Speed control method for high-speed water pump engine

Abstract

The invention discloses a speed control method for a high-speed water pump engine, which belongs to the technical field of PID (Proportion Integration Differentiation) control optimization and specifically comprises the following steps of: 1, constructing a speed control system for the high-speed water pump engine; step 2, improving a whale migration optimization algorithm: D1, generating an initial population of the algorithm by using a mixed sine and cosine mapping strategy; d2, improving a whale migration optimization algorithm by using an adaptive convergence step length strategy fused with crossover variation to update a mathematical model of an individual position; thirdly, parameter optimization is conducted on a PID controller module in the high-speed water pump engine speed control system through the improved whale migration optimization algorithm; 4, applying the optimal control parameters obtained in the step 3 to a PID controller module in a high-speed water pump engine speed control system; a PID controller module in the high-speed water pump engine speed control system is optimized through the improved whale migration optimization algorithm, and the adaptability and robustness of the whole control system are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of PID control optimization, and in particular relates to a speed control method for a high-speed water pump engine. Background Art

[0002] The speed control technology of high-speed water pump engines is widely used in petrochemical, electric power, fire protection, aerospace and other fields. The speed control technology of high-speed water pump engines can accurately adjust the speed of the water pump according to system requirements to ensure the stable operation of the water pump under different loads and working conditions. By changing the speed of the motor, the flow and pressure can be directly controlled to meet various operating requirements. By accurately controlling the speed, the high-speed water pump engine can optimize the operating efficiency under different workloads, avoid overload and unnecessary energy waste, and reduce system operating costs and equipment wear. The PID controller plays a core role in the speed control system of the water pump. The PID controller calculates the error between the target speed and the actual speed and adjusts the motor input signal (such as voltage, current or frequency) to accurately control the speed of the water pump.

[0003] PID controller (proportional-integral-differential controller) is a feedback control technology widely used in industrial automation and process control. It adjusts the control quantity to make the system output as close to the target value as possible by processing the error signal (i.e. the difference between the set value and the actual value) in real time. The PID controller consists of three parts: proportional (P) control, integral (I) control and differential (D) control. The PID controller has the advantages of simple structure, easy implementation and strong real-time performance. It is suitable for many systems that require precise adjustment. However, its performance is strongly dependent on parameter adjustment and cannot adapt to changes in system parameters. Therefore, further optimization or improvement may be required in complex or dynamically changing environments.

[0004] The Whale Migration Optimization Algorithm (WMA) is a bio-inspired optimization algorithm based on the migration behavior of humpback whale groups. The algorithm simulates the process of global and local search of whale groups during migration through collective cooperation, leadership guidance and follower strategies. Compared with traditional optimization methods, WMA effectively balances the trade-off between global exploration and local exploitation by introducing a leader-follower mechanism, thereby avoiding falling into local optimal solutions and accelerating the convergence of the algorithm. WMA performs well in a variety of standard optimization problems and has higher accuracy and faster convergence speed than other common optimization algorithms such as particle swarm optimization (PSO) and whale optimization algorithm (WOA). Summary of the invention

[0005] The purpose of the invention is to improve the mathematical model of the initial population and updated individual positions of the whale migration optimization algorithm. The improved whale migration optimization algorithm has a faster convergence speed and better optimization accuracy in the optimization process, can reach the vicinity of the optimal solution in a shorter iteration, and the algorithm has stronger adaptability. The improved whale migration optimization algorithm is used for parameter adjustment of the PID controller of the high-speed water pump engine speed control system, which solves the problem of poor system adaptability caused by fixed parameters. The optimal PID control parameters are found through the improved whale migration optimization algorithm, which improves the control accuracy of the high-speed water pump engine speed control system, so that the water pump can quickly reach the target speed, and can better adapt to environmental interference in a high-speed environment to maintain a stable state, reducing the impact of steady-state errors on control performance.

[0006] In order to achieve the above object, the present invention adopts the following technical solution.

[0007] A high-speed water pump engine speed control method, the specific steps are as follows.

[0008] Step 1: Construct a high-speed water pump engine speed control system, the control system includes: an error calculation module, a PID controller module, an improved whale migration optimization algorithm module, a high-speed water pump engine control module, and a speed feedback module.

