MCR-WPT system planar coil structure parameter optimization method based on improved four-vector optimization algorithm

Abstract

The invention provides an MCR-WPT system planar coil structure parameter optimization method based on an improved four-vector optimization algorithm. Analyzing an S-S topology compensation structure network, and deducing the energy transmission efficiency of the MCR-WPT system; analyzing the influence of the physical structure of the coil on the characteristic parameters of the coil, and calculating the self-inductance value of the coil; calculating a mutual inductance coefficient value between the coupling coils; calculating alternating current resistance; calculating a coupling coefficient between coupling coils, and analyzing frequency splitting to establish constraint conditions; determining an optimization variable, and taking the energy transmission efficiency as a target function value and an optimization target; setting a constraint condition according to the critical coupling coefficient, and adjusting a parameter range according to the constraint condition; and optimizing the energy transmission efficiency, namely a target function, by adopting an improved four-vector optimization algorithm according to coil setting parameters.

Description

Technical Field

[0001] The present application relates to the technical field of electronic equipment, and in particular to a method for optimizing the structural parameters of a planar coil of an MCR-WPT system based on an improved four-vector optimization algorithm. Background Art

[0002] In wireless power transmission (WPT) technology, magnetically coupled resonant (MCR) wireless power transmission systems have received extensive attention and application due to their high efficiency, safety, and long-distance transmission characteristics. However, how to effectively improve the energy transmission efficiency of MCR-WPT systems has become an important topic in current research. During the transmission process, traditional wireless power transmission systems are prone to energy loss due to factors such as coil design, frequency selection, and compensation topology, which affects the overall performance of the system.

[0003] To this end, researchers have proposed a variety of improvement methods to optimize the performance of the MCR-WPT system, especially to optimize the coupling coil structure in the system. The physical structural parameters of the coil, such as wire diameter, pitch, and coil spacing, will directly affect the resonant frequency, coupling coefficient, and transmission efficiency of the system. In addition, the skin effect and proximity effect will also increase the AC resistance of the coil under high-frequency working conditions, further leading to energy loss.

[0004] Therefore, rationally designing the coupling coil and optimizing its structural parameters are crucial to improving the efficiency of the wireless power transfer system. Summary of the invention

[0005] The present application provides a method for optimizing the structural parameters of a planar coil of an MCR-WPT system based on an improved four-vector optimization algorithm, which can be used to solve the technical problem of power loss in the process of power transmission under high-frequency conditions.

[0006] The present application provides a method for optimizing the structural parameters of a planar coil of an MCR-WPT system based on an improved four-vector optimization algorithm, the method comprising:

[0007] Step S1, analyzing the SS topology compensation structure network and deriving the energy transmission efficiency of the MCR-WPT system;

[0008] Step S2: Analyze the influence of the physical structure of the coil on the characteristic parameters of the coil, including: coil self-inductance, mutual inductance, resistance, and coupling coefficient;

[0009] Step S3: Calculate the self-inductance of the coil;

[0010] Step S4: Calculate the mutual inductance value between the coupled coils;

[0011] Step S5: calculating the AC resistance of the Litz wire under high frequency AC;

[0012] Step S6: Calculate the coupling coefficient between the coupling coils, analyze the frequency splitting and establish the constraint conditions;

[0013] Step S6: Determine the optimization variables, and use the energy transmission efficiency as the objective function value and optimization target;

[0014] Step S8: Set the constraint condition according to the critical coupling coefficient: k≤k s , and adjust the parameter range according to the constraints;

[0015] Step S9: optimizing the energy transmission efficiency, ie, the objective function, using an improved four-vector optimization algorithm according to the coil setting parameters.

[0016] The present invention optimizes the coupling coil structure parameters by using an improved four-vector optimization algorithm. Compared with the original four-vector optimization algorithm, the convergence speed is faster, the accuracy is higher, and the results are more stable. First, the SPM chaotic mapping is used to generate the initial population, reduce the randomness of generating the initial population, improve the population diversity, and make it converge quickly to obtain the global optimal solution as much as possible; then the vertical and horizontal cross strategy is used to update the position for the first time. The vertical and horizontal cross strategy includes horizontal cross and vertical cross. The population searches through horizontal cross to reduce the search blind spots, so that the algorithm has a better global search ability. The vertical cross can promote some stagnant dimensions of the population to get rid of the premature convergence of the dimension, so that the algorithm jumps out of the local optimum; finally, the adaptive coefficient α is dynamically adjusted and Gaussian perturbation is added to the position update formula of the original algorithm to update the population position for the second time. The dynamic adjustment of the adaptive coefficient can make the algorithm more exploratory in the early stage through the nonlinear dynamic update of the adaptive coefficient, and gradually refine it in the later stage. Introducing Gaussian perturbation during position update can increase randomness and increase the probability of finding the global optimal solution.

