Antenna design method based on collaborative hybrid electric eel algorithm

Abstract

The invention relates to the field of intelligent optimization algorithms, and provides an antenna design method based on a collaborative hybrid electric eel algorithm. The method comprises three stages of interaction, rest and hunting: in the interaction stage, introducing a differential variation strategy of DE, generating a new solution in combination with a random direction vector to enhance the global search capability, and if the individual fitness is insufficient, executing random disturbance to expand the search direction; in the rest stage, a PSO speed-position updating formula is adopted, and an individual extreme value and a global extreme value are utilized to guide local fine search; in the hunting stage, a Metropolis criterion of SA is combined, an inferior solution is accepted by probability to avoid local optimum, and exploration intensity is controlled through dynamic annealing temperature. According to the algorithm, self-adaptive mode switching is achieved by dynamically adjusting an energy attenuation factor and a simulated annealing temperature, meanwhile, a boundary reflection method is adopted to ensure that a solution is in a feasible region, and stability is improved. Experiments show that SHEEA can quickly jump out of local optimum in a complex multi-peak function test, and performance indexes are remarkably improved in multi-frequency antenna design.

Description

Technical Field

[0001] This invention relates to the field of intelligent optimization algorithms, and more specifically, to an antenna design method based on a hybrid intelligent optimization algorithm—the Cooperative Hybrid Electric Eel Algorithm (SHEEA)—that is based on the Electric Eel Foraging Optimization Algorithm (EEFO). Background Technology

[0002] In the field of antenna design, traditional optimization methods often face problems such as parameter interdependence, susceptibility to local optima, and slow iteration speed. These problems lead to complex and inefficient antenna design processes, making it difficult to meet the high performance requirements of modern communication systems. Therefore, developing an efficient and global optimization algorithm is particularly important.

[0003] The Electric Eel Foraging Algorithm (EEFO), as an emerging heuristic optimization algorithm, simulates the foraging behavior of electric eels and possesses strong global search capabilities. However, EEFO still suffers from slow convergence speed and susceptibility to local optima when dealing with complex multimodal problems. To overcome these shortcomings, this invention proposes a Collaborative Hybrid Electric Eel Algorithm (SHEEA), which significantly improves algorithm performance by introducing multiple optimization strategies. Summary of the Invention

[0004] The method of this invention achieves a balance between global exploration and local development by integrating the core mechanisms of differential evolution (DE), particle swarm optimization (PSO) and simulated annealing (SA), and is particularly suitable for solving complex engineering optimization problems such as antenna design.

[0005] The technical solution adopted in this invention is as follows:

[0006] An antenna design method based on a cooperative hybrid electric eel algorithm includes the following steps:

[0007] Step 1: Set the maximum number of iterations MaxIt, the population size PopSize, the problem dimension Dim, and the upper and lower bounds of the parameters lb and ub, and initialize the number of iterations It = 1;

[0008] Step 2: Each individual position corresponds to a set of antenna structure geometric parameters. Randomly generate the initial population position and ensure that the parameters are within the range of [lb, ub]. Then calculate the initial global optimal fitness and evaluate the antenna performance through the objective function.

[0009] Step 3: Calculate the energy decay factor E0 and the simulated annealing temperature T: E0 = 4·sin(1-It / MaxIt), T = 1000 / it;

[0010] Step 4: Randomly select RandNrm dimensions to generate a random direction vector DirectVector; where RandNum is in the range (2 ~ Dim);

[0011] Step 5: Calculate the current energy: E = E0·log(1 / rand). If E > 1, proceed to step 6; otherwise, proceed to step 7 with the set probability and to step 8 with the remaining probability; where rand is a random number.

[0012] Step 6: Randomly select an individual position in the population according to the random direction vector. When the randomly selected individual position has better fitness than the current individual position, move it towards the population mean or towards the random individual position with a set probability, and perform differential mutation operation as needed. When the current individual position has better fitness than the randomly selected individual position in the population, push it in the opposite direction towards the population mean or towards the random individual position with a set probability, and perform random perturbation operation as needed. Then proceed to step 9.