[0009] Step 2: Improve the whale migration optimization algorithm, including two improvements: D1. Use the mixed sine-cosine mapping strategy to generate the initial population of the algorithm. This strategy uses Tent mapping to generate the mapping value xn, and selects sine or cosine mapping to generate the position of the initial population of the algorithm according to the distribution of xn; D2. An adaptive convergence step strategy integrating crossover and mutation is used to improve the mathematical model of the stage in which experienced whales or leaders discover and search for new areas in the whale migration optimization algorithm. This strategy randomly selects four individuals in the population for crossover and mutation, and determines the size of the convergence step by the fitness value of the current individual. When the individual fitness value is far away from the optimal fitness value, the step size is increased to accelerate the movement to the optimal area. On the contrary, the step size is reduced for local development.

[0010] Step 3: Use the improved whale migration optimization algorithm to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system, and obtain a set of optimal control parameters Kp, Ki, and Kd through algorithm optimization.

[0011] Step 4: Use the optimal control parameters obtained in step 3 in the PID controller module in the high-speed water pump engine speed control system to optimize the speed control of the system.

[0012] Furthermore, in the step 1, the relationship between the various modules of the constructed high-speed water pump engine speed control system is as follows: the error calculation module obtains the real-time speed error e(t) by calculating the target speed and the actual speed obtained by the speed feedback module, and the real-time error e(t) is input into the PID controller module, and the parameters of the PID controller module are adjusted by the improved whale migration optimization algorithm, and the parameter output control quantity u(t) obtained by the adjustment is sent to the high-speed water pump engine control module for speed control. The mathematical model of the high-speed water pump engine control module is shown in formula (1): (1); In formula (1), represents the speed, J represents the moment of inertia of the motor, u(t) represents the control quantity output by the PID controller, B represents the damping coefficient of the motor, k represents a constant related to the system resistance, Q represents the flow rate of the water pump, Represents the back electromotive force constant of the motor; (2); In formula (2), Kp represents proportional gain, Ki represents integral gain, Kd represents differential gain, and e(t) represents real-time error.

[0013] Furthermore, in D1, the initial population of the algorithm is generated using a mixed sine-cosine mapping strategy, and the specific mathematical model is: (3); In formula (3), w represents the initial population position, lb represents the lower limit of the search space, and ub represents the lower limit of the search space. represents the Tent mapping value, and the calculation formula is shown in formula (4), μ represents the mapping control coefficient and its value is 0.8; (4); In formula (4), Indicates the updated Tent map value.

[0014] Furthermore, the hybrid sine-cosine mapping strategy performs complementary mapping of sine mapping and cos mapping, which can avoid the generated individuals from being concentrated in a certain area and enhance the search range of the initial population. Adjustment using the Tent mapping value can enhance the diversity of the initial population. The initial population generated by this strategy is not prone to skewness, which is helpful for global search in the early stages of the algorithm.

[0015] Furthermore, in D2, an adaptive convergence step strategy integrating crossover and mutation is used to improve the mathematical model of the phase of discovery and search for new areas by experienced whales or leaders in the whale migration optimization algorithm. The improved specific mathematical model is: (5); In formula (5), w(iter+1) represents the updated individual position, w(iter) represents the current individual position, iter represents the current number of iterations, λ() represents the adaptive step function, and the calculation formula is shown in formula (6). f represents the fitness value of the current individual. represents the optimal fitness value, rand represents a random number between [0,1], represents the position of the optimal individual, F represents the variation factor with a value of 0.5, , , , represents three randomly selected individual positions; (6); In formula (6), λ0 represents the basic step coefficient, f represents the fitness value of the current individual, represents the optimal fitness value, and ε represents a very small constant to prevent the denominator of the formula from taking 0.

[0016] Furthermore, crossover mutation effectively enhances the global search capability of the algorithm by randomly selecting individuals to generate mutation vectors, avoiding falling into local optimality. The adaptive step size dynamically adjusts the step size according to the difference between the fitness value of the individual and the optimal individual, so that individuals with poor fitness values ​​can quickly approach the optimal area, while individuals with good fitness values ​​can be finely developed with small steps, thereby achieving an efficient balance between global exploration and local development, and improving the convergence speed and accuracy of the algorithm.

