, three optimization algorithms (Arctic Puffin Optimization (APO), Particle Swarm Optimization (PSO), and Artificial Jellyfish Optimization (JS)) were used to solve the same array antenna optimization problem. To ensure the consistency and comparability of the results, all calculations were normalized based on free-space wavelengths. To visually demonstrate the performance of different algorithms, the radiation modes of the synthesized array antenna were compared and analyzed. The array radiation patterns obtained by different algorithms are shown below. Figure 3 As shown, the performance of the CEAM-APO, APO, PSO, and JS algorithms in sidelobe level control is compared in detail. Specifically, the APO, PSO, and JS algorithms achieved maximum sidelobe levels of -22.19 dB, -15.04 dB, and -19.60 dB, respectively. Notably, the CEAM-APO algorithm performed best among these algorithms, producing a maximum sidelobe level of -22.75 dB, which is significantly better than the other optimized algorithms. Furthermore, the excitation current amplitudes obtained by these optimized algorithms are shown in Table 3. The experimental results demonstrate that the CEAM-APO algorithm has significant advantages in controlling sidelobe levels and can provide a better solution for array antenna design.

[0108] Table 3. Magnitude of excitation current under 20 array elements for different optimization algorithms

[0109] ,

[0110] In the null control problem, a linear array antenna model with 20 elements is designed, where the element positions are symmetrical with respect to the array center. The goal is to determine the excitation current magnitude of each element in the array antenna so that two desired nulls are formed at angles of 10° and 20° on the radiation pattern, and the expected level of these nulls is -50 dB. The fitness function used here is defined as follows:

[0111] ,

[0112] In the formula, Indicates the sidelobe level. To calculate the zero-depression depth, Let K be the desired zero-trap depth. Furthermore, K represents the number of zeros required. , The penalty coefficients were set to 10 for each algorithm to ensure consistency and comparability of the results. All algorithms were run under conditions of 50 iterations and a population size of 20. In this study, the optimization effects of the CEAM-APO, APO, PSO, and SS algorithms on the excitation current of the array antenna were applied and compared to achieve the desired null depth.

[0113] The sidelobe levels of the array antenna after optimization by different algorithms are shown in Table 4. All calculations were normalized based on free-space wavelengths. Figure 4 The diagram shows the optimal radiation pattern for any given iteration of all algorithms. It's noteworthy that while the PSO algorithm performs well in sidelobe level control, it fails to achieve the expected -50dB null depth at both the 10° and 20° positions. The SS algorithm achieves the expected null depth at 10°, but its performance at 20° is the worst, at -26.41dB. The APO algorithm achieves good null depths at both 10° and 20°, but neither reaches the expected depth. In terms of maximum sidelobe level, the APO algorithm achieves -10.98dB, the SS algorithm reaches -15.29dB, and the PSO algorithm reaches -8.77dB. Meanwhile, the proposed CEAM-APO algorithm performs best, with a maximum sidelobe level as low as -13.88dB. At both 10° and 20°, the CEAM-APO algorithm achieves the deepest null depth, reaching the expected -54.38dB at the 20° null position, significantly outperforming other optimization algorithms. The excitation current amplitudes obtained from these algorithm optimizations are shown in Table 5. Experimental results demonstrate that the CEAM-APO algorithm has significant advantages in controlling sidelobe levels and can provide a better solution for antenna array design.

[0114] Table 4. Sidelobe levels of different optimization algorithms with two desired zeros (0° and 20°).

[0115] ,

[0116] Table 5. Magnitude of excitation current under 20 array elements for different optimization algorithms

[0117] .

[0118] Please see Figure 5 The diagram shows a structural block diagram of a sparse array optimization system based on an improved puffin optimization algorithm according to this application.

[0119] like Figure 5 As shown, the sparse array optimization system 200 includes a construction module 210 and a solution module 220.

