Fast synthesis method of large sparse array based on interpolation theory

Abstract

The application discloses a large-scale sparse array fast synthesis method based on interpolation theory, which realizes efficient and reliable array layout synthesis under multiple constraint conditions by constructing a position updating strategy based on interpolation theory, dynamically and iteratively optimizing array element positions, and introducing a selection coefficient to realize adaptive adjustment of the updating strategy; the position updating strategy comprises exploration strategy and development strategy; the exploration strategy adopts global search to update the array element positions, discretizes an array aperture region into a grid vertex set, and enables the array element to jump to any grid vertex under the premise of meeting a minimum array element spacing constraint, so that large-scale position jumping is realized; the development strategy constructs a local search region, and performs position interpolation on the array element positions within the local search region. Meanwhile, a fast directivity diagram calculation method is combined, so that the time cost of directivity diagram evaluation is significantly reduced, and the calculation efficiency of large-scale array synthesis optimization is improved.

Description

Technical Field

[0001] This invention belongs to the field of array antenna optimization design, specifically involving a fast synthesis method for large-scale sparse arrays based on interpolation theory. Background Technology

[0002] Antennas, as devices used to transmit and receive electromagnetic waves, are widely used in military and civilian fields such as radio communication, radar detection, satellite navigation, remote sensing monitoring, and broadcasting systems. In many traditional applications, a single antenna can usually meet the basic operating requirements of the system. However, due to limitations in radiating aperture and structural form, a single antenna still has certain shortcomings in terms of directivity and gain. As engineering applications increasingly demand high gain, strong directivity, and beam controllability and scanning capabilities, a single antenna is difficult to meet the performance requirements of complex systems. To solve this problem, the method of arranging multiple antenna elements into an array antenna according to certain rules is often adopted. By adjusting the positional distribution between array elements and the excitation amplitude and phase, flexible beamforming and pointing adjustment can be achieved, thereby obtaining excellent radiation characteristics such as narrow beam, low sidelobes, and high gain.

[0003] In array antenna research, uniform arrays are widely used due to their simple structure and ease of implementation. However, to avoid grating lobes, the element spacing is usually limited to within half a wavelength. When it is necessary to increase the array aperture to obtain higher gain or narrower beams, the number of elements often increases significantly, which not only significantly increases system cost but also makes it difficult to control the overall weight, posing challenges to practical engineering applications. To balance radiation performance and implementation cost, researchers have proposed non-uniformly arranged sparse arrays and conducted extensive research. Sparse arrays, by reasonably reducing the number of elements within a fixed aperture, can still achieve radiation characteristics similar to uniform arrays, and are beneficial for reducing hardware costs and system complexity. Therefore, sparse arrays demonstrate significant application value in large-scale array design.

[0004] Rapid optimization of large-scale sparse array arrangements presents the following challenges:

[0005] Traditional sparse array optimization methods often rely on complex encoding mechanisms or require large-scale parallel searches. When faced with non-uniform arrays, non-convex constraints, and high-dimensional optimization spaces, they often suffer from slow convergence speeds, are prone to getting trapped in local optima, or struggle to strictly satisfy distance constraints. Especially when the array size is large, the computational cost of the radiation pattern increases dramatically, making it difficult to sustain the optimization process. Achieving efficient and reliable array layout optimization under multiple constraints, including minimum element spacing, array aperture, and the number of elements, is a major challenge of this invention. Summary of the Invention

[0006] The purpose of this invention is to provide a fast synthesis method for large-scale sparse arrays based on interpolation theory.

[0007] The technical solution to achieve the purpose of this invention is: a fast synthesis method for large-scale sparse arrays based on interpolation theory, comprising the following steps:

[0008] Step 1: Set the maximum number of iterations, grid discretization density, selection factor, and minimum element spacing;

[0009] Step 2: Based on the array size, number of array elements, and minimum element spacing, randomly generate an initial array layout that satisfies the constraints within the array aperture; calculate the radiation pattern of the initial array layout, and use the peak sidelobe level as the fitness value of the current layout.