[0017] Furthermore, in step three, the improved whale migration optimization algorithm is used to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system, and the specific steps are as follows: S1. Initialize the parameters of the improved whale migration optimization algorithm, including the population size N, the problem dimension dim, the maximum number of iterations max_iter, the upper limit ub and the lower limit lb of the search space. The initial population position of the algorithm is generated by using the mixed sine-cosine mapping strategy based on the initial parameters of the algorithm. The specific mathematical model is shown in formula (3); S2. By introducing the improved whale migration optimization algorithm into the PID controller parameter tuning process, the corresponding relationship between the algorithm individual position vector w(iter) and the PID parameters is established: where the first, second and third dimensions of the vector represent the proportional coefficient Kp, the integral coefficient Ki and the differential coefficient Kd respectively. During the iteration process, the algorithm continuously adjusts the position of the individual in the solution space, thereby continuously updating the corresponding PID parameter values. With the help of the algorithm optimization, the optimal solution of the system performance indicators is gradually approached, and finally a set of PID controller parameters with the best response performance is obtained; S3. Set the fitness value function of the improved whale migration optimization algorithm, calculate the fitness value of individuals in the initial population of the algorithm through the fitness value function, and sort them according to the size of the fitness value. The specific fitness value function is: (7); In formula (7), J represents the fitness value, e(t) represents the real-time error value, and T represents the system operation time; S4. Update the individual positions in the population through the mathematical model of the improved whale migration optimization algorithm, determine whether the updated individual fitness value is better than the individual fitness value before the update, retain the excellent individuals, and update the fitness value ranking in the population. The specific mathematical model is: S41, the algorithm enters the inexperienced whale movement stage and updates the position. First, the average position of the individuals with the top NL fitness values ​​in the population is calculated. NL is the number of leaders, and 1 / 3 of the population is taken. The specific update formula for this stage is: (7); In formula (7), w(iter+1) represents the updated individual position, w(iter) represents the current individual position, w(iter-1) represents the individual position of the previous iteration, iter represents the current iteration number, and rand represents a random number between [0,1]. represents the position of the optimal individual, represents the average position of the leaders; S42, the algorithm enters the stage where experienced whales or leaders discover and search new areas and update their positions. The specific update formula for this stage is shown in formula (5); S5. Determine whether the current number of iterations has reached the maximum number of iterations. If not, return to execute S4 to search for the optimal solution. If so, complete the algorithm search and output the optimal solution.

[0018] By adopting the above technical scheme, the beneficial effects of the present invention are as follows: by improving the whale migration optimization algorithm, the adaptability and performance of the algorithm are improved, and it can better adapt to the controlled environment of high-speed water pump engine speed control, and can more accurately adjust the control parameters of the PID controller, improve the response speed and steady-state performance of the system, and effectively enhance the control accuracy and stability, thereby realizing efficient and stable control of the speed of high-speed water pump engine. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The present invention is a flow chart of a high-speed water pump engine speed control method.

[0020] Figure 2 To construct a model diagram of the high-speed water pump engine speed control system.

[0021] Figure 3 A comparison chart of the changes in fitness values ​​during the optimization process of the improved whale migration optimization algorithm and the standard whale migration optimization algorithm.

[0022] . Figure 4 Comparison chart of the response of the PID controller of the optimized system for the improved whale migration optimization algorithm and the standard whale migration optimization algorithm. DETAILED DESCRIPTION

[0023] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0024] The present invention provides a technical solution: a high-speed water pump engine speed control method, specifically comprising the following steps: Figure 1 shown.

[0025] Step 1: Construct a high-speed water pump engine speed control system, the control system includes: an error calculation module, a PID controller module, an improved whale migration optimization algorithm module, a high-speed water pump engine control module, and a speed feedback module.

[0026] Step 2: Improve the whale migration optimization algorithm, including two improvements: D1. Use the mixed sine-cosine mapping strategy to generate the initial population of the algorithm. This strategy uses Tent mapping to generate the mapping value xn, and selects sine or cosine mapping to generate the position of the initial population of the algorithm according to the distribution of xn; D2. An adaptive convergence step strategy integrating crossover and mutation is used to improve the mathematical model of the stage in which experienced whales or leaders discover and search for new areas in the whale migration optimization algorithm. This strategy randomly selects four individuals in the population for crossover and mutation, and determines the size of the convergence step by the fitness value of the current individual. When the individual fitness value is far away from the optimal fitness value, the step size is increased to accelerate the movement to the optimal area. On the contrary, the step size is reduced for local development.

