A hybrid optimization method combining genetic algorithm and material distribution method

Abstract

The present invention discloses a hybrid optimization method for microwave circuits and antennas, which combines genetic algorithm with material distribution method, and belongs to the technical field of microwave circuit and antenna optimization. The method comprises: step 1: using two nested grids to divide the optimization area to obtain coarse and fine grids; step 2: using genetic algorithm to optimize the coarse grid to obtain a relatively simple structure; step 3: mapping the material distribution of the simple structure to the fine grid, using material distribution method to optimize, and obtaining the optimal antenna model. The optimization method combines the advantages of genetic algorithm and material distribution method, has fast convergence speed, complex topological structure, and avoids falling into a poor local optimal solution.

Description

Technical field:

[0001] The invention relates to the technical field of microwave circuit or antenna design optimization, and in particular to a hybrid optimization method combining a genetic algorithm and a material distribution method. Background technology:

[0002] Optimization problems have a long history, and can be traced back to the optimization theory proposed by Lagrange. In the field of structural mechanics, the use of optimization theory to achieve inverse design of devices has a history of 63 years, and many mature optimization algorithms have been produced. However, the use of optimization theory to achieve device design in the electromagnetic field started relatively late. In 1978, Marrocco and Pironneau first applied optimization theory to the design of electromagnets in "Optimum design with lagrangian finite elements: Design of an electromagnet" (Computer methods in applied mechanics and engineering, 1978, 15 (3): 277-308), which opened the history of optimization in the electromagnetic field.

[0003] Topological optimization has a higher degree of freedom in optimization. It can optimize the shape, size and topological connectivity of the optimization area and is applied to the inverse design of microwave circuits or antennas. The gradient-based material distribution method (Scalar Isotropic Material with Penalization Method, SIMP) has strong topological search capabilities and is relatively simple to implement. It is widely used in planar antenna design. In 2014, E. Hassan et al. used the material distribution method to optimize monopole antennas in the article "Topology optimization of metallic antennas" (IEEE Transactions on Antennas and Propagation, 2014, 62 (5): 2488-2500). In 2017, J. Wang et al. used the material distribution method to optimize patch antennas in the article "Antenna radiation characteristics optimization by a hybrid topological method" (IEEE Transactions on Antennas and Propagation, 2017, 65 (6): 2843-2854).

[0004] The gradient optimization algorithm is a local optimization algorithm that is very sensitive to the setting of initial values. Different initial variables will lead to large differences in the optimization convergence speed, number of iterations and final optimization results. In order to reduce the dependence of the gradient optimization algorithm on the initial value, the method of random initial value and multiple starts is generally used to obtain the optimal solution during the optimization process, but this method is inefficient. In 2004, S. Kucherenko and Y. Sytsko used low-discrepancy sequences (LDS) in the article "Application of deterministic low-discrepancy sequences in global optimization" (Computational Optimization and Applications, 2005, 30: 297-318) to achieve global gradient optimization and reduce the algorithm's dependence on the initial value, but for high-dimensional problems, this method is inefficient. In 2021, Z. Wang et al. used the time reversal method to obtain the initial value for the inverse design in nanophotonics based on a time-reversal technique (Opticsletters, 2021, 46(12): 2815-2818) in the article "Method to obtain the initial value for the inverse design in nanophotonics based on a time-reversal technique" (Opticsletters, 2021, 46(12): 2815-2818), and used physical mechanisms to determine the optimized initial structure, achieving good optimization results.

[0005] Genetic algorithm is a global optimization algorithm that can optimize the global optimal solution, but it has a slow convergence speed for large-scale variable problems. JM Johnson and Y. Rahmat-Samii used genetic algorithm to optimize patch antennas in the article "Genetic algorithms and method of moments (GA / MOM) for the design of integrated antennas" (IEEE Transactions on Antennas and Propagation, 1999, 47 (10): 1606-1614). The optimization area was divided into 49 square grids, with fewer optimization variables and faster algorithm convergence speed, resulting in a broadband patch antenna.

[0006] Using the structure optimized by genetic algorithm as the initial structure of material distribution method can avoid falling into poor local optimal solution, reduce the total optimization time and improve optimization efficiency. Summary of the invention:

[0007] The present invention proposes a hybrid optimization method that combines genetic algorithm and material distribution method, which can be used for topological optimization design of microwave circuits and antennas, and effectively avoids the gradient algorithm from falling into the local optimal solution. The method first divides the optimization area with a small number of grids, and uses genetic algorithm to optimize to obtain a relatively simple structure; then, the simple structure is mapped to the optimization variable of the material distribution method, and the material distribution method is used to further optimize the structure of the antenna, further reduce the objective function value, and obtain a microwave circuit or antenna with better performance.