[0010] Step 3: Calculate the selection coefficients for different location update strategies;

[0011] Step 4: Randomly select an array element in the current array as the object to be moved, and select the exploration strategy or development strategy for the current iteration according to the selection coefficient, thereby updating the array element position and obtaining a new array layout;

[0012] Step 5: Recalculate the radiation pattern based on the updated array layout, and use the peak sidelobe level as the fitness value of the new array layout;

[0013] Step 6: If the fitness value of the new array is better than that of the array before the iteration, then retain the layout of the new array; otherwise, retain the original layout.

[0014] Step 7: If the number of iterations reaches the maximum number of iterations, or the fitness value meets the preset optimization target, the iteration terminates and the optimal array layout is output; if the termination condition is not met, return to step 4 to continue the next iteration.

[0015] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described above.

[0016] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the above-described method.

[0017] A computer program product includes a computer program that, when executed by a processor, implements the steps of the above-described method.

[0018] Compared with the prior art, the present invention has the following significant advantages: (1) It introduces interpolation theory into sparse array synthesis, and realizes the jump search of array elements in the global range and the fine adjustment in the local area through position interpolation, thereby realizing the efficient and controllable movement of array element positions and significantly improving the comprehensive optimization capability of array layout. (2) By adaptively adjusting the position update strategy through the selection coefficient in the iteration process, the dynamic balance from exploration to development in the search stage is realized, improving the convergence efficiency and the stability of the solution. (3) In the iterative optimization process, a fast pattern calculation method is introduced, which significantly reduces the time overhead of pattern calculation, so that the method still maintains high computational efficiency in the high-dimensional optimization scenario of large-scale arrays.

[0019] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the initial array layout formation in this invention.

[0021] Figure 2 This is a schematic diagram of position update under the exploration strategy in this invention.

[0022] Figure 3 This is a schematic diagram of the construction of a local optimization region under the development strategy of this invention when there is no distance constraint.

[0023] Figure 4 This is a schematic diagram of the local optimization region construction under the distance constraint development strategy in this invention.

[0024] Figure 5 This is a flowchart of the rapid synthesis method in this invention.

[0025] Figure 6 This is a diagram showing the positional distribution of the narrowband sparse array in this invention.

[0026] Figure 7 (a) and (b) are side and top views of the three-dimensional radiation pattern of the narrowband sparse array in this invention.

[0027] Figure 8 The narrowband sparse array in this invention and Direction diagrams of the two cross-sections.

[0028] Figure 9 This is a diagram showing the location distribution of the ultra-wideband sparse array in this invention.

[0029] Figure 10 In the figures (a) and (b), the ultra-wideband sparse array in this invention operates at a frequency of [frequency missing]. Down Side and top views of a three-dimensional orientation diagram.

[0030] Figure 11 In the figures (a) and (b), the ultra-wideband sparse array in this invention operates at a frequency of [frequency missing]. Down Side and top views of a three-dimensional orientation diagram.

[0031] Figure 12 The ultra-wideband sparse array in this invention operates at a frequency of Down The directional cross-section.

[0032] Figure 13 In the figures (a) and (b), the ultra-wideband sparse array in this invention operates at a frequency of [frequency missing]. Down Side and top views of a three-dimensional orientation diagram.

[0033] Figure 14 In the figures (a) and (b), the ultra-wideband sparse array in this invention operates at a frequency of [frequency missing]. Down Side and top views of a three-dimensional orientation diagram.

[0034] Figure 15 The ultra-wideband sparse array in this invention operates at a frequency of Down The directional cross-section.

