A method for optimal design of technical parameters of a performance improved passive suspension system

Abstract

The application discloses a technical parameter optimal design method of a performance-improved passive suspension system, which can optimally design two types of technical parameters, i.e., a stiffness coefficient of a spring and a damping coefficient of a damper in the passive suspension system, from the perspective of improving the driving stability and safety of a vehicle. Specifically, the method does not depend on the experience of technicians, and the optimal technical parameters of the suspension spring and the damper do not need to be determined through continuous attempts. Instead, a nonlinear passive suspension system model of a whole vehicle four-wheel is built, and the HHO algorithm is used to search the stability and safety of the vehicle when driving on an uneven road under the condition of different stiffness coefficients and damping coefficients, so that the corresponding technical parameters are optimally designed. The optimal design of the technical parameters measures the stability and handling stability indexes of the vehicle driving, and the performance-improved passive suspension system can be designed according to the technical parameters.

Description

Technical Field

[0001] This invention relates to a design method for a vehicle passive suspension system, and more particularly to a method for optimizing the technical parameters of a performance-improving passive suspension system. Background Technology

[0002] The design of a vehicle's chassis suspension system is a crucial step in the automobile manufacturing process. It must not only meet the requirements for vehicle stability but also ensure adequate suspension safety. Currently, passive suspension systems are the most common choice in vehicle design due to their simple structure, low cost, and high reliability. The design of a passive suspension system requires selecting appropriate suspension springs and dampers to ensure vehicle stability and safety when driving on uneven roads. Different springs and dampers possess different stiffness and damping coefficients, and the design of these technical parameters is of great significance in ensuring the stability and safety requirements of the suspension system. However, in practice, the stiffness and damping coefficients—two key technical parameters in suspension system design—are usually determined through trial and error by experienced technicians using a combination of methods.

[0003] Vehicle ride stability refers to the ability of a vehicle to withstand strong impacts from external stimuli or internal excitations generated by its components during normal driving. These impacts are transmitted to passengers or cargo, affecting ride comfort or damaging cargo performance. Prolonged exposure to such harsh conditions can lead to severe fatigue and chronic illnesses. Therefore, improving vehicle stability by reducing vertical, pitch, and roll accelerations is a primary goal of suspension system design. Furthermore, vehicle handling stability and tire load are key indicators of suspension system safety, and these are also crucial considerations in the design of improved passive suspension systems.

[0004] In recent years, the concept of optimal suspension system design has received increasing attention. How to optimize the selection and design of the best stiffness and damping coefficients is a key technical challenge in designing improved passive suspension systems. Traditional optimization techniques are insufficient to solve this type of optimization design problem. Therefore, optimizing the key technical parameters of the suspension system to improve its performance remains a challenging technical problem that requires further research. Summary of the Invention

[0005] The main technical problem this invention aims to solve is: how to use the Harris Hawk Optimization (HHO) algorithm to optimally design two key technical parameters in a suspension system—the stiffness coefficient of the springs and the damping coefficient of the dampers—from the perspective of improving vehicle ride comfort and safety. Specifically, this invention constructs a nonlinear passive suspension system model of the entire vehicle's four wheels, uses the HHO algorithm to search for different stiffness and damping coefficients, and measures the vehicle's ride comfort and safety on uneven roads to optimally design the corresponding technical parameters.

[0006] The technical solution adopted by the method of the present invention to solve the above problems is as follows: a method for optimal design of technical parameters of a performance-improving passive suspension system, comprising the following steps:

[0007] Step (1): Determine the parameters of the vehicle to be designed, specifically including the vehicle body mass M, the unsprung mass m of the suspension springs, the linear elastic coefficient k1 and nonlinear elastic coefficient k2 of the tires, the lateral distance L1 between the center of gravity of the left front suspension and the center of gravity of the vehicle, the lateral distance L2 between the center of gravity of the right front suspension and the center of gravity of the vehicle, and the longitudinal distance L between the center of gravity of the vehicle and the center of gravity of the front suspension. f The longitudinal distance L between the vehicle's center of gravity and the rear suspension's center of gravity r The vehicle's pitch inertia I1 and roll inertia I2 are then used to establish four equations as shown in formula ①:

[0008]