[0120] The construction module 210 is configured to construct an array antenna pattern optimization model under preset constraints, with the objective function of minimizing peak sidelobe levels, based on the array element switching state matrix and the excitation amplitude matrix. The solution module 220 is configured to solve the array antenna pattern optimization model using an improved puffin optimization algorithm to obtain the lowest peak sidelobe levels and array element distribution, specifically including:

[0121] Calculate the peak sidelobe level for each initial element distribution to obtain the current lowest peak sidelobe level and the corresponding optimal element distribution;

[0122] In the initialization phase, a dynamic back-learning strategy based on the Tent-Logistic-Cosine chaotic mapping is used to generate the initial array element distribution;

[0123] In the middle of the iteration, the positions of the array elements are updated according to the rules of the air flight stage and the rules of the diving foraging stage. A deep fusion strategy based on the nonlinear chaotic perturbation adaptive step size strategy and the piecewise variable-scale convex lens imaging strategy is introduced to adaptively adjust the mutation probability.

[0124] At the end of the iteration, a dynamic weight-driven neighborhood-difference collaborative mutation mechanism is activated to fine-tune the array element positions. The target lowest peak sidelobe level of the updated array element distribution is calculated. If the target lowest peak sidelobe level is better than the current lowest peak sidelobe level, it is replaced with the updated array element distribution.

[0125] Update the globally optimal array element distribution and the corresponding lowest peak sidelobe level;

[0126] Determine if the termination condition is met. If not, update the iteration count and continue iterating. Otherwise, output the globally optimal array element distribution and the lowest peak sidelobe level for each generation.

[0127] It should be understood that Figure 2 The modules and references described in the document Figure 1 The steps described in the text correspond to those in the method described above. Therefore, the operations, features, and corresponding technical effects described above also apply to the method described in the text. Figure 2 The various modules in the document will not be described in detail here.

[0128] In other embodiments, the present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein when the program instructions are executed by a processor, the processor performs the sparse array optimization method based on the improved puffin optimization algorithm in any of the above method embodiments.

[0129] In one embodiment, the computer-readable storage medium of the present invention stores computer-executable instructions, which are configured as follows:

[0130] Based on the array element switching state matrix and excitation amplitude matrix, an array antenna pattern optimization model is constructed under preset constraints with the objective function of minimizing peak sidelobe level.

[0131] The array antenna pattern optimization model is solved using the improved Arctic Puffin optimization algorithm to obtain the lowest peak sidelobe level and array element distribution, specifically including:

[0132] Calculate the peak sidelobe level for each initial element distribution to obtain the current lowest peak sidelobe level and the corresponding optimal element distribution;

[0133] In the initialization phase, a dynamic back-learning strategy based on the Tent-Logistic-Cosine chaotic mapping is used to generate the initial array element distribution;

[0134] In the middle of the iteration, the positions of the array elements are updated according to the rules of the air flight stage and the rules of the diving foraging stage. A deep fusion strategy based on the nonlinear chaotic perturbation adaptive step size strategy and the piecewise variable-scale convex lens imaging strategy is introduced to adaptively adjust the mutation probability.

[0135] At the end of the iteration, a dynamic weight-driven neighborhood-difference collaborative mutation mechanism is activated to fine-tune the array element positions. The target lowest peak sidelobe level of the updated array element distribution is calculated. If the target lowest peak sidelobe level is better than the current lowest peak sidelobe level, it is replaced with the updated array element distribution.

[0136] Update the globally optimal array element distribution and the corresponding lowest peak sidelobe level;

[0137] Determine if the termination condition is met. If not, update the iteration count and continue iterating. Otherwise, output the globally optimal array element distribution and the lowest peak sidelobe level for each generation.

[0138] Computer-readable storage media may include a stored program area and a stored data area, wherein the stored program area may store an operating system and an application program required for at least one function; the stored data area may store data created based on the use of a sparse array optimization system based on an improved Puffin optimization algorithm, etc. Furthermore, the computer-readable storage medium may include high-speed random access memory, and may also include memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, the computer-readable storage medium may optionally include memory remotely configured relative to a processor, which can be connected to the sparse array optimization system based on the improved Puffin optimization algorithm via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0139] Figure 6 This is a schematic diagram of the structure of the electronic device provided in the embodiment of the present invention, such as... Figure 6 As shown, the device includes a processor 310 and a memory 320. The electronic device may also include an input device 330 and an output device 340. The processor 310, memory 320, input device 330, and output device 340 can be connected via a bus or other means. Figure 6 Taking a bus connection as an example, memory 320 is the computer-readable storage medium described above. Processor 310 executes various server functions and data processing by running non-volatile software programs, instructions, and modules stored in memory 320, thereby implementing the sparse array optimization method based on the improved puffin optimization algorithm described in the above method embodiment. Input device 330 can receive input digital or character information and generate key signal inputs related to user settings and function control of the sparse array optimization system based on the improved puffin optimization algorithm. Output device 340 may include a display screen or other display device.