[0035] Figure 16 This describes the peak sidelobe level variation of the ultra-wideband sparse array in this invention when the beam is pointed to (0°, 0°) at different frequencies. Detailed Implementation

[0036] This invention proposes a fast synthesis method for large-scale sparse arrays. The basic idea is to optimize the element arrangement to minimize the array's normal radiation and sidelobe levels during scanning, while ensuring minimum spacing between elements of the same and different frequencies, and simultaneously improving computational efficiency and reducing computation time. However, traditional optimization methods require judging the spacing of all elements, leading to low algorithm efficiency. Furthermore, in the optimization of large-scale arrays, the computational load of the radiation pattern increases dramatically, making continuous optimization difficult. Therefore, it is necessary to improve the element arrangement optimization algorithm.

[0037] To achieve rapid synthesis of array element arrangements, this invention provides a fast synthesis method for large-scale sparse arrays, improving the efficiency and reliability of array layout optimization under multiple constraints. This invention constructs an element position update strategy based on interpolation theory and introduces selection coefficients to adaptively adjust the update mode during the iteration process. This allows the array elements to perform both global jump-type position searches to enhance exploration capabilities and fine-grained position adjustments in local regions to improve convergence quality, while strictly satisfying the minimum element spacing constraint. This achieves efficient and controllable iterative optimization of element positions, significantly enhancing array synthesis capabilities. Simultaneously, this invention combines a fast radiation pattern calculation method to accelerate the radiation pattern evaluation stage, significantly reducing iterative computational overhead and maintaining high computational efficiency in large-scale array synthesis optimization. Simulation results demonstrate that this invention has significant advantages in peak sidelobe level suppression and solution efficiency improvement, providing an effective method for the rapid synthesis design of large-scale sparse arrays.

[0038] This invention provides a fast synthesis method for large-scale sparse arrays, comprising the following steps:

[0039] The first step is to set the maximum number of iterations, the grid discretization density, the selection factor, and the minimum element spacing.

[0040] The second step is to randomly generate an initial array layout that meets the constraints within the array aperture, based on the array size, the number of array elements, and the minimum element spacing, such as... Figure 1 As shown. The radiation pattern of the initial array layout is calculated, and the peak sidelobe level is used as the fitness value of the current layout. The initial array layout is to randomly place N array elements within the array aperture, satisfying the minimum element spacing constraint in Chebyshev distance form.

[0041] The third step is to calculate the selection coefficients for different position update strategies based on the iteration progress. The specific steps are as follows.

[0042] Selection coefficient The expression is:

[0043] (1)

[0044] Where c is a constant, and the parameter is... It can be calculated using the following formula:

[0045] (2)

[0046] in, Indicates the current iteration number. The maximum number of iterations, It is an adjustment factor used to control the magnitude of change.

[0047] A random number is generated during each iteration. This allows for adaptive switching between two location update strategies: exploration and development. If... If so, then choose an exploration strategy for global search optimization; if If the solution is not found, a development strategy is chosen to perform local optimization in order to enhance the ability to perform fine optimization of the region near the current solution.

[0048] The fourth step involves randomly selecting an element from the current array as the object to be moved, and then choosing between an exploration or development strategy for the current iteration based on a selection coefficient. This updates the element's position, resulting in a new array layout. The position update strategy is as follows:

[0049] (1) Exploration strategy

[0050] The exploration strategy primarily employs a global search approach to update the positions of array elements. This strategy aims to grant array elements a large degree of freedom in their positional search, allowing them to explore extensively across the entire array aperture. This enables elements to jump out of their current positions and achieve significant positional leaps, avoiding getting trapped in local optima and improving global optimization performance. The core idea of ​​this exploration strategy is as follows: First, the array aperture region is discretized into a series of grid vertices; second, under the premise of satisfying the minimum spacing constraint, the array element selects to jump to any grid vertex position. This method not only ensures that the array elements have a high degree of positional freedom globally but also enables positional leap updates while satisfying the minimum spacing constraint. The specific implementation process is as follows:

[0051] First, it is necessary to The array aperture is discretized into a uniform grid, the grid consisting of side lengths... The array is composed of square elements. To effectively control the coupling effect between elements, the spacing between elements needs to meet the minimum spacing constraint. Given a grid size and minimum spacing The constraint relationship is expressed as follows:

[0052] (3)

[0053] In the formula, w is a positive integer used to adjust the density of the mesh, which needs to be controlled within a reasonable range: when w=1, the mesh size is equal to the minimum spacing of the array elements. While it can quickly locate the layout region with better performance, the grid is too sparse, making it difficult to achieve further optimization. When the value of w is too large, the grid is too dense, and the search space tends to be continuous. Although it can provide more candidate solution locations, the computational complexity will increase significantly.