[0009] In the above formula ①, the range of the differential time interval Δt is 0.002≤Δt≤0.02. When i is equal to 1, 2, 3 and 4 respectively, they represent the left front suspension, right front suspension, left rear suspension and right rear suspension respectively. and Let T represent the changes in the vehicle's vertical velocity, pitch velocity, roll velocity, and suspension vertical velocity at time j, respectively. Θ(j-1) and Φ(j-1) represent the specific values ​​of the vehicle's pitch angle Θ and roll angle Φ at time j-1, respectively. sin[Θ(j-1)] represents the sine function value used to calculate Θ(j-1). The specific value T of the suspension's tire elasticity at time j is also shown. i (j)=k1·Δy i (j)+k2·[Δy i (j)] 3 Δy i (j)=y i (j)-z i (j-1) represents the change in the tire's vertical displacement at time j, z i (j-1) represents the vertical displacement z of the suspension.i The specific value of y at time j-1. i (j) represents the height of the tire contact patch at time j; the specific value S of the suspension spring force at time j-1. i (j-1) and the specific value D of the damping force of the damper at time j-1. i The calculation method for (j-1) is shown in formula ②:

[0010]

[0011] In equation ② above, k lin and k non c represents the linear stiffness coefficient and nonlinear stiffness coefficient of the suspension spring, respectively. lin c sys and c non These represent the linear damping coefficient, symmetrical damping coefficient, and nonlinear damping coefficient of the damper, respectively; Δz i (j-1) represents the change in vertical displacement of the suspension at time j-1. This represents the change in the vertical velocity of the suspension at time j-1; when At that time, the sign function when At that time, the sign function Δz i (j-1) and The calculation methods are shown in formulas ③ and ④, respectively.

[0012]

[0013]

[0014] in, This represents the specific value of the vehicle's pitch velocity at time j-1. Z(j-1) represents the specific value of the vehicle body roll rate at time j-1. Let z represent the vertical displacement and vertical velocity of the vehicle body at time j-1, respectively. i (j-1) and These represent the specific values ​​of the vertical displacement and vertical velocity of the suspension at time j-1, respectively.

[0015] Step (2): After randomly generating a 4×N dimensional data matrix Y from a normal distribution with a mean of 0 and a standard deviation of 0.01, determine k in sequence. lin k non c lin c sys and c non The selection range, i.e. in, These respectively represent the minimum value of the selection range. These represent the maximum values ​​of the selection range, and N equals the total number of times the vehicle travels.

[0016] It should be noted that, in order for a passive suspension system to improve driving stability and safety, the linear stiffness coefficient k of the suspension springs needs to be optimally designed. lin and nonlinear stiffness coefficient k non And the linear damping coefficient c of the damper lin Symmetrical damping coefficient c sys and nonlinear damping coefficient c non These are the five technical parameters.

[0017] Furthermore, different suspension springs have different linear stiffness coefficients and nonlinear stiffness coefficients. Among the available suspension springs, the largest linear stiffness coefficient... and the minimum linear stiffness coefficient This determines the linear stiffness coefficient k. lin The selection range; similarly, the nonlinear stiffness coefficient k non And the linear damping coefficient c of the damper lin Symmetrical damping coefficient c sys and nonlinear damping coefficient c non Each has its own selection range.

[0018] Step (3): Determine the calculation process of the loss degree J of the HHO algorithm, as shown in steps (3.1) to (3.5).

[0019] Step (3.1): Initialize j = 1, and set the values ​​respectively. Z(0)=0, Θ(0)=0, Φ(0)=0, and z i (0) = 0; where i = 1, 2, 3, 4.

[0020] Step (3.2): Set y1(j), y2(j), y3(j), and y4(j) to be equal to the four data points of the j-th column vector in the data matrix Y, and then according to T i (j)=k1·Δy i (j)+k2·[Δy i (j)] 3 Calculate T1(j), T2(j), T3(j), T4(j) respectively, and calculate S1(j-1), S2(j-1), S3(j-1), S4(j-1) and D1(j-1), D2(j-1), D3(j-1), D4(j-1) according to formula ②.

[0021] Step (3.3): Calculate based on the equation in formula ① and Then, according to the formulas respectively and Calculate in sequence Z(j), Θ(j), Φ(j), and z i (j).