[0027] Step 3: Use the improved whale migration optimization algorithm to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system, and obtain a set of optimal control parameters Kp, Ki, and Kd through algorithm optimization.

[0028] Step 4: Use the optimal control parameters obtained in step 3 in the PID controller module in the high-speed water pump engine speed control system to optimize the speed control of the system.

[0029] Furthermore, in the step 1, the relationship between the various modules of the constructed high-speed water pump engine speed control system is as follows: the error calculation module obtains the real-time speed error e(t) by calculating the target speed and the actual speed obtained by the speed feedback module, and the real-time error e(t) is input into the PID controller module, and the parameters of the PID controller module are adjusted by the improved whale migration optimization algorithm, and the parameter output control quantity u(t) obtained by the adjustment is sent to the high-speed water pump engine control module for speed control. The mathematical model of the high-speed water pump engine control module is shown in formula (1): (1); In formula (1), represents the speed, J represents the moment of inertia of the motor, u(t) represents the control quantity output by the PID controller, B represents the damping coefficient of the motor, k represents a constant related to the system resistance, Q represents the flow rate of the water pump, Represents the back electromotive force constant of the motor; (2); In formula (2), Kp represents proportional gain, Ki represents integral gain, Kd represents differential gain, and e(t) represents real-time error.

[0030] Furthermore, in D1, the initial population of the algorithm is generated using a mixed sine-cosine mapping strategy, and the specific mathematical model is: (3); In formula (3), w represents the initial population position, lb represents the lower limit of the search space, and ub represents the lower limit of the search space. represents the Tent mapping value, and the calculation formula is shown in formula (4), μ represents the mapping control coefficient and its value is 0.8; (4); In formula (4), Indicates the updated Tent map value.

[0031] Furthermore, in D2, an adaptive convergence step strategy integrating crossover and mutation is used to improve the mathematical model of the phase of discovery and search for new areas by experienced whales or leaders in the whale migration optimization algorithm. The improved specific mathematical model is: (5); In formula (5), w(iter+1) represents the updated individual position, w(iter) represents the current individual position, iter represents the current number of iterations, λ() represents the adaptive step function, and the calculation formula is shown in formula (6). f represents the fitness value of the current individual. represents the optimal fitness value, rand represents a random number between [0,1], represents the position of the optimal individual, F represents the variation factor with a value of 0.5, , , , represents three randomly selected individual positions; (6); In formula (6), λ0 represents the basic step coefficient, f represents the fitness value of the current individual, represents the optimal fitness value, and ε represents a very small constant to prevent the denominator of the formula from taking 0.

[0032] Furthermore, in step three, the improved whale migration optimization algorithm is used to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system, and the specific steps are as follows: S1. Initialize the parameters of the improved whale migration optimization algorithm, including the population size N, the problem dimension dim, the maximum number of iterations max_iter, the upper limit ub and the lower limit lb of the search space. The initial population position of the algorithm is generated by using the mixed sine-cosine mapping strategy based on the initial parameters of the algorithm. The specific mathematical model is shown in formula (3); S2. By introducing the improved whale migration optimization algorithm into the PID controller parameter tuning process, the corresponding relationship between the algorithm individual position vector w(iter) and the PID parameters is established: where the first, second and third dimensions of the vector represent the proportional coefficient Kp, the integral coefficient Ki and the differential coefficient Kd respectively. During the iteration process, the algorithm continuously adjusts the position of the individual in the solution space, thereby continuously updating the corresponding PID parameter values. With the help of the algorithm optimization, the optimal solution of the system performance indicators is gradually approached, and finally a set of PID controller parameters with the best response performance is obtained; S3. Set the fitness value function of the improved whale migration optimization algorithm, calculate the fitness value of individuals in the initial population of the algorithm through the fitness value function, and sort them according to the size of the fitness value. The specific fitness value function is: (7); In formula (7), J represents the fitness value, e(t) represents the real-time error value, and T represents the system operation time; S4. Update the individual positions in the population through the mathematical model of the improved whale migration optimization algorithm, determine whether the updated individual fitness value is better than the individual fitness value before the update, retain the excellent individuals, and update the fitness value ranking in the population. The specific mathematical model is: S41, the algorithm enters the inexperienced whale movement stage and updates the position. First, the average position of the individuals with the top NL fitness values ​​in the population is calculated. NL is the number of leaders, and 1 / 3 of the population is taken. The specific update formula for this stage is: (7); In formula (7), w(iter+1) represents the updated individual position, w(iter) represents the current individual position, w(iter-1) represents the individual position of the previous iteration, iter represents the current iteration number, and rand represents a random number between [0,1]. represents the position of the optimal individual, represents the average position of the leaders; S42, the algorithm enters the stage where experienced whales or leaders discover and search new areas and update their positions. The specific update formula for this stage is shown in formula (5); S5. Determine whether the current number of iterations has reached the maximum number of iterations. If not, return to execute S4 to search for the optimal solution. If so, complete the algorithm search and output the optimal solution.