[0008] The technical solution of the present invention is as follows: the optimization method firstly adopts a genetic algorithm to perform a global search for simple structures, and then adopts a material distribution method to optimize complex structures.

[0009] A hybrid optimization method combining a genetic algorithm and a material distribution method comprises the following steps:

[0010] Step 1: Create an initial model of the microwave circuit or antenna, and perform nested meshing on the area to be optimized to obtain coarse and fine meshes. The material density distribution obtained by optimizing the coarse mesh can be fully mapped on the fine mesh to ensure the connectivity between the genetic algorithm optimization stage and the material distribution method optimization stage;

[0011] Step 2: Use genetic algorithm to optimize the material in the coarse grid in step 1 to obtain a relatively simple structure. In this stage, the electromagnetic model grid is relatively coarse, and the time for an electromagnetic simulation is very short, which can achieve fast iteration and convergence, and obtain a simple structure with good electromagnetic response, and the structure has global optimal properties;

[0012] Step 3: Map the material distribution of the simple structure obtained in step 2 to the fine grid in step 1 as the initial value, and use the material distribution method to optimize the material in the fine grid. In the coarse grid distribution, the simple structure in step 2 is the global optimal structure. After refining the grid, the material distribution method can further reduce the objective function.

[0013] Furthermore, the specific implementation method of step 1 is:

[0014] Step 1.1: Use the positive direction grid to divide the optimization area to obtain a chessboard-shaped coarse grid;

[0015] Step 1.2: Perform finite element meshing on the basis of the coarse mesh in step 1.1 to obtain a triangular fine mesh. All graphics generated by the coarse mesh can be completely mapped on the fine mesh.

[0016] Furthermore, the specific implementation method of step 2 is:

[0017] Step 2.1: Binary encode the coarse grid in step 1 and use a random method to generate the initial population of the genetic algorithm to ensure the diversity of the initial population;

[0018] Step 2.2: Use the finite element method to calculate the objective function and perform linear sorting as the fitness of the individuals to avoid slow convergence or loss of diversity caused by improper scaling of the objective function;

[0019] Step 2.3: Use the tournament algorithm to select appropriate parent samples and simulate the elimination system to ensure selection intensity while avoiding diversity loss;

[0020] Step 2.4: Perform crossover and mutation to obtain sub-populations;

[0021] Step 2.5: Merge the parent population with the child population, and use the tournament algorithm to select the new generation population. Merging the parent population with the child population can retain elite individuals and ensure that the genetic algorithm achieves global convergence;

[0022] Step 2.6: Repeat steps 2.2-2.5 until the algorithm converges and the optimal distribution of coarse grid materials is obtained;

[0023] Further, the specific implementation method of step 3 is:

[0024] Step 3.1: Map the optimal distribution of coarse grid materials obtained in step 2 to the fine grid as the initial variable value of the material distribution method;

[0025] Step 3.2: Use the finite element method and the adjoint sensitivity analysis method to obtain the objective function value and gradient value of the optimization variable;

[0026] Step 3.3: Use the MMA algorithm to generate new optimization variable values. The MMA algorithm is a gradient optimization algorithm that can achieve rapid convergence of large-scale variable optimization problems.

[0027] Step 3.4: Repeat steps 3.2-3.3 until the algorithm converges and the optimal result of the material distribution method is obtained.

[0028] The beneficial effects of the present invention are as follows: the present invention proposes a method for jointly optimizing microwave circuits or antennas using a genetic algorithm and a material distribution method. The genetic algorithm can realize a global search of a simple structure, and use it as the initial structure of the material distribution method. A microwave circuit or antenna with better performance can be obtained through a one-time optimization, which effectively prevents the material distribution method from falling into a local optimal solution. The hybrid optimization of the genetic algorithm and the material distribution method can integrate the advantages of the two algorithms: 1. Rapid convergence is achieved; 2. The obtained topological structure is relatively complex and the objective function is low; 3. The gradient algorithm is prevented from falling into a poor local optimal solution. Description of the drawings:

[0029] Figure 1 Implement a flowchart for the algorithm;

[0030] Figure 2 is a schematic diagram of the patch antenna structure;

[0031] Figure 3 To optimize the regional mesh generation results;