[0022] Step (3.4): Determine if j is less than N; if yes, set j = j + 1 and then return to step (3.2); if no, then... The maximum and minimum values ​​in the data are recorded as follows: and Will The maximum and minimum values ​​in the data are recorded as follows: and Will The maximum and minimum values ​​in the data are recorded as follows: and T i (1), T i (2), ..., T i The maximum and minimum values ​​in (N) are recorded as T. i (max) and T i After (min), proceed to step (3.5).

[0023] Step (3.5): Calculate the loss degree J according to formula ⑤ as shown below:

[0024]

[0025] In equation ⑤ above, w z w Θ w Φ and w T These represent the four weighting coefficients used to calculate the loss J, where j = 1, 2, ..., N.

[0026] As can be seen from the definition of loss degree J in equation ⑤ above, its first three sub-items involve the vertical acceleration of the vehicle body, pitch acceleration, and roll acceleration. These three indicators measure the stability of vehicle driving. The fourth sub-item of loss degree J involves tire elasticity. Positive tire elasticity may lead to increased ground friction, thereby increasing energy consumption. Negative tire elasticity indicates insufficient grip, thus affecting vehicle handling performance.

[0027] Step (4): After setting the population size of the HHO algorithm to H and the maximum number of iterations to F, randomly generate a 5×H dimensional real matrix P; where the H data points in the first row vector of P are uniformly distributed from the interval The random numbers generated above, the H data points in the second row vector of P are all uniformly distributed from the interval The random numbers generated above, the H data points in the 3rd row vector of P are all uniformly distributed from the interval The random numbers generated above, the H data points in the 4th row vector of P are all uniformly distributed from the interval The random numbers generated above, the H data points in the 5th row vector of P are all uniformly distributed from the interval The random number generated above.

[0028] Step (5): After setting the iteration number γ = 1, execute the iterative optimization process of the HHO algorithm. After each iteration optimization process, the iteration number needs to be incremented by 1 until the iteration number equals F, thus obtaining the optimal solution vector h0.

[0029] Step (6): Set k lin k non c lin c sys and c non After assigning each of the five data points to the optimal solution vector h0, k is set. lin k non c lin c sys and c non The values ​​are equal to the first, second, third, fourth, and fifth data points in h0, respectively. Then, suspension springs and dampers that match these five technical parameters are designed and selected.

[0030] It should be noted that the iterative optimization process of the HHO algorithm in step (5) above to find the optimal solution vector is specifically completed according to steps (5.1) to (5.7) as shown below.

[0031] Step (5.1): Calculate the loss values ​​J1, J2, ..., J6 corresponding to the 1st column vector, 2nd column vector, ..., Hth column vector in P according to steps (i) to (iii) as shown below. H .

[0032] Step (1): Set b = 1.

[0033] Step (2): Assign the 5 data points of the b-th column vector in P to k respectively. lin k non c lin c sys and c nonThen, steps (3.1) to (3.5) are executed to calculate the loss degree J.

[0034] Step (3): Set the loss J corresponding to the column vector of column b in P. b After setting =J, determine if b is less than H; if yes, set b = b + 1 and return to step (II); if no, obtain the loss values ​​J1, J2, ..., J corresponding to the 1st column vector, 2nd column vector, ..., Hth column vector in P, respectively. H .

[0035] Step (5.2): Set J1, J2, ..., J H The column vector corresponding to the minimum value in the data is the optimal solution vector h0. Calculate the current energy value E of the target. γ =2.E0.(1-γ / F), and after randomly generating a random number R0 based on a normal distribution with a mean of 0.5 and a standard deviation of 1, then determine E. γ absolute value | E γ | Is it less than 1? If not, then execute step (5.3) to update each column vector in P, and then jump to step (5.7); if yes, then execute step (5.4) to update each column vector in P, and then jump to step (5.7); where E0 is a constant between -1 and +1.

[0036] Step (5.3): Generate two random numbers R1 and R2 from the interval [0, 1] according to a uniform distribution, and then generate a random integer ε from the interval [1, H]. Update each column vector in P according to the formula shown in step ⑥ below:

[0037]

[0038] In equation ⑥ above, h n and h ε Let p represent the column vectors of the nth and εth columns in the real matrix P, respectively. max It is by This forms a 5×1 dimensional column vector, p min It is by This forms a 5×1 dimensional column vector. Let P be the mean vector of all H column vectors in P, where n = 1, 2, ..., H.