[0054] Secondly, after mesh generation, the set of all vertices is defined as the candidate solution space for the positions of the array elements, using... This is represented as:

[0055] (4)

[0056] in, and They represent the first The y-coordinates of the q-th grid point and the q-th grid point It is a function that rounds down. It is the number of vertices along the x-axis. It represents the number of vertices along the y-axis.

[0057] After obtaining the feasible solution space for the element positions, a new mesh vertex that satisfies all constraints is found in this space region to update the element positions. This requires traversing the set of candidate solutions. We collect all vertices in the array and randomly select a feasible solution from them. Then, we check whether the distance between this position and all other array elements in the array satisfies the minimum spacing constraint. If it does, we update the position of array element P to this vertex; otherwise, we continue to select the next feasible solution for judgment until we find a grid vertex that meets the conditions. Figure 2 A schematic diagram of the updated array layout is shown.

[0058] (2) Development Strategy

[0059] In the development strategy, the approach gradually shifts from global search to local optimization to obtain the optimal solution. The core of this strategy lies in constructing a suitable local optimization region model while satisfying the minimum spacing constraint. Therefore, by adding small perturbations to the positions of the array elements, the overall array distribution density can be maintained while satisfying the minimum spacing constraint, thus achieving effective optimization of the array radiation pattern.

[0060] For the array element P to be moved, its position is denoted as... The nearest array element searched in its four directions (up, down, left, and right) is denoted as follows: , , , The corresponding coordinates are represented as , , , The feasible solution set for the positions of the matrix elements in the four directions is denoted as:

[0061] (5)

[0062] (6)

[0063] (7)

[0064] (8)

[0065] in, It represents the set consisting of all array elements in the current array. Represents a set The coordinates of the nth element in the array are represented as follows: .

[0066] If any of the above sets is not empty, then select the array elements from it. The mathematical expression for the nearest array element is as follows:

[0067] 1) If ,but:

[0068] (9)

[0069] 2) If ,but:

[0070] (10)

[0071] 3) If ,but:

[0072] (11)

[0073] 4) If ,but:

[0074] (12)

[0075] Candidates , , , Next, it is necessary to further verify whether the following constraints are met:

[0076] for It needs to meet the following requirements:

[0077] (13)

[0078] for It needs to meet the following requirements:

[0079] (14)

[0080] for It needs to meet the following requirements:

[0081] (15)

[0082] for It needs to meet the following requirements:

[0083] (16)

[0084] Traversing a collection All candidate array elements are examined, and their satisfaction with the constraints in equations (13)-(16) is checked sequentially. If a candidate array element satisfies any set of orientation conditions, then it can be confirmed that the array element satisfies the constraints in equations (13)-(16). , , , One of them. When equations (13)-(16) cannot be satisfied simultaneously, the set will continue to be used. Search for the next candidate array element in order to attempt to determine , , , If set If the array is empty, or if no array element can satisfy the above constraints after traversing all candidate array elements in set C, then, based on the boundary position of the array aperture, it is determined whether the spatial constraints in that direction can be directly satisfied by the boundary conditions.