[0017] The implementation of the present invention optimizes the planar coil structural parameters in the magnetic coupling resonant wireless power transmission (MCR-WPT) system to significantly improve the energy transmission efficiency of the system and simplify the calculation process. First, the SS topology compensation structure is selected as the basis of the circuit design, and the energy transmission efficiency formula of the system is derived as the objective function of the optimization. While taking into account a variety of influencing factors, the formula ensures the simplicity and accuracy of the calculation, so that the optimization process is more efficient while ensuring that the result is within the error tolerance range. In addition, the present invention adopts Litz wire to wind the coupling coil, successfully solves the resistance loss problem caused by the skin effect and the proximity effect under high frequency conditions, and further reduces the energy loss under high frequency. This design not only ensures that the optimization result has a high accuracy, but also maintains the simplicity of the calculation process, ensuring that the ideal optimization result can be obtained in a short time, meeting the requirements of practical applications. Through multiple iterations, the present invention can output the optimal coil physical parameters, so that the MCR-WPT system operates in the optimal coupling state, which not only improves the system efficiency, but also simplifies the calculation process, and provides an efficient and easy-to-implement optimization solution for the wireless power transmission system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic diagram of the process of the present invention;

[0019] Figure 2 It is a schematic diagram of the SS topology structure in the present invention;

[0020] Figure 3 It is a flow chart of the improved four-vector optimization algorithm in the present invention;

[0021] Figure 4 It is a schematic diagram of the transient model of the coupling coil in the present invention. DETAILED DESCRIPTION

[0022] In order to make the objectives, technical solutions and advantages of the present application clearer, the implementation methods of the present application will be further described in detail below with reference to the accompanying drawings.

[0023] The following first introduces the embodiments of the present application in conjunction with the accompanying drawings.

[0024] As shown in FIG. (1), the present invention is a method for optimizing the structural parameters of a planar coil of an MCR-WPT system based on an improved four-vector optimization algorithm, and the method comprises the following steps:

[0025] Step S1, analyzing the SS topology compensation structure network, and calculating and deriving the energy transmission efficiency formula of the MCR-WPT system;

[0026] The coil structure is optimized by adjusting the coil wire diameter, thread diameter, spacing and power supply frequency;

[0027] According to the coupling coil parameters, the improved four-vector optimization algorithm is used to optimize the optimal specific parameters of the coil structure. The energy transmission efficiency formula of the MCR-WPT system, that is, the objective function is:

[0028]

[0029] Where η represents the energy transfer efficiency of the system; ω is the resonant angular frequency of the system; M is the mutual inductance of the coupling coil; R1 and R2 represent the internal resistance of the primary and secondary coils respectively; R L Indicates the load size of the system;

[0030] Step S2: Analyze the influence of the physical structure of the coil on the characteristic parameters of the coil; design the parameters of the coupling coil to determine the transmission efficiency, specifically including: coil self-inductance, mutual inductance, resistance, and coupling coefficient.

[0031] Step S3: Calculate the self-inductance of the coil. When current passes through the coil in a closed loop, the change in current will cause a corresponding change in the magnetic field around the coil. According to the principle of electromagnetic induction, this change in magnetic field will generate an induced electromotive force in the coil. This phenomenon is called self-inductance:

[0032]

[0033] Where: L is the self-inductance, N is the number of turns, μ0 is the vacuum permeability, r avg The average wire diameter r max is the outer radius of the coil, r min is the inner radius of the coil, C1=2.46, C2=0.2.

[0034] Step S4: Calculate the mutual inductance between the coupled coils. When the current in a current-carrying loop changes, this change will induce an induced current in another adjacent loop. This phenomenon is called mutual inductance.