[0039] Step (5.4): After generating a random number R3 from the interval [0, 1] according to a uniform distribution, determine whether the condition |E is satisfied. γ |≥0.5 and R0≥0.5; if so, then according to formula h n =h0-h n -E γ ·|2·(1-R3)·h0-h n|Update each column vector in P; if not, then check if the condition is met|E γ If |E ≥ 0.5 and R0 < 0.5, then generate three random numbers R4, R5, and R6 from the interval [0, 1] according to a uniform distribution, and then execute step (5.5); otherwise, then determine whether the condition |E is satisfied. γ | < 0.5 and R0 ≥ 0.5; if so, then according to h n =h0-E γ ·|h0-h n | Update each column vector in P; otherwise, perform step (5.6) to update each column vector in P.

[0040] Step (5.5): According to the formula x = h0 - E γ ·|2·(1-R3)·h0-h n After calculating the pseudo-vector x, calculate the Levi flight value LF according to the formula ⑦ shown below, and then update each column vector in P according to the formula ⑧ shown below.

[0041]

[0042]

[0043] In equation ⑦ above, the gamma function Γ(2.5) = 1.3293 and the gamma function Γ(1.25) = 0.9064; in equation ⑧ above, J(x) represents assigning the five data points of the pseudo-vector x to k respectively. lin k non c lin c sys and c non Then, the loss degree, J(x+R5·L), obtained from steps (3.1) to (3.5) is calculated. F ) represents x + R5·L F The five data points are assigned to k. lin k non c lin c sys and c non Then, the loss degree is calculated through step (3).

[0044] It should be noted that the five data points in the pseudo-vector x are assigned to k respectively. lin k non c lin c sys and c non That is, setting k lin k non c lin c sys and c nonThese are respectively equal to the 1st, 2nd, 3rd, 4th, and 5th data points in the pseudo-vector x.

[0045] Step (5.6): According to the formula After calculating the pseudo-vector x, calculate the Lévy flight value L according to formula ⑦. F Then, update each column vector in P according to formula ⑧.

[0046] Step (5.7): Determine whether γ is less than F; if yes, set γ = γ + 1 and then return to step (5.1); if no, the final optimal solution vector h0 is obtained.

[0047] The advantages of the method of the present invention, based on the above implementation steps, are as follows.

[0048] The method of this invention, when implementing the optimal design of a passive suspension system, does not rely on the experience of technical personnel, nor does it require continuous trial and error to determine the optimal technical parameters of the suspension springs and dampers. Instead, the method uses the HHO algorithm combined with a whole-vehicle suspension system model of a four-wheeled vehicle to optimize and search for the optimal technical parameters. The optimization design of these technical parameters considers the vehicle's ride smoothness and handling stability indicators. Based on these technical parameters, a performance-improved passive suspension system can be designed. Attached Figure Description

[0049] Figure 1 This is a schematic diagram illustrating the implementation process of the method of the present invention. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0051] This invention discloses an optimal design method for the technical parameters of a performance-improving passive suspension system, which is described below in conjunction with... Figure 1 The implementation flowchart shown below illustrates the specific implementation method of the present invention.

[0052] Step (1): Determine the parameters of the vehicle to be designed, specifically including the vehicle body mass M, the unsprung mass m of the suspension springs, the linear elastic coefficient k1 and nonlinear elastic coefficient k2 of the tires, the torque L1 between the center of gravity of the left front suspension and the center of gravity of the vehicle, the torque L2 between the center of gravity of the right front suspension and the center of gravity of the vehicle, and the torque L between the center of gravity of the vehicle and the center of gravity of the front suspension. f The torque L between the vehicle's center of gravity and the rear suspension's center of gravity r The vehicle's pitch inertia I1 and roll inertia I2 are then used to establish four equations as shown in formula ①.

[0053] The four equations in equation ① above are derived from the mechanism model of the four-wheel vehicle suspension system, namely:

[0054]

[0055] in, and These represent the vehicle's vertical acceleration, vehicle pitch acceleration, vehicle roll acceleration, and suspension vertical acceleration, respectively. The second-order differential equation in equation ⑨ above is established using Newton's laws of motion: mass multiplied by acceleration equals the net external force.

[0056] Step (2): After randomly generating a 4×N dimensional data matrix Y from a normal distribution with a mean of 0 and a standard deviation of 0.01, determine k in sequence. lin k non c lin c sys and c non The selection range.