[0085] When no minimum spacing constraint is applied, if , , , They exist in the corresponding directions, such as Figure 3 As shown in Figure (a). If there are no neighboring array elements satisfying the constraints in a certain direction, the spatial boundary in that direction is replaced by the array aperture boundary, as shown in Figure (a). Figure 3 As shown in Figure (b), after further introducing the Chebyshev distance minimum spacing constraint, its feasible search range is... Figure 4 The yellow area indicates that any candidate position within this area can meet the minimum distance requirement between array elements, thus ensuring that the new position of an array element will not conflict with other array elements around it, nor will it exceed the array aperture range. This effectively avoids the occurrence of infeasible solutions due to unreasonable local optimization range.

[0086] Ultimately, the local optimization range can be determined, and this range is related to... , , , Or, the aperture boundaries are adjacent, for any point within the local optimization region Its location is , can be represented as:

[0087] (17)

[0088] in, , They are , x-coordinate , They are , The ordinate, It is a minimum spacing constraint. , yes Random numbers.

[0089] If no neighboring array element satisfying the spacing constraint is found on a certain side, the boundary in that direction is replaced by the array aperture boundary. In this case, the formula needs to be adjusted accordingly based on the missing constraint. For example, when there is no array element satisfying the requirements on the left side, the local optimization region can be represented as:

[0090] (18)

[0091] If the same situation exists in other directions, a similar correction method can be used. Let this region be denoted as... Through the above processing, it can be ensured that the generated new position not only meets the minimum spacing constraint requirement, but also always lies within the effective aperture range of the array.

[0092] Under certain conditions, the local optimization range can be expanded. If the following conditions are met:

[0093] (19)

[0094] or

[0095] (20)

[0096] in, Each can be taken , , , If any one of them is satisfied, it means that there is still a feasible range of values ​​in the horizontal direction; similarly, let Each can be taken , , , If any one of these conditions is met, it means that there is still a feasible range of values ​​in the vertical direction. For example, if the interval This indicates that the current array element can perform extended local optimization in the upper region. Under this condition, assuming , , , All exist, and the positions of the left, right, and bottom boundaries can be determined. The position of the top boundary is determined by dividing the top of element P by... The nearest neighbor The decision is made. The extended local optimization range can be expressed as:

[0097] (twenty one)

[0098] yes The ordinate. For other conditions that are met... or The same method can be used to calculate its extended local optimization region. According to equations (19) and (20), it can be extended to 0~8 local optimization range regions, denoted as... , The value of is determined by the number of expressions (19) and (20).

[0099] In the development strategy, one can start from... and A region is randomly selected and its position is interpolated to generate a new array element that satisfies the constraints. .

[0100] The flowchart of the proposed fast synthesis method for large-scale sparse arrays based on interpolation theory is shown below. Figure 5 As shown.

[0101] The fifth step is to recalculate the radiation pattern based on the updated array layout and use the peak sidelobe level as the fitness value of the new array layout.

[0102] Let the array layout before iteration be The new array layout is Comparing the array layout before and after the iteration, only the i-th element moved. The formula for calculating the radiation pattern can be expressed as:

[0103] (twenty two)

[0104] in, It is an array Direction map, It is a new array layout Direction map, and This represents the contribution of element i to the array pattern before and after its position is updated. By replacing the contribution of element i to the array pattern, the pattern of the new array layout can be obtained quickly without having to repeatedly accumulate and calculate for all elements.

[0105] The fitness value function can be set as follows:

[0106] (twenty three)

[0107] Wherein, PSLL is the peak sidelobe level.

[0108] Step 6: If the fitness value of the new array is better than that of the array before the iteration, then retain the layout of the new array; otherwise, retain the original layout.

[0109] Combined with examples Figure 6 The image shows the element distribution of a narrowband sparse array. In this example, the number of elements... The array aperture is A rectangular planar array, in which The minimum spacing between array elements is set to the wavelength corresponding to the operating frequency. . Figure 7 (a) and (b) in the diagram are the side view and top view of the three-dimensional orientation diagram. Figure 8 yes and The radiation patterns of the two cross-sections have a peak sidelobe level of -17.22 dB.