[0013] Step 7: Individuals in the population randomly walk according to a random direction vector to generate candidate positions and generate random numbers. If the random number is less than the set value, the velocity is updated and then step 9 is executed; otherwise, step 9 is executed directly.

[0014] Step 8: Individuals in the population walk randomly according to a random direction vector, calculate the predicted position of the individual at the next moment and update the velocity, and then calculate the fitness difference deltaF. If deltaF>0 or exp(deltaF / T)>rand, where rand is a random number, then accept the new individual position and proceed to step 9; otherwise, retain the original individual position and proceed to step 10.

[0015] Step 9: Determine whether the parameters corresponding to the new individual position are within the range of [lb, ub]. If they are, retain the new individual position; otherwise, retain the original individual position.

[0016] Step 10: Update the individual's historical best position pBest and global best fitness gBest, and store the current global best fitness; then let It = It + 1, return to step 3, and continue until the maximum number of iterations is reached;

[0017] Step 11: After the iteration is complete, output the global optimal position, i.e., the optimal parameter vector, and the global optimal fitness.

[0018] Furthermore, the formula for calculating the global optimal fitness is as follows:

[0019]

[0020] In the formula, gbest represents the global optimal fitness, bandwidth1 represents the first segment return loss bandwidth, bandwidth2 represents the second segment return loss bandwidth, bandwidth3 represents the third segment return loss bandwidth; gainrhcp1 represents the first segment right-hand circular polarization gain, gainrhcp2 represents the second segment right-hand circular polarization gain; axial1 represents the first segment axial ratio bandwidth, axial2 represents the second segment axial ratio bandwidth; fd1 represents the return loss value at the first extreme point, fd2 represents the return loss value at the second extreme point, fd3 represents the return loss value at the third extreme point; the return loss bandwidth, gain, axial ratio bandwidth, and return loss value are calculated based on the geometric parameters of the antenna structure.

[0021] Furthermore, the speed update formula in step 7 is:

[0022] v i (t+1)=ω·v i (t)+c1·r1·(pbest,ix i (t))

[0023] In the formula, v i (t+1) is the velocity vector of individual i in the next iteration; ω is the inertia weight; v i (t) is the current velocity vector of individual i; c1 is the cognitive acceleration coefficient; r1 is a random number in the interval [0,1]; pbest,i is the historical best position of individual i; x i (t) is the current position vector of individual i.

[0024] Furthermore, in step 8, the predicted position of the individual at the next moment is:

[0025] H i (t+1)=x i (t)+β×|x prey (t)|

[0026] In the formula, H i (t+1) is the predicted position of individual i at the next time step, x i (t) is the current position of individual i, and β is the position update coefficient; β decays with the number of iterations It, and β0 = 1;

[0027] β=β0·e -λIt

[0028] Speed ​​updated to:

[0029] v i (t+1)=H i (t+1)+η×(H i (t+1)-round(rand)×xi (t));

[0030] In the formula, λ and η are both set coefficients.

[0031] The advantages of this invention compared to the prior art are:

[0032] 1. This invention adopts a multi-strategy fusion mechanism, organically integrating the differential mutation strategy of differential evolution (DE), the velocity-position update formula of particle swarm optimization (PSO), and the Metropolis criterion of simulated annealing (SA) into the EEFO framework, thereby achieving a balance between global exploration and local exploitation.

[0033] 2. This invention enables the algorithm to adaptively switch between exploration and development modes during the iteration process by dynamically adjusting the energy decay factor (E0) and simulated annealing temperature (T), effectively avoiding premature convergence.

[0034] 3. This invention employs a strict boundary reflection method to ensure that the newly generated solution is within the feasible region, thereby improving the stability and convergence of the algorithm. Attached Figure Description

[0035] Figure 1 This is a flowchart of the method of the present invention.