[0057] Four-wheeled vehicles have four suspensions, each equipped with one suspension spring and one damper. All suspension springs and dampers use the same stiffness coefficient.

[0058] Step (3): Determine the calculation process of the loss of the HHO algorithm, as shown in steps (3.1) to (3.5) above.

[0059] Step (4): After setting the population size of the HHO algorithm to H and the maximum number of iterations to F, a 5×H dimensional real matrix P is randomly generated. The main purpose of this step is to set the parameters of the HHO algorithm and generate H initial solution vectors.

[0060] Step (5): After setting the iteration number γ = 1, execute the iterative optimization process of the HHO algorithm. After each iteration optimization process, the iteration number needs to be incremented by 1 until the iteration number equals F, thus obtaining the optimal solution vector h0.

[0061] Step (6): Set k lin k non c lin c sys and c non After determining that each of the five data points is equal to the optimal solution vector h0, the design selects suspension springs and dampers that are identical to these five technical parameters.

Claims

1. A method for optimal design of technical parameters of a performance-improving passive suspension system, characterized in that, Specifically, the steps are as follows: Step (1): Determine the parameters of the vehicle to be designed, specifically including the vehicle body mass. Unsprung mass of suspension springs The linear elastic coefficient of the tire and nonlinear elastic coefficient The torque between the center of gravity of the left front suspension and the center of gravity of the vehicle The torque between the center of gravity of the right front suspension and the center of gravity of the vehicle The torque between the vehicle's center of gravity and the front suspension's center of gravity The torque between the vehicle's center of gravity and the rear suspension's center of gravity The vehicle's pitch moment of inertia and tilt moment of inertia Then construct the four equations as shown in formula ①: ① Among them, when When the values ​​are 1, 2, 3, and 4, they represent the left front suspension, right front suspension, left rear suspension, and right rear suspension, respectively. Indicates the difference time interval. , , and The vertical velocity of the vehicle body, the pitch velocity of the vehicle body, the roll velocity of the vehicle body, and the vertical velocity of the suspension are represented in sequence. The change at each moment and These represent the vehicle body pitch angles. and vehicle body roll angle In the The specific value at that moment; the tire elasticity of the suspension at the... The specific value at that moment , Indicates the vertical displacement of the tire in the th... The change at each moment; the spring force of the suspension spring at the th moment. The specific value at that moment The damping force of the damper in the first... The specific value at that moment The calculation method is shown in formula ②: ② In equation ② above, and These represent the linear stiffness coefficient and the nonlinear stiffness coefficient of the suspension spring, respectively. , and These represent the linear damping coefficient, symmetrical damping coefficient, and nonlinear damping coefficient of the damper, respectively. Indicates the vertical displacement of the suspension in the 1st... The change at each moment Indicates the vertical speed of the suspension in the first... The change at each moment; when At that time, the sign function ;when At that time, the sign function ; and The calculation methods are shown in formulas ③ and ④ respectively: ③ ④ in, Indicates the vehicle body pitch rate at the 1st... The specific value at a given moment Indicates the vehicle body roll rate at the twentieth minute. The specific value at a given moment and These represent the vertical displacement and vertical velocity of the vehicle body on the [number]th [day]. The specific value at a given moment and These represent the vertical displacement and vertical velocity of the suspension on the [number]th [year]. The specific value at each moment; Step (2): Randomly generate a value from a normal distribution with a mean of 0 and a standard deviation of 0.