[0140] The aforementioned electronic device can execute the method provided in the embodiments of the present invention, and has the corresponding functional modules and beneficial effects for executing the method. Technical details not described in detail in this embodiment can be found in the method provided in the embodiments of the present invention.

[0141] In one implementation, the above-described electronic device is applied to a sparse array optimization system based on an improved puffin optimization algorithm, for a client, and includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to:

[0142] Based on the array element switching state matrix and excitation amplitude matrix, an array antenna pattern optimization model is constructed under preset constraints with the objective function of minimizing peak sidelobe level.

[0143] The array antenna pattern optimization model is solved using the improved Arctic Puffin optimization algorithm to obtain the lowest peak sidelobe level and array element distribution, specifically including:

[0144] Calculate the peak sidelobe level for each initial element distribution to obtain the current lowest peak sidelobe level and the corresponding optimal element distribution;

[0145] In the initialization phase, a dynamic back-learning strategy based on the Tent-Logistic-Cosine chaotic mapping is used to generate the initial array element distribution;

[0146] In the middle of the iteration, the positions of the array elements are updated according to the rules of the air flight stage and the rules of the diving foraging stage. A deep fusion strategy based on the nonlinear chaotic perturbation adaptive step size strategy and the piecewise variable-scale convex lens imaging strategy is introduced to adaptively adjust the mutation probability.

[0147] At the end of the iteration, a dynamic weight-driven neighborhood-difference collaborative mutation mechanism is activated to fine-tune the array element positions. The target lowest peak sidelobe level of the updated array element distribution is calculated. If the target lowest peak sidelobe level is better than the current lowest peak sidelobe level, it is replaced with the updated array element distribution.

[0148] Update the globally optimal array element distribution and the corresponding lowest peak sidelobe level;

[0149] Determine if the termination condition is met. If not, update the iteration count and continue iterating. Otherwise, output the globally optimal array element distribution and the lowest peak sidelobe level for each generation.

[0150] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of various embodiments or some parts of embodiments.

[0151] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A sparse planar array optimization method based on improved Arctic tern optimization algorithm, characterized in that, include: Based on the array element switching state matrix and excitation amplitude matrix, an array antenna pattern optimization model is constructed under preset constraints with the objective function of minimizing peak sidelobe level. The array antenna pattern optimization model is solved using the improved Arctic Puffin optimization algorithm to obtain the lowest peak sidelobe level and array element distribution, specifically including: Calculate the peak sidelobe level for each initial element distribution to obtain the current lowest peak sidelobe level and the corresponding optimal element distribution; In the initialization phase, an initial array element distribution is generated using a dynamic back-learning strategy based on the Tent-Logistic-Cosine chaotic map. The expression for this dynamic back-learning strategy is as follows: ， In the formula, To initialize the population using random generation, , All are random numbers distributed between 0 and 1. For reverse initial population, This represents the lower bound of the current problem. This represents the upper limit of the current problem. The expression for the Tent-Logistic-Cosine chaotic mapping is: ， In the formula, This provides the location information of the Arctic puffin at time i+1. A random number between 0 and 1 This provides the location information of the Arctic puffin at time i. In the middle of the iteration, the array element positions are updated according to the rules of the air flight stage and the diving foraging stage, and a deep fusion strategy based on the nonlinear chaotic perturbation adaptive step size strategy and the piecewise variable-scale convex lens imaging strategy is introduced to adaptively adjust the mutation probability. At the end of the iteration, a dynamic weight-driven neighborhood-difference collaborative mutation mechanism is activated to fine-tune the array element positions. The target lowest peak sidelobe level of the updated array element distribution is calculated. If the target lowest peak sidelobe level is better than the current lowest peak sidelobe level, it is replaced with the updated array element distribution. Update the globally optimal array element distribution and the corresponding lowest peak sidelobe level; Determine if the termination condition is met. If not, update the iteration count and continue iterating. Otherwise, output the globally optimal array element distribution and the lowest peak sidelobe level for each generation.