[0036] Figure 2 This is a comparison chart of the convergence curves of this invention.

[0037] Figure 3 This is an antenna diagram designed using the method of this invention.

[0038] Figure 4 This is a comparison diagram of the antenna design and application of the present invention. Detailed Implementation

[0039] The following is in conjunction with the appendix Figure 1-4 The specific embodiments of the present invention will be described in further detail below.

[0040] An antenna design method based on the cooperative hybrid electric eel algorithm starts from initialization, first calculating dynamic parameters E0 and T, and then proceeding to the step of updating the group position.

[0041] Next, the process enters a decision node to check if the energy is greater than 1. If the energy is greater than 1, a DE differential mutation or random perturbation operation is performed; if the energy is not greater than 1, it further checks if the random perturbation is less than 1 / 3. If the random perturbation is less than 1 / 3, a PSO velocity update is performed; if it is not less than 1 / 3, it continues to check if the random perturbation is less than 1 / 2. If the random perturbation is less than 1 / 2, a migration strategy is executed; if it is not less than 1 / 2, a hunting strategy is executed.

[0042] Regardless of which strategy is employed, boundary reflection processing will then be performed, followed by evaluation of the new position. Afterward, the process enters another decision node to check if the acceptance criteria are met. If the acceptance criteria are met, the individual / global optimal solution is updated, and the optimal solution is recorded in a CSV file. Finally, it is determined whether the maximum number of iterations has been reached. If it has, the process ends; otherwise, it returns to the update group position step to continue execution.

[0043] like Figure 1 As shown, it includes the following steps:

[0044] Step 1: Set the maximum number of iterations MaxIt, the population size PopSize, the problem dimension Dim, and the upper and lower bounds of the parameters lb and ub, and initialize the number of iterations It = 1.

[0045] Step 2: Each individual position corresponds to a set of antenna structure geometric parameters. The initial population position is randomly generated, and the parameters are ensured to be within the range of [lb, ub]. Then, the initial global optimal fitness is calculated, and the antenna performance is evaluated through the objective function.

[0046] Step 3: Calculate the energy decay factor E0 and the simulated annealing temperature T: E0 = 4·sin(1-It / MaxIt), T = 1000 / It.

[0047] Step 4: Randomly select RandNum dimensions to generate a random direction vector DirectVector; where RandNum is in the range (2 ~ Dim).

[0048] Step 5: Calculate the current energy: E = E0·log(1 / rand). If E>1, proceed to step 6; otherwise, proceed to step 7 with a probability of 1 / 3 and to step 8 with a probability of 2 / 3; where rand is a random number.

[0049] Step 6: Randomly select an individual position in the population according to the random direction vector. When the randomly selected individual position has better fitness than the current individual position, move towards the population mean or towards the random individual position with a set probability (50% in this embodiment), and perform differential mutation operation as needed. When the current individual position has better fitness than the randomly selected individual position in the population, push in the opposite direction towards the population mean or towards the random individual position with a set probability (50% in this embodiment), and perform random perturbation operation as needed. Then proceed to step 9.

[0050] Step 7: Individuals in the population randomly walk according to a random direction vector to generate candidate positions and generate random numbers. If the random number is less than a set value, update the velocity and then proceed to step 9; otherwise, directly proceed to step 9. The velocity update formula is:

[0051] v i (t+1)=ω·v i (t)+c1·r1·(pbest,ix i (t))

[0052] In the formula, v i (t+1) is the velocity vector of individual i in the next iteration; ω is the inertia weight; v i (t) is the current velocity vector of individual i; c1 is the cognitive acceleration coefficient; r1 is a random number in the interval [0,1]; pbest,i is the historical best position of individual i; x i (t) is the current position vector of individual i.