[0110] Combined with examples Figure 9 The image shows the element distribution of an ultra-wideband sparse array. A rectangular planar array with a bandwidth ratio of 4:1 is constructed, and its operating frequency band is [missing information]. ,satisfy The array aperture is set to... Number of array elements Minimum element spacing ,in and They are frequencies and Corresponding wavelength. Scan angle range . Figure 10 and Figure 11 The operating frequency is Place and The normalized radiation patterns are shown, where (a) and (b) correspond to the side view and top view of the three-dimensional radiation pattern, respectively, with peak sidelobe levels of -17.69dB and -17.68dB, respectively. Figure 12 Operating frequency hour Direction diagram of the cross section. Figure 13 and Figure 14 The operating frequency is Place and The normalized radiation patterns are shown, where (a) and (b) correspond to the side view and top view of the three-dimensional radiation pattern, respectively, with peak sidelobe levels of -17.51dB and -17.48dB, respectively. Figure 15 yes hour Direction diagram of the cross section. Figure 16This shows the peak sidelobe level changes of the optimized array when the beam is pointed to (0°, 0°) at different frequencies.

Claims

1. A fast synthesis method for large-scale sparse arrays based on interpolation theory, characterized in that, The steps include the following: Step 1: Set the maximum number of iterations, grid discretization density, selection factor, and minimum element spacing; Step 2: Based on the array size, number of array elements, and minimum array element spacing, randomly generate an initial array layout that satisfies the constraints within the array aperture. Calculate the radiation pattern of the initial array layout and use the peak sidelobe level as the fitness value of the current layout; Step 3: Calculate the selection coefficients for different location update strategies; Step 4: Randomly select an array element in the current array as the object to be moved, and select the exploration strategy or development strategy for the current iteration according to the selection coefficient, thereby updating the array element position and obtaining a new array layout; Step 5: Recalculate the radiation pattern based on the updated array layout, and use the peak sidelobe level as the fitness value of the new array layout; Step 6: If the fitness value of the new array is better than that of the array before the iteration, then retain the layout of the new array; otherwise, retain the original layout. Step 7: If the number of iterations reaches the maximum number of iterations, or the fitness value meets the preset optimization target, the iteration terminates and the optimal array layout is output. If the termination condition is not met, return to step 4 to continue the next iteration.

2. The fast synthesis method for large-scale sparse arrays based on interpolation theory according to claim 1, characterized in that, The initial array layout described in step 2 involves randomly placing N array elements within the array aperture, while satisfying the minimum element spacing constraint in the form of Chebyshev distance.

3. The fast synthesis method for large-scale sparse arrays based on interpolation theory according to claim 1, characterized in that, Step 3, which involves calculating the selection coefficients for different location update strategies, is as follows: Selection coefficient The expression is: (1) Where c is a constant, and the parameter is... It is calculated by the following formula: (2) in, Indicates the current iteration number. The maximum number of iterations, This is an adjustment factor used to control the magnitude of change. A random number is generated during each iteration. Based on this, it adaptively switches between the two location update strategies: exploration and development; if If so, then choose an exploration strategy for global search optimization; if If so, then a development strategy should be chosen to perform local optimization.