[0032] Figure 4 It is the iterative process and optimization results of the genetic algorithm;

[0033] Figure 5 Iterative process and optimization results of material distribution method;

[0034] Figure 6 are the S parameters and radiation pattern of the microstrip antenna. Specific implementation method:

[0035] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0036] This embodiment provides a method for hybrid optimization of microwave devices or antennas by combining genetic algorithm and material distribution method. Taking microstrip patch antenna as an example, a specific optimization process is given. The algorithm process is as follows: Figure 1 shown. Figure 2 The structure diagram of the patch antenna is given. The antenna model is a back-fed patch antenna. The dielectric substrate of the antenna is Rogers RT / duroid 5880 (ε r =2.2, tanδ=0.0009), the upper surface of the dielectric substrate is a square with a side length of Lg=70mm, printed with a radiation patch with a side length of Lp=60mm, the thickness of the dielectric substrate is h=3mm, the lower surface of the dielectric substrate is a metal ground, the feeding port is located at the center of the antenna, and the optimized frequency is 5.8GHz.

[0037] The optimized area of ​​the antenna is the radiation patch on the upper surface of the dielectric substrate. Figure 3 The nested mesh partitioning strategy is demonstrated. First, the optimization area is partitioned using a square mesh with a side length of 6 mm, generating 100 meshes. On this basis, the optimization area is partitioned using a triangular mesh, resulting in 5442 meshes, with each square mesh corresponding to dozens of triangular meshes.

[0038] The present invention optimizes the high-gain linear polarization antenna, and the objective function is:

[0039]

[0040] Among them, f co is the target value of the main polarization of the antenna, θ1 is the optimized angle of the main polarization, and f cxis the cross-polarization target value of the antenna, θ2 is the optimized angle of cross-polarization, |S| is the S parameter value of the antenna, and w i (i=1, 2, 3) is the weight of the target value, w i >0.

[0041] The material in the positive direction grid is used as the optimization variable p1∈{0, 1} of the genetic algorithm. When the material in the grid is air, the optimization variable p1=0; when the material in the grid is metal, the optimization variable p1=1. In the genetic algorithm, the upper and lower symmetric structure is used to reduce the optimization variables to 50. The population size of each generation is 10, 50 iterations are performed, and the crossover probability of the population is set to 0.7 and the mutation probability is 0.5. Figure 4 (a) shows the optimization process of the genetic algorithm. The algorithm achieved convergence after 43 iterations and the optimization time was 6.5 hours. During the evolution process, the objective function curve showed a downward trend. The tournament method was used to select samples in each generation of evolution to ensure the diversity of the population, so the objective function curve would rise slightly at some points. The simple structure obtained by the genetic algorithm is as follows Figure 4 As shown in (b), the genetic algorithm is a global optimization algorithm. The structure is the global optimal solution and the objective function has been optimized to the minimum value.

[0042] In order to further obtain better optimization results, the material distribution method is used to further optimize the above simple structure. The optimization variable p2 is continuously distributed in the interval [0, 1]. When p2 = 0, the material in the grid is air; when p2 = 1, the material in the grid is metal; p2 has no practical significance when taking the middle value, and the middle value is removed by the filter function during the optimization process. Figure 5 (a) shows the optimization process of the material distribution method. The material distribution method achieves convergence after 87 iterations of the algorithm, and the optimization time is 2.5h.

[0043] HFSS software was used to Figure 5 The antenna in the simulation is simulated, and the simulated S parameters and radiation patterns are shown in Figure 6 As shown, the bandwidth of the antenna is 5.6-5.9 GHz, and a high gain of 12.4 dBi is achieved in the 0° direction.

[0044] The invention proposes a method for jointly optimizing microwave circuits or antennas using a genetic algorithm and a material distribution method. The invention can achieve better optimization effects through a single topology optimization, prevent the material distribution method from converging to a poor local optimal solution, reduce the number of material distribution method runs, and improve optimization efficiency.