[0033] Furthermore, in order to verify that the present invention has certain advantages, experiments were conducted using simulation software Matlab and Simulink. The standard whale migration optimization algorithm was improved by Matlab, and a simulation model was constructed by Simulink, including an error calculation module, a PID controller module, an improved whale migration optimization algorithm module, a high-speed water pump engine control module, and a speed feedback module. The mathematical model of the high-speed water pump engine control module was Laplace transformed, and the transformed transfer function was used as the model controlled function, and was set according to the actual water pump parameters as follows: , s represents the variable in the complex frequency domain. In the main function, the initial parameters of the algorithm are set, the maximum number of iterations is set to 30, the problem dimension is set to 3, the population size is set to 100, the upper limit of the search space is set to 50, and the lower limit is set to 0.001. The improved whale migration optimization algorithm and the standard whale migration optimization algorithm functions are called in turn, and the optimization records are retained for visualization, such as Figure 3 and Figure 4 shown.

[0034] Furthermore, Figure 3A comparison chart of the fitness value changes during the optimization process of the improved whale migration optimization algorithm and the standard whale migration optimization algorithm is shown in the figure. It can be seen from the figure that the standard whale migration optimization algorithm falls into the local optimal solution after reaching the optimal value and cannot jump out for a long time, while the improved whale migration optimization algorithm can jump out of the local optimal solution and continue to optimize downward in a shorter number of iterations. The individual position fitness value finally found is lower, indicating that the improved whale migration optimization algorithm has stronger optimization performance. Figure 4 The response comparison chart of the PID controller of the optimization system of the improved whale migration optimization algorithm and the standard whale migration optimization algorithm is shown in the figure. The target value is set to 1 unit. It can be seen from the figure that the overshoot of the response curve of the PID controller of the optimization system of the improved whale migration optimization algorithm is very small, and it quickly maintains a stable state after reaching the target value. The steady-state error in the tuning process is smaller and the control performance is better.

Claims

1. A high-speed water pump engine speed control method, characterized in that: The specific steps are as follows: Step 1: construct a high-speed water pump engine speed control system, the control system includes: an error calculation module, a PID controller module, an improved whale migration optimization algorithm module, a high-speed water pump engine control module, and a speed feedback module; Step 2: Improve the whale migration optimization algorithm, including two improvements: D1. Use the mixed sine-cosine mapping strategy to generate the initial population of the algorithm. This strategy uses Tent mapping to generate the mapping value xn, and selects sine or cosine mapping to generate the position of the initial population of the algorithm according to the distribution of xn; D2. An adaptive convergence step strategy integrating crossover and mutation is used to improve the mathematical model of the stage of experienced whales or leaders discovering and searching new areas in the whale migration optimization algorithm. This strategy randomly selects four individuals in the population for crossover and mutation, and determines the size of the convergence step by the fitness value of the current individual. When the individual fitness value is far from the optimal fitness value, the step size is increased to accelerate the movement to the optimal area. On the contrary, the step size is reduced for local development. Step 3: Optimize the parameters of the PID controller module in the high-speed water pump engine speed control system using the improved whale migration optimization algorithm, and obtain a set of optimal control parameters Kp, Ki, and Kd through algorithm optimization; Step 4: Use the optimal control parameters obtained in step 3 in the PID controller module in the high-speed water pump engine speed control system to optimize the speed control of the system.