[0035]

[0036] Where M is the mutual inductance, μ0 is the vacuum permeability, N r is the number of turns of the primary coil, N t is the number of turns of the secondary coil, r r is the average radius of the primary coil, r t is the average radius of the secondary coil, and h is the distance between the coils.

[0037] Step S5: Calculate the AC resistance of the Litz wire under high-frequency AC. The resistance of the coil is the main factor affecting the energy transmission efficiency of the MCR-WPT system. Under high-frequency current, the conductor will be affected by the skin effect and the proximity effect. No current passes through the inside of the conductor, and the current is concentrated on the surface of the conductor. When the distance between the conductors is too close, the current will be attracted to the adjacent side. This causes the resistance to increase. In order to reduce the loss caused by the increase in the AC resistance of the coil under high-frequency conditions and improve the energy transmission efficiency of the MCR-WPT system, Litz wire is used for winding when making the coil. The interior of the Litz wire is wound with multiple mutually insulated and thinner wires, so it is less affected by the skin effect and the proximity effect.

[0038]

[0039] Where k is the number of Litz strands, d str is the single strand diameter, r avg is the average line diameter, δ is the skin depth, is the conductor spacing, R ac is the AC resistance, ρ is the resistivity, and N is the number of turns.

[0040] Step S6: Calculate the coupling coefficient between the coupled coils and analyze the frequency splitting to establish the constraint conditions. The coupling coefficient is calculated by the relationship between the mutual inductance and the self-inductance of the two coils:

[0041]

[0042] Where M is the mutual inductance of the coils, L1 and L2 represent the self-inductance of coil one and coil two respectively.

[0043] The coupling strength reflects to a certain extent how much the changing magnetic field is transmitted from the transmitter to the receiver. The coupling coefficient indicates the tightness of the coupling between the primary coil and the secondary coil. When k = 1, the components are tightly coupled, and the coupling coefficient of the power transformer is close to 1. When k = 0, there is no coupling between the coils, and they are independent of each other.

[0044] Frequency splitting is a common problem in MCR-WPT systems. Frequency splitting refers to the system's resonance point splitting from a single extreme point into two extreme points at the resonant frequency, resulting in a decrease in the system's transmission efficiency at the original resonant point. In the design and practical application of the MCR-WPT system, in order to achieve effective coupling of the circuits at both ends and good matching of the loops, the coils at the transmitting and receiving ends have the same specifications and parameters to ensure the numerical consistency of the resonant capacitor; the critical coupling coefficients for SS are:

[0045]

[0046] The calculation formula of quality factor Q is:

[0047] In the MCR-WPT system, when k>k, the system is in over-coupling, and when k=k, the system is in critical

[0048] When k < k, the system is under-coupled. When the coupling degree between the coupling coils exceeds the critical coupling point of the system,

[0049] The resonant frequency of the system will split from the original single maximum point into two maximum points, and the output coil will present a double-peak characteristic. When the operating frequency of the system is at the two maximum points after the split, the efficiency of the system will increase, and when the operating frequency of the system is at the original resonant point, the efficiency of the system will decrease.

[0050] Step S7: Calculate the self-inductance, mutual inductance, resistance, coupling coefficient and transmission efficiency of the coil according to the set coupling coil parameter range.

[0051] Based on the maximum transmission efficiency, the specific wire diameter, spiral diameter, spacing and power supply frequency of the corresponding coil can be deduced.

[0052] The power frequency, the wire diameter and pitch of the tiny planar coil and the distance between the two coils are used as optimization variables; the energy transmission efficiency is used as the objective function value and the optimization target.

[0053] Step S8: Set the constraint condition according to the critical coupling coefficient: k≤k s , and adjust the parameter range according to the constraints.

[0054] Step S9: optimizing the energy transmission efficiency, ie, the objective function, using an improved four-vector optimization algorithm according to the coil setting parameters.

[0055] The maximum transmission efficiency formula is used as the objective function, and the resonant frequency, coil outer diameter, inner diameter, single-strand wire diameter, coil spacing, and coil turns are used as known parameter ranges. The objective function is optimized using the improved four-vector optimization algorithm to calculate the coil's self-inductance, mutual inductance, resistance, and coupling coefficient. The objective function at maximum efficiency, the specific values ​​of the resonant frequency, coil outer diameter, inner diameter, single-strand wire diameter, coil spacing, and coil turns are obtained;

[0056] Step S91: Initialize the population data using SPM chaotic mapping according to the set parameters, generate the initial population position as evenly as possible within the constraint range, and calculate the fitness of each individual in the population;

[0057] Step S92: Determine the four vectors as the initial leaders, and select the four individual positions with the smallest fitness values ​​of the population after initialization as the initial leaders;

[0058] Step S93: Use the vertical and horizontal crossover strategy to randomly match each individual in the population as a parent to generate a new offspring and retain individuals with smaller fitness values, and update the population position for the first time.