[0053] Step 8: Individuals in the population walk randomly according to a random direction vector, calculate the predicted position of the individual at the next moment and update the velocity, and then calculate the fitness difference deltaF. If deltaF>0 or exp(deltaF / T)>rand, where rand is a random number, then accept the new individual position and proceed to step 9; otherwise, retain the original individual position and proceed to step 10.

[0054] The predicted position of the individual at the next moment is:

[0055] H i (t+1)=x i (t)+β×|x prey (t)|

[0056] In the formula, H i (t+1) is the predicted position of individual i at the next time step, x i (t) is the current position of individual i, and β is the position update coefficient; β decays with the number of iterations It, and β0 = 1;

[0057] β=β0·e -λIt

[0058] Speed ​​updated to:

[0059] v i (t+1)=H i (t+1)+η×(H i (t+1)-round(rand)×x i (t));

[0060] In the formula, λ and η are both set coefficients.

[0061] Step 9: Determine whether the parameters corresponding to the new individual position are within the range of [lb, ub]. If they are, retain the new individual position; otherwise, retain the original individual position.

[0062] Step 10: Update the individual's historical best position pBest and global best fitness gBest, and store the current global best fitness; then let It = It + 1, return to step 3, until the maximum number of iterations is reached.

[0063] Step 11: After the iteration is complete, output the global optimal position, i.e., the optimal parameter vector, and the global optimal fitness.

[0064] Figure 2 This paper compares the collaborative hybrid electric eel algorithm with traditional algorithms in solving complex problems. The complex multimodal function Ackley test in the CEC2017 test set was used. The collaborative hybrid electric eel algorithm proposed in this patent escaped the local optimum in the 20th generation due to the simulated annealing mechanism, achieving the effect that traditional optimization algorithms cannot achieve.

[0065] Figure 3 It is an antenna designed using the cooperative hybrid electric eel algorithm.

[0066] The population consists of PopSize candidate antenna design parameters. Each individual is a 16-dimensional vector x = [x(1), x(2), ..., x(16)], corresponding to the geometric parameters of the antenna structure. Taking a multi-frequency circularly polarized antenna as an example:

[0067] m1=x(1); l1=x(2); l3=x(3); a=x(4); b=x(5); c=x(6); l5=x(7); ws=x(8); ls=x( 9); gl=x(10); we=x(11); w6=x(12); l4=x(13); p1=x(14); gl2=x(15); a1=x(16);

[0068] These parameters control the antenna's size, slot shape, feed location, etc., and directly affect the antenna's multi-frequency characteristics.

[0069] Figure 4 This demonstrates the application effect of the cooperative hybrid electric eel algorithm in multi-frequency antenna design. In the antenna design, a fitness function is constructed to calculate return loss, axial ratio, and gain.

[0070] The formula for calculating the global optimal fitness is:

[0071]

[0072] In the formula, gbest represents the global optimal fitness, bandwidth1 represents the first segment return loss bandwidth, bandwidth2 represents the second segment return loss bandwidth, bandwidth3 represents the third segment return loss bandwidth; gainrhcp1 represents the first segment right-hand circular polarization gain, gainrhcp2 represents the second segment right-hand circular polarization gain; axial1 represents the first segment axial ratio bandwidth, axial2 represents the second segment axial ratio bandwidth; fd1 represents the return loss value at the first extreme point, fd2 represents the return loss value at the second extreme point, fd3 represents the return loss value at the third extreme point; the return loss bandwidth, gain, axial ratio bandwidth, and return loss value are calculated based on the geometric parameters of the antenna structure.