4. The fast synthesis method for large-scale sparse arrays based on interpolation theory according to claim 3, characterized in that: The two location update strategies described in step 4 are as follows: (1) Exploration strategy The exploration strategy involves updating the array element positions using a global search approach. First, the array aperture region is discretized into a series of grid vertices. Second, each array element, while satisfying the minimum spacing constraint, jumps to any grid vertex position. The specific implementation process is as follows: First, it is necessary to The array aperture is discretized into a uniform grid, the grid consisting of side lengths... The array is composed of square elements. To effectively control the coupling effect between elements, the spacing between elements needs to meet the minimum spacing constraint. ; Given grid size and minimum spacing The constraint relationship is expressed as follows: (3) In the formula, w is a positive integer used to adjust the density of the grid; Secondly, after mesh generation, the set of all vertices is defined as the candidate solution space for the positions of the array elements, using... This is represented as: (4) in, and They represent the first The y-coordinates of the q-th grid point and the q-th grid point It is a function that rounds down. It is the number of vertices along the x-axis. It represents the number of vertices along the y-axis. After obtaining the feasible solution space for the element positions, a new mesh vertex that satisfies all constraints is found in this space region to update the element positions. This requires traversing the set of candidate solutions. We find all vertices in the array and randomly select a feasible solution from them. Then, we check whether the distance between the position and the other array elements in the array satisfies the minimum spacing constraint. If it does, we update the position of array element P to the vertex. Otherwise, we continue to select the next feasible solution for judgment until we find a grid vertex that meets the conditions. (2) Development Strategy For the array element P to be moved, its position is denoted as... The nearest array element searched in its four directions (up, down, left, and right) is denoted as follows: , , , The corresponding coordinates are represented as , , , The feasible solution set for the positions of the matrix elements in the four directions is denoted as: (5) (6) (7) (8) in, It represents the set consisting of all array elements in the current array. Represents a set The coordinates of the nth element in the array are represented as follows: ; If any of the above sets is not empty, then select the array elements from it. The mathematical expression for the nearest array element is as follows: 1) If ,but: (9) 2) If ,but: (10) 3) If ,but: (11) 4) If ,but: (12) Candidates , , , Next, it is necessary to further verify whether the following constraints are met: for It needs to meet the following requirements: (13) for It needs to meet the following requirements: (14) for It needs to meet the following requirements: (15) for It needs to meet the following requirements: (16) Traversing a collection All candidate array elements are examined, and their satisfaction with the constraints in equations (13)-(16) is checked sequentially. If a candidate array element satisfies any set of orientation conditions, it can be confirmed that the array element satisfies the constraints in equations (13)-(16). , , , One of them; when equations (13)-(16) cannot be satisfied simultaneously, it will continue in the set. Search for the next candidate array element in order to attempt to determine , , , If set If the array is empty, or if no array element can satisfy the above constraints after traversing all candidate array elements in set C, then, in combination with the boundary position of the array aperture, it is determined whether the spatial constraints in this direction can be directly replaced by boundary conditions. Finally, the local optimization range can be determined, and this range is related to... , , , Or, the aperture boundaries are adjacent, for any point within the local optimization region Its location is , can be represented as: (17) in, , They are , x-coordinate , They are , The ordinate, It is a minimum spacing constraint. , yes Random numbers; If no neighboring array element satisfying the spacing constraint is found on a certain side, the boundary in that direction is replaced by the array aperture boundary. In this case, the formula needs to be adjusted accordingly based on the missing constraint conditions. When there is no array element satisfying the requirements on the left side, the local optimization region is represented as follows: (18) The area is denoted as Through the above processing, it is ensured that the generated new position not only meets the minimum spacing constraint requirement, but also always lies within the effective aperture range of the array. Under certain conditions, the local optimization range can be expanded. If the following conditions are met: (19) or (20) in, Each can be taken , , , If any one of them is satisfied, it means that there is still a feasible range of values ​​in the horizontal direction; similarly, let Each can be taken , , , If any one of them is satisfied, it means that there is still a feasible range of values ​​in the vertical direction; for If the interval This indicates that the current array element can perform extended local optimization in the upper region. Under this condition, assuming , , , All exist, determining the left, right, and bottom boundary positions; the top boundary position is determined by the array elements. Above except The nearest neighbor The decision; the extended local optimization range can be expressed as: (21) yes The ordinate; for other conditions that satisfy the criteria... or The same method is used to calculate its extended local optimization region; according to equations (19) and (20), it can be extended to 0~8 local optimization range regions, denoted as , The value of is determined by the number of expressions (19) and (20); In the development strategy, from and A region is randomly selected and its position is interpolated to generate a new array element that satisfies the constraints. .

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method described in any one of claims 1-4.

7. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method described in any one of claims 1-4.

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