2. The sparse array optimization method based on the improved Arctic puffin optimization algorithm according to claim 1, characterized in that, The expression for the deep fusion strategy is: ， ， ， ， In the formula, For the first The dynamic scaling factor for each stage, , Let j be the scaling adjustment factor for the j-th stage. and These are the disturbance amplitude coefficients for stages 1 and 2. and Let θ be a uniformly random number in the interval [0,1], and let θ be the phase switching ratio. This represents the lower bound of the current problem. The upper limit of the current problem, This represents the current iteration number. The maximum number of iterations, To select the probability, Let i be the values ​​of individuals after the (t+1)th iteration. Let i be the position of the i-th individual after the (t+1)-th gathering and foraging iteration. Let i be the updated position of the i-th individual. A uniformly random number within the interval [0,1]. To adjust the adaptive factor for the Arctic puffin's position in the water, Let be the position of the i-th individual.

3. The sparse array optimization method based on the improved Arctic puffin optimization algorithm according to claim 1, characterized in that, The expression for the neighborhood-difference co-mutation mechanism is: ， ， ， ， In the formula, and These are the maximum and minimum values ​​of the difference scaling factor, respectively. and These are the minimum and maximum values ​​of the neighborhood scaling factor. Neighborhood-difference fusion weights, The neighborhood scaling factor. This represents the cumulative number of successes of the neighborhood mutation strategy up to iteration t. This represents the cumulative number of successes of the random differential mutation strategy at iteration t. Let be the optimal position in the neighborhood of an individual in generation t. Let be the position vector of the i-th individual in generation t. , These are the positions of two distinct individuals randomly selected from the population. To prevent small constants with a denominator of zero, The nonlinear attenuation coefficient is... The amplitude of the chaotic disturbance. This is the difference scaling factor.

4. A sparse array optimization system based on an improved puffin optimization algorithm, characterized in that, include: The module is configured to construct an array antenna pattern optimization model with the objective function of minimizing peak sidelobe level under preset constraints, based on the array element switching state matrix and excitation amplitude matrix. The solution module is configured to solve the array antenna pattern optimization model according to the improved Arctic Puffin optimization algorithm to obtain the lowest peak sidelobe level and array element distribution, specifically including: Calculate the peak sidelobe level for each initial element distribution to obtain the current lowest peak sidelobe level and the corresponding optimal element distribution; In the initialization phase, an initial array element distribution is generated using a dynamic back-learning strategy based on the Tent-Logistic-Cosine chaotic map. The expression for this dynamic back-learning strategy is as follows: ， In the formula, To initialize the population using random generation, , All are random numbers distributed between 0 and 1. For reverse initial population, This represents the lower bound of the current problem. This represents the upper limit of the current problem. The expression for the Tent-Logistic-Cosine chaotic mapping is: ， In the formula, This provides the location information of the Arctic puffin at time i+1. A random number between 0 and 1 This provides the location information of the Arctic puffin at time i. In the middle of the iteration, the array element positions are updated according to the rules of the air flight stage and the diving foraging stage, and a deep fusion strategy based on the nonlinear chaotic perturbation adaptive step size strategy and the piecewise variable-scale convex lens imaging strategy is introduced to adaptively adjust the mutation probability. At the end of the iteration, a dynamic weight-driven neighborhood-difference collaborative mutation mechanism is activated to fine-tune the array element positions. The target lowest peak sidelobe level of the updated array element distribution is calculated. If the target lowest peak sidelobe level is better than the current lowest peak sidelobe level, it is replaced with the updated array element distribution. Update the globally optimal array element distribution and the corresponding lowest peak sidelobe level; Determine if the termination condition is met. If not, update the iteration count and continue iterating. Otherwise, output the globally optimal array element distribution and the lowest peak sidelobe level for each generation.

5. An electronic device, characterized in that, include: At least one processor, and a memory communicatively connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method according to any one of claims 1 to 3.

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