Claims

1. An antenna design method based on a cooperative hybrid electric eel algorithm, characterized in that, Includes the following steps: Step 1: Set the maximum number of iterations MaxIt, the population size PopSize, the problem dimension Dim, and the upper and lower bounds of the parameters lb and ub, and initialize the number of iterations It = 1; Step 2: Each individual position corresponds to a set of antenna structure geometric parameters. Randomly generate the initial population position and ensure that the parameters are within the range of [lb, ub]. Then calculate the initial global optimal fitness and evaluate the antenna performance through the objective function. Step 3: Calculate the energy decay factor E0 and the simulated annealing temperature T: E0 = 4·sin(1-It / MaxIt), T = 1000 / It; Step 4: Randomly select RandNum dimensions to generate a random direction vector DirectVector; where RandNum is in the range (2 ~ Dim); Step 5: Calculate the current energy: E = E0·log(1 / rand). If E > 1, proceed to step 6; otherwise, proceed to step 7 with the set probability and to step 8 with the remaining probability; where rand is a random number. Step 6: Randomly select an individual position in the population according to the random direction vector. When the randomly selected individual position has better fitness than the current individual position, move it towards the population mean or towards the random individual position with a set probability, and perform differential mutation operation as needed. When the current individual position has better fitness than the randomly selected individual position in the population, push it in the opposite direction towards the population mean or towards the random individual position with a set probability, and perform random perturbation operation as needed. Then proceed to step 9. Step 7: Individuals in the population randomly walk according to a random direction vector to generate candidate positions and generate random numbers. If the random number is less than the set value, the velocity is updated and then step 9 is executed; otherwise, step 9 is executed directly. Step 8: Individuals in the population walk randomly according to a random direction vector, calculate the predicted position of the individual at the next moment and update the velocity, and then calculate the fitness difference deltaF. If deltaF>0 or exp(deltaF / T)>rand, where rand is a random number, then accept the new individual position and proceed to step 9; otherwise, retain the original individual position and proceed to step 10. Step 9: Determine whether the parameters corresponding to the new individual position are within the range of [lb, ub]. If they are, retain the new individual position; otherwise, retain the original individual position. Step 10: Update the individual's historical best position pBest and global best fitness gBest, and store the current global best fitness; then let It = It + 1, return to step 3, and continue until the maximum number of iterations is reached; Step 11: After the iteration is complete, output the global optimal position, i.e., the optimal parameter vector, and the global optimal fitness.

2. The antenna design method based on the cooperative hybrid electric eel algorithm according to claim 1, characterized in that, The formula for calculating the global optimal fitness is: In the formula, gbest represents the global optimal fitness, bandwidth1 represents the first segment return loss bandwidth, bandwidth2 represents the second segment return loss bandwidth, bandwidth3 represents the third segment return loss bandwidth; gainrhcp1 represents the first segment right-hand circular polarization gain, gainrhcp2 represents the second segment right-hand circular polarization gain; axial1 represents the first segment axial ratio bandwidth, axial2 represents the second segment axial ratio bandwidth. fd1 represents the return loss value at the first extreme point, fd2 represents the return loss value at the second extreme point, and fd3 represents the return loss value at the third extreme point; the return loss bandwidth, gain, axial ratio bandwidth, and return loss value are calculated based on the geometric parameters of the antenna structure.

3. The antenna design method based on the cooperative hybrid electric eel algorithm according to claim 1, characterized in that, The speed update formula in step 7 is: v i (t+1)=ω·v i (t)+c1·r1·(pbest,i-x i (t)) In the formula, v i (t+1) is the velocity vector of individual i in the next iteration; ω is the inertia weight; v i (t) is the current velocity vector of individual i; c1 is the cognitive acceleration coefficient; r1 is a random number in the interval [0,1]. pbest,i is the historical best position of individual i; x i (t) is the current position vector of individual i.

4. The antenna design method based on the cooperative hybrid electric eel algorithm according to claim 1, characterized in that, In step 8, the predicted position of the individual at the next moment is: H i (t+1)=x i (t)+β×|x prey (t)| In the formula, H i (t+1) is the predicted position of individual i at the next time step, x i (t) is the current position of individual i, and β is the position update coefficient; β decays with the number of iterations It, and β0 = 1; β＝β0·e -λIt Speed ​​updated to: v i (t+1)=H i (t+1)+η×(H i (t+1)-round(rand)×x i (t)); In the formula, λ and η are both set coefficients.

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