2. A high-speed water pump engine speed control method according to claim 1, characterized in that: In the step 1, the high-speed water pump engine speed control system is constructed, and the relationship between the various modules is as follows: the error calculation module obtains the real-time speed error e(t) by calculating the target speed and the actual speed obtained by the speed feedback module, and the real-time error e(t) is input into the PID controller module, and the parameters of the PID controller module are adjusted through the improved whale migration optimization algorithm, and the parameter output control quantity u(t) obtained by the adjustment is sent to the high-speed water pump engine control module for speed control.

3. A high-speed water pump engine speed control method according to claim 2, characterized in that: In D1, the initial population of the algorithm is generated using a mixed sine-cosine mapping strategy, and the specific mathematical model is: (3)； In formula (3), w represents the initial population position, lb represents the lower limit of the search space, and ub represents the lower limit of the search space. represents the Tent mapping value, and the calculation formula is shown in formula (4), μ represents the mapping control coefficient and its value is 0.8; (4)； In formula (4), Indicates the updated Tent map value.

4. A high-speed water pump engine speed control method according to claim 3, characterized in that: In D2, an adaptive convergence step size strategy integrating crossover and mutation is used to improve the mathematical model of the phase of experienced whales or leaders discovering and searching new areas in the whale migration optimization algorithm. The improved specific mathematical model is: (5)； In formula (5), w(iter+1) represents the updated individual position, w(iter) represents the current individual position, iter represents the current number of iterations, λ() represents the adaptive step function, and the calculation formula is shown in formula (6). f represents the fitness value of the current individual. represents the optimal fitness value, rand represents a random number between [0,1], represents the position of the optimal individual, F represents the variation factor with a value of 0.5, , , , represents three randomly selected individual positions; (6)； In formula (6), λ0 represents the basic step coefficient, f represents the fitness value of the current individual, represents the optimal fitness value, and ε represents a very small constant to prevent the denominator of the formula from taking 0.

5. A high-speed water pump engine speed control method according to claim 4, characterized in that: In the step three, the improved whale migration optimization algorithm is used to optimize the parameters of the PID controller module in the high-speed water pump engine speed control system, and the specific steps are as follows: S1. Initialize the parameters of the improved whale migration optimization algorithm, including the population size N, the problem dimension dim, the maximum number of iterations max_iter, the upper limit ub and lower limit lb of the search space, and use the mixed sine-cosine mapping strategy to generate the initial population position of the algorithm through the initial parameters of the algorithm; S2. By introducing the improved whale migration optimization algorithm into the PID controller parameter tuning process, the corresponding relationship between the algorithm individual position vector w(iter) and the PID parameters is established: where the first, second and third dimensions of the vector represent the proportional coefficient Kp, the integral coefficient Ki and the differential coefficient Kd respectively. During the iteration process, the algorithm continuously adjusts the position of the individual in the solution space, thereby continuously updating the corresponding PID parameter values. With the help of the algorithm optimization, the optimal solution of the system performance indicators is gradually approached, and finally a set of PID controller parameters with the best response performance is obtained; S3. Set the fitness value function of the improved whale migration optimization algorithm, calculate the fitness value of individuals in the initial population of the algorithm through the fitness value function, and sort them according to the size of the fitness value. The specific fitness value function is: (7)； In formula (7), J represents the fitness value, e(t) represents the real-time error value, and T represents the system operation time; S4. Update the individual positions in the population through the mathematical model of the improved whale migration optimization algorithm, determine whether the updated individual fitness value is better than the individual fitness value before the update, retain the excellent individuals, and update the fitness value ranking in the population. The specific mathematical model is: S41, the algorithm enters the movement phase of the inexperienced whale and performs position update; S42, the algorithm enters the stage of experienced whales or leaders discovering and searching new areas and updating their positions; S5. Determine whether the current number of iterations has reached the maximum number of iterations. If not, return to execute S4 to search for the optimal solution. If so, complete the algorithm search and output the optimal solution.

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