01. 3D data matrix Then, determine them one by one. , , , and The selection range, i.e. , , , , ;in, These respectively represent the minimum value of the selection range. These respectively represent the maximum values ​​within the selection range. Equal to the total number of hours the vehicle travels; Step (3): Determine the loss of the HHO algorithm The calculation process is shown in steps (3.1) to (3.5); Step (3.1): Initialization and set them respectively , , , , , , and ;in, ; Step (3.2): Settings They are respectively equal to the data matrix The Middle After the four data points of the column vector, then according to Calculate separately And calculate according to formula ② and ; Step (3.3): Calculate based on the equation in formula ① , , and Then, according to the formulas respectively , , , , , , and Calculate in sequence , , , , , , and ; Step (3.4): Judgment Is it less than If so, then set Then, return to step (3.2); otherwise, proceed with... The maximum and minimum values ​​in the data are recorded as follows: and ,Will The maximum and minimum values ​​in the data are recorded as follows: and ,Will The maximum and minimum values ​​in the data are recorded as follows: and ,Will The maximum and minimum values ​​in the data are recorded as follows: and Then, proceed to step (3.5). Step (3.5): Calculate the loss degree according to Formula ⑤ shown below. : ⑤ In equation ⑤ above, , , and Indicates the calculation of loss degree The four weighting coefficients, ; Step (4): Set the population number of the HHO algorithm to equal The maximum number of iterations equals Then, a random one is generated. 3D real matrix ;in, The first row vector All data are uniformly distributed from intervals. The random number generated above, The second row vector All data are uniformly distributed from intervals. The random number generated above, The third row vector All data are uniformly distributed from intervals. The random number generated above, The 4th row vector All data are uniformly distributed from intervals. The random number generated above, The 5th row vector All data are uniformly distributed from intervals. Random numbers generated above; Step (5): Set the number of iterations Then, the iterative optimization process of the HHO algorithm is executed. After each iteration, the iteration count is incremented by 1 until the iteration count equals 1 / 2. Thus, the optimal solution vector is obtained. ; Step (6): Settings , , , and They are respectively equal to the optimal solution vector After obtaining the five data points, the suspension springs and dampers that match these five technical parameters are then designed and selected.

2. The optimal design method for technical parameters of a performance-improving passive suspension system according to claim 1, characterized in that, In step (5), the iterative optimization process of the HHO algorithm is performed to solve for the optimal solution vector. The specific implementation process is as follows: Step (5.1): Calculate according to steps (i) to (iii) as shown below. The first column vector, the second column vector, and so on up to the first column vector. Loss values ​​corresponding to the column vectors ; Step 1: Settings ; Step 2: The Middle The five data points of the column vector are assigned values ​​to... , , , and Then, steps (3.1) to (3.5) are executed to calculate the loss. ; Step 3: Settings The Middle Loss corresponding to the column vector of the column Then, make a judgment Is it less than If so, then set Then, return to step 2; otherwise, obtain... The first column vector, the second column vector, and so on up to the first column vector. Loss values ​​corresponding to the column vectors ; Step (5.2): The column vector corresponding to the minimum value in the vector is the optimal solution vector. Calculate the target's current energy value A random number is generated based on a normal distribution with a mean of 0.5 and a standard deviation of 1. Then, make a judgment. absolute value Is it less than 1? If not, proceed to step (5.3) to update. After processing each column vector in the table, proceed to step (5.7); if so, execute step (5.4) to update. After processing each column vector in the table, proceed to step (5.7); where, It is between and The constants between, F Indicates the maximum number of iterations; Step (5.3): From the interval according to a uniform distribution Generate two random numbers and Then from the interval Generate a random integer Then, update according to formula ⑥ as shown below. The column vectors in: ⑥ In equation ⑥ above, and Represent real matrices respectively The Middle Column and number The column vector of a column. It is by A composition A column vector of dimension, It is by A composition A column vector of dimension, express All The mean vector of n column vectors ; Step (5.4): From the interval according to a uniform distribution Generate a random number Then, determine whether the conditions are met. and If so, then according to the formula renew Each column vector in the array; if not, then check whether the condition is satisfied. and If so, then follow the uniform distribution from the interval Generate three random numbers. , and Then, proceed to step (5.5); if not, then determine whether the conditions are met. and If so, then according to renew Each column vector in the array; otherwise, proceed to step (5.6) to update. The column vectors in; Step (5.5): According to the formula Calculate pseudo-vectors Then, calculate the Levi flight value according to formula ⑦ shown below. Then update according to formula ⑧ as shown below. The column vectors in: ⑦ ⑧ In equation ⑦ above, the gamma function Gamma function In the above formula ⑧, This indicates that the pseudo-vector The five data points are assigned values ​​to... , , , and Then, the loss degree obtained from steps (3.1) to (3.5) is calculated. Indicates will The five data points are assigned to the corresponding values. , , , and Then, the loss degree is calculated through step (3); Step (5.6): According to the formula Calculate pseudo-vectors Then, calculate the Levi flight value according to formula ⑦. Then update according to formula ⑧ The column vectors in; Step (5.7): Determine Is it less than If so, then set Then, return to step (5.1); otherwise, the final optimal solution vector is obtained. .

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