[0059] Step S94: Select the four individuals with the smallest new fitness values ​​as the four-vector positions of the leader, update the position of the best agent according to the motion equation after the four-vector passes through Gaussian perturbation, and finally select the average position of the positions of the four best agents to update the population position for the second time;

[0060] Step S95: Determine whether the number of population iterations has reached the maximum number of iterations; if so, output the result and end the iteration; if not, continue to repeat steps S94 to S95.

[0061] In the improved four-vector optimization algorithm, the principle is to guide the search strategy through the four best-performing leaders in the group, ensure balanced exploration and utilization in the search space, avoid local minimum, and alleviate the problem of slow convergence. In the optimization process, each leader is a potential solution, and new leaders are gradually replaced during the iteration process as the fitness changes. The four vectors in the numerical simulation population continuously lead the population to update and optimize the problem: in the population initialization stage of the algorithm, the SPM chaotic mapping is introduced to reduce the randomness of generating the initial population, improve the population diversity, and make it converge quickly to obtain the global optimal solution as much as possible; in the position update stage of the algorithm, the cross-strategy based on the genetic algorithm is introduced to realize the global search of the algorithm and avoid the algorithm from converging prematurely; the dynamic adaptive coefficient makes the algorithm more exploratory in the early stage and gradually refined in the later stage; adding slight Gaussian perturbations increases randomness and increases the probability of finding the global optimal solution; including:

[0062] SPM Chaos Mapping:

[0063] Population initialization is generally randomly generated, and chaos mapping is one of the common and better initialization methods. The chaotic sequence generated by SPM chaos mapping is relatively uniform, ergodic and random, which helps the algorithm to explore more extensively in the search space. The expression is:

[0064]

[0065] Where mod is the modulus of the function, x(i) is the individual position, x(i+1) is the new individual position, r is a random number between 0 and 1, which is used to introduce randomness into the mapping function and increase the unpredictability of the sequence; η and μ are control parameters, both with values ​​between 0 and 1; they are used to determine the segmentation of the mapping function and affect the distribution and randomness of the chaotic sequence;

[0066] Cross-cutting strategy:

[0067] The vertical and horizontal crossover strategy includes horizontal crossover and vertical crossover. The population searches through horizontal crossover to reduce search blind spots, so that the algorithm has better global search capabilities. The expression is:

[0068]

[0069] Where SM i1 and SM i2 is the parent individual after pairing, and its offspring is and SM i1j and SM i2j Respectively represent SM i1 and SM i2 The j-th dimension of , j = 1, 2, ..., dim, dim is the dimension, r1 and r2 are random numbers between (0, 1), c1 and c2 are random numbers between (-1, 1);

[0070] Vertical crossover promotes some stagnant dimensions of the population to get rid of premature dimensional convergence, so that the algorithm jumps out of the local optimum. The expression is:

[0071]

[0072] Where SM ij1 and SM ij2 is the parent individual after pairing, and its offspring is r is a random number between (0,1).

[0073] Dynamic adaptive coefficients and slight Gaussian perturbations:

[0074] The adaptive coefficient α is one of the core mechanisms of the algorithm. It is responsible for adjusting the step size of the algorithm during the search process, thereby balancing exploration and utilization, and directly affects whether the algorithm can effectively find the global optimal solution. The nonlinear dynamic update of the adaptive coefficient makes the algorithm more exploratory in the early stage and gradually refined in the later stage. The expression is:

[0075] α(t)=α0×exp(-β×t)

[0076] Where β is the decay rate, and t is the current number of iterations;

[0077] Since the four vectors as leaders guide the update of the entire population and select the top four optimal solutions of the population during the convergence phase of the algorithm, the update mechanism of the four vectors is one of the keys to avoid falling into the local optimum. For this reason, Gaussian perturbation is introduced during position update to increase randomness and increase the probability of finding the global optimal solution; the expression is:

[0078]

[0079] Where X n,irepresents the updated position of the nth best agent in dimension i, where n ranges from 1 to 4; P n,i is the current position of the nth best agent in dimension i; represents the current average position of all agents in dimension i; represents the central position of the nth best agent and all agents in the i-th dimension The absolute distance between them; α(t) is the adaptive coefficient. ξ1, ξ2, ξ3 represent random numbers uniformly distributed in [0,1]; η is a Gaussian perturbation, expressed as:

[0080] η=σ×N(0,1)

[0081] Where σ is the intensity of the disturbance, and N(0, 1) represents a normal distribution with a mean of 0 and a variance of 1.

[0082] Based on the optimization results, the MCR-WPT system was simulated and analyzed in detail using MAXWELL electromagnetic simulation software to verify the effectiveness of the optimized parameters. Finite element calculation can simulate the actual situation to a large extent, reduce cost consumption, and optimize the design prototype in the early stage. In specific implementation, the optimized coupling coil structure parameter range is power frequency 50KHz-150KHz, coupling coil wire diameter 0.1mm-1mm, pitch 0.01mm-1mm, spacing 3mm-5mm, outer diameter 30mm, inner diameter 6mm.

[0083] The above-described embodiments of the present application do not constitute a limitation on the protection scope of the present application.

Claims

1. A method for optimizing the structural parameters of a planar coil of an MCR-WPT system based on an improved four-vector optimization algorithm, characterized in that: The method comprises: Step S1, analyzing the SS topology compensation structure network and deriving the energy transmission efficiency of the MCR-WPT system; Step S2: Analyze the influence of the physical structure of the coil on the characteristic parameters of the coil, including: coil self-inductance, mutual inductance, resistance, and coupling coefficient; Step S3: Calculate the self-inductance of the coil; Step S4: Calculate the mutual inductance value between the coupled coils; Step S5: calculating the AC resistance of the Litz wire under high frequency AC; Step S6: Calculate the coupling coefficient between the coupling coils, analyze the frequency splitting and establish the constraint conditions; Step S6: Determine the optimization variables, and use the energy transmission efficiency as the objective function value and optimization target; Step S8: Set the constraint condition according to the critical coupling coefficient: k≤k s , and adjust the parameter range according to the constraints; Step S9: optimizing the energy transmission efficiency, ie, the objective function, using an improved four-vector optimization algorithm according to the coil setting parameters.

2. The method according to claim 1, characterized in that: Step S1, analyzing the SS topology compensation structure network and deriving the energy transmission efficiency of the MCR-WPT system; include According to the coupling coil parameters, the improved four-vector optimization algorithm is used to optimize the optimal specific parameters of the coil structure. The energy transmission efficiency formula of the MCR-WPT system, that is, the objective function is: Where η represents the energy transfer efficiency of the system; ω is the resonant angular frequency of the system; M is the mutual inductance of the coupling coil; R1 and R2 represent the internal resistance of the primary and secondary coils respectively; R L Indicates the load size of the system.

3. The method according to claim 1, characterized in that In step S3, the self-inductance of the coil is determined by the following method: Where: L is the self-inductance, N is the number of turns, μ0 is the vacuum permeability, r avg The average wire diameter r max is the outer radius of the coil, r min is the inner radius of the coil, C1=2.46, C2=0.

2.

4. The method according to claim 1, characterized in that: In step S4, the mutual inductance value between the coupled coils is determined by the following method: Where M is the mutual inductance, μ0 is the vacuum permeability, N r is the number of turns of the primary coil, N t is the number of turns of the secondary coil, r r is the average radius of the primary coil, r t is the average radius of the secondary coil, and h is the distance between the coils.

5. The method according to claim 1, characterized in that In step S5, the AC resistance of the Litz wire under high frequency AC is determined by the following method: Where k is the number of Litz strands, d str is the single strand diameter, r avg is the average line diameter, δ is the skin depth, is the conductor spacing, R ac is the AC resistance, ρ is the resistivity, and N is the number of turns.