[0045] The above descriptions are only preferred embodiments of the present invention, and all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

Claims

1. A hybrid optimization method combining genetic algorithm and material distribution method, characterized in that: The following steps are included: Step 1: Create an initial model of a microwave circuit or antenna, perform nested meshing on the area to be optimized, and obtain coarse and fine meshes. The material density distribution obtained by optimizing the coarse mesh can be fully mapped to the material density distribution of the fine mesh. Step 2: Use genetic algorithm to optimize the material in the coarse grid in step 1 to obtain a relatively simple structure; Step 3: Map the material distribution of the simple structure obtained in step 2 to the fine grid in step 1 as the initial value, and use the material distribution method to optimize the material in the fine grid. In the coarse grid distribution, the simple structure in step 2 is the global optimal structure. After refining the grid, the material distribution method can further reduce the objective function; The specific implementation method of step 3 is: Step 3.1: Map the optimal distribution of coarse grid materials obtained in step 2 to the fine grid as the initial variable value of the material distribution method; Step 3.2: Use the finite element method and the adjoint sensitivity analysis method to obtain the objective function value and gradient value of the optimization variable; Step 3.3: Use the MMA algorithm to generate new optimization variable values. The MMA algorithm is a gradient optimization algorithm that can achieve rapid convergence of large-scale variable optimization problems. Step 3.4: Repeat steps 3.2-3.3 until the algorithm converges and the optimal result of the material distribution method is obtained; Step 1 uses a back-feed patch antenna as the antenna model. The dielectric substrate of the antenna is Rogers RT / duroid5880 (ε r =2.2, tanδ=0.0009), the upper surface of the dielectric substrate is a square with a side length of Lg=70mm, printed with a radiation patch with a side length of Lp=60mm, the thickness of the dielectric substrate is h=3mm, the lower surface of the dielectric substrate is a metal ground, the feeding port is located at the center of the antenna, and the optimized frequency is 5.8GHz; The optimized area of ​​the antenna is the radiation patch on the upper surface of the dielectric substrate. First, the optimized area is divided into square grids with a side length of 6 mm, generating 100 grids. On this basis, the optimized area is divided into triangular grids to obtain 5442 grids, each of which corresponds to dozens of triangular grids. Optimize the high-gain linearly polarized antenna, the objective function is: Among them, f co is the target value of the main polarization of the antenna, θ1 is the optimized angle of the main polarization, and f cx is the cross-polarization target value of the antenna, θ2 is the optimized angle of cross-polarization, |S| is the S parameter value of the antenna, and w i (i=1,2,3) is the weight of the target value, w i >0; The material in the positive direction grid is used as the optimization variable p1∈{0,1} of the genetic algorithm. When the material in the grid is air, the optimization variable p1=0; when the material in the grid is metal, the optimization variable p1=1. In the genetic algorithm, the upper and lower symmetrical structure is used to reduce the optimization variables to 50. The population size of each generation is 10, and 50 iterations are performed. The crossover probability of the population is set to 0.7 and the mutation probability is set to 0.

5.

2. A hybrid optimization method combining genetic algorithm and material distribution method as claimed in claim 1, characterized in that: The optimization area is divided into coarse and fine nested grids. First, the optimization area is divided using a coarse grid to obtain the optimization variables of the genetic algorithm; then the optimization area is divided based on the coarse grid to obtain the optimization variables of the material distribution method.

3. A hybrid optimization method combining genetic algorithm and material distribution method as claimed in claim 1, characterized in that: The material distribution of the simple structure obtained by genetic algorithm optimization is mapped to the fine grid as the initial structure optimized by material distribution method.

4. A hybrid optimization method combining genetic algorithm and material distribution method as claimed in claim 1, characterized in that: In the step 1, the optimization area is divided by using a positive direction grid to obtain a chessboard-shaped coarse grid.

5. A hybrid optimization method combining genetic algorithm and material distribution method as claimed in claim 4, characterized in that: All graphics generated by the coarse grid can be completely mapped on the fine grid.

6. A hybrid optimization method combining genetic algorithm and material distribution method as claimed in claim 1, characterized in that: The specific implementation method of step 2 is: Step 2.1: Binary encode the coarse grid in step 1 and use a random method to generate the initial population of the genetic algorithm to ensure the diversity of the initial population; Step 2.2: Use the finite element method to calculate the objective function and perform linear sorting as the fitness of the individuals to avoid slow convergence or loss of diversity caused by improper scaling of the objective function; Step 2.3: Use the tournament algorithm to select appropriate parent samples and simulate the elimination system to ensure selection intensity while avoiding diversity loss; Step 2.4: Perform crossover and mutation to obtain sub-populations; Step 2.5: Merge the parent population with the child population, and use the tournament algorithm to select a new generation of population. Merging the parent population with the child population can retain elite individuals and ensure that the genetic algorithm achieves global convergence; Step 2.6: Repeat steps 2.2-2.5 until the algorithm converges and the optimal distribution of coarse grid material is obtained.

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