6. The method according to claim 1, characterized in that Step S6: Calculate the coupling coefficient between the coupling coils and analyze the frequency splitting to establish the constraint conditions, including: The coupling coefficient is derived from the relationship between the mutual inductance and the self-inductance of the two coils: Where M is the mutual inductance of the coils, L1 and L2 represent the self-inductance of coil one and coil two respectively; The coupling coefficient indicates the degree of coupling between the primary coil and the secondary coil. When k = 1, the components are tightly coupled and the coupling coefficient of the power transformer is close to 1. When k = 0, there is no coupling between the coils and they are independent of each other. The coils at the transmitting and receiving ends have the same specifications and parameters to ensure the numerical consistency of the resonant capacitance; the critical coupling coefficients for SS are: The calculation formula of quality factor Q is: In the MCR-WPT system, when k>ks, the system is in over-coupling, when k=ks, the system is in critical coupling, and when k<k s The system is undercoupled.

7. The method according to claim 1, characterized in that Step S7 includes: Calculate the self-inductance, mutual inductance, resistance, coupling coefficient and transmission efficiency of the coil according to the set coupling coil parameter range; According to the maximum transmission efficiency, the specific wire diameter, spiral diameter, spacing and power frequency of the corresponding coil can be deduced; The power frequency, the wire diameter and pitch of the tiny planar coil and the distance between the two coils are used as optimization variables; the energy transmission efficiency is used as the objective function value and the optimization target.

8. The method according to claim 1, characterized in that Step S9: optimizing the energy transmission efficiency, i.e., the objective function, using an improved four-vector optimization algorithm according to the coil setting parameters, including: The maximum transmission efficiency formula is used as the objective function, and the resonant frequency, coil outer diameter, inner diameter, single-strand wire diameter, coil spacing, and coil turns are used as known parameter ranges. The objective function is optimized using the improved four-vector optimization algorithm to calculate the coil's self-inductance, mutual inductance, resistance, and coupling coefficient. The objective function at maximum efficiency, the specific values ​​of the resonant frequency, coil outer diameter, inner diameter, single-strand wire diameter, coil spacing, and coil turns are obtained; Optimization methods include: Step S91: Initialize the population data using SPM chaotic mapping according to the set parameters, generate the initial population position as evenly as possible within the constraint range, and calculate the fitness of each individual in the population; Step S92: Determine the four vectors as the initial leaders, and select the four individual positions with the smallest fitness values ​​of the population after initialization as the initial leaders; Step S93: Use the vertical and horizontal crossover strategy to randomly match each individual in the population as a parent to generate a new offspring and retain individuals with smaller fitness values, and update the population position for the first time. Step S94: Select the four individuals with the smallest new fitness values ​​as the four-vector positions of the leader, update the position of the best agent according to the motion equation after the four-vector passes through Gaussian perturbation, and finally select the average position of the positions of the four best agents to update the population position for the second time; Step S95: determine whether the population iteration number has reached the maximum iteration number; if so, output the result and end the iteration; if not, continue to repeat steps S94 to S95; In the population initialization stage of the four-vector optimization algorithm, the SPM chaotic mapping is introduced to reduce the randomness of generating the initial population. In the position update stage of the algorithm, a vertical and horizontal cross strategy based on the genetic algorithm is introduced to realize the global search of the algorithm and avoid premature convergence of the algorithm. The dynamic adaptive coefficient is used to make the algorithm more exploratory in the early stage and gradually refined in the later stage. Slight Gaussian perturbations are added to increase randomness and increase the probability of finding the global optimal solution.

9. The method according to claim 8, characterized in that The SPM chaos map expression is: Where mod is the modulus of the function, x(i) is the individual position, x(i+1) is the new individual position, r is a random number between 0 and 1, which is used to introduce randomness into the mapping function and increase the unpredictability of the sequence; η and μ are control parameters, and their values ​​are both between 0 and 1.

10. The method according to claim 8, characterized in that The crossover strategy includes horizontal crossover and vertical crossover, and the expression is: Where SM i1 and SM i2 is the parent individual after pairing, and its offspring is and SM i1j and SM i2j Respectively represent SM i1 and SM i2 The j-th dimension of , j = 1, 2, ..., dim, dim is the dimension, r1 and r2 are random numbers between (0, 1), c1 and c2 are random numbers between (-1, 1); Vertical crossover promotes some stagnant dimensions of the population to get rid of premature dimensional convergence, so that the algorithm jumps out of the local optimum. The expression is: Where SM ij1 and SM ij2 is the parent individual after pairing, and its offspring is r is a random number between (0,1).

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