Method for implementing engineering optimization based on arithmetic optimization algorithm improved by multiple strategies

Abstract

The application discloses a kind of arithmetic optimization algorithm based on multi-strategy improvement engineering optimization method, steps are as follows: first, engineering problem is formalized, and the parameter of input multi-strategy improved arithmetic optimization algorithm is determined.Second, compare r1 using sine factor improvement with mathematical optimizer acceleration function MOA, reconstruct the search phase of arithmetic optimization algorithm, to balance the proportion of exploration phase and development phase in arithmetic optimization algorithm.Then, the golden sine strategy is used to guide individual to approach optimal solution, to realize algorithm fine search.Using Runge-Kutta algorithm enhanced solution quality ESQ mechanism further improves the quality of current optimal solution, makes it jump out of local optimum, searches to optimal solution.The algorithm is further applied to benchmark test function and engineering optimization problem instance, and the test results show that the improved algorithm has strong search ability, high convergence precision, fast convergence speed, and good effect for the engineering optimization problem.

Description

Technical Field

[0001] This invention belongs to the field of swarm intelligence optimization algorithms, specifically relating to a method for engineering optimization based on a multi-strategy improved arithmetic optimization algorithm. Background Technology

[0002] In recent years, as the complexity of engineering optimization problems has continued to increase, traditional computational methods have become increasingly inadequate for solving complex engineering optimization problems, such as UAV trajectory planning, image segmentation, machine learning feature selection, and computer vision image thresholding. Intelligent optimization algorithms, due to their simple concepts, ease of implementation, and strong stability, have entered the field of vision of ordinary technical personnel, resulting in a surge of applications and developments in recent years. Inspired by the complex behaviors of animals or the patterns of development in nature, developers have proposed many heuristic swarm intelligence optimization algorithms, such as the chimpanzee optimization algorithm, the sparrow search algorithm, the Harris eagle algorithm, and genetic algorithms.

[0003] In recent years, among the many swarm intelligence optimization algorithms developed, arithmetic optimization algorithms have received widespread attention due to their simple parameters and strong optimization capabilities. Arithmetic optimization algorithms, a novel metaheuristic algorithm proposed in 2021, are based on the four basic arithmetic operations. They improve the dispersion of the global search through multiplication and division, and enhance the accuracy of the local search through addition and subtraction. While this algorithm exhibits a certain level of accuracy and stability, it suffers from slower convergence speeds and a tendency to get trapped in local optima in the later stages of iteration when faced with increasingly complex optimization problems. This prevents the algorithm from converging to the optimal value, significantly impacting its effectiveness.

[0004] Therefore, in order to improve the performance of arithmetic optimization algorithms when facing practical engineering problems, it is essential to improve the arithmetic optimization algorithms to solve problems such as low convergence accuracy and easy getting trapped in local optima. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a multi-strategy improved arithmetic optimization algorithm for solving pressure vessel design problems. This invention aims to overcome the deficiencies of arithmetic optimization algorithms in the search process, such as weak global search capability in the early stages, slow convergence speed in the later stages, low convergence accuracy, and susceptibility to local optima. It aims to improve the optimization performance and effectiveness of arithmetic optimization algorithms, reduce the complexity of solving pressure vessel design problems, and decrease manufacturing costs.

[0006] To achieve the above objectives, this invention provides a method for engineering optimization based on a multi-strategy improved arithmetic optimization algorithm, comprising the following steps:

[0007] S1. For complex pressure vessel design problems, determine the optimization parameters: The pressure vessel design problem includes parameters such as the cross-sectional length of the cylindrical portion of the pressure vessel (…). L ), the inner diameter of the cylindrical part ( R The wall thickness of the cylindrical part ( T s Head wall thickness ( T l The pressure vessel design problem involves minimizing the cost of pressure vessel manufacturing.

[0008] S2. Optimize using a multi-strategy improved arithmetic optimization algorithm, including the following sub-steps:

[0009] Step 1: Randomly generate an initial population. The population contains... m Only individuals, and each individual has a dimension of n During the initialization phase, an initial population matrix is ​​generated using the following equation:

[0010]

[0011] in, X To initialize the population matrix, Let represent an individual in the population, and each individual has a dimension of . n There are in the population m Individual, These are the maximum and minimum values ​​for the individual dimension, respectively. The value is a custom value used to constrain the range of values ​​for individuals in the population. rand(0,1) is a random number in the range [0,1].

[0012] In the parameter tuning problem of motor stable operation based on PID control, n Corresponding to the number of parameters to be optimized, therefore, n =3, Represents the parameters to be optimized { k p , k i , k d}of m One candidate value, m This represents the number of candidate values, which is a user-defined value. The algorithm iterates multiple times to obtain the final value. m The optimal value is selected from the candidate values.

[0013] Step 2: Set the fitness function, calculate the fitness value of each individual in the population, obtain the optimal solution for the initial population, and begin the iteration;

[0014] Step 3: Calculate the Mathematical Optimizer Acceleration Function MOA, the Mathematical Optimizer Probability Function MOP, and the value of r1 improved by the sine factor, and compare the value of r1 with that of MOA. If r1 < MOA, the population individuals enter the exploration stage; otherwise, they enter the exploitation stage.

[0015] The formula for the Mathematical Optimizer Acceleration Function MOA is as follows:

[0016]

[0017] Where, t is the current iteration number, T max is the maximum iteration number, MOA max and MOA min are the maximum value 1 and the minimum value 0.2 of the Mathematical Optimizer Acceleration Function respectively.

[0018] In the exploration stage, the update of the population is completed by multiplication and division in basic arithmetic operations. Individuals are updated using multiplication and division, and the movement range of individuals increases, enabling individuals to conduct global searches. The individual update formula in the exploration stage is as follows:

[0019]

[0020] Where, is the value of the t -th iteration of the optimal individual in the n -th dimension; r 2 is a random number belonging to [0, 1]; ε is the minimum constant, μ is the optimization process control constant, with a value of 0.499; ub n and lb n represent the boundaries of the n -th dimension value of the individual; MOP is the Mathematical Optimizer Probability Function, and its mathematical model is as shown in the formula:

[0021]

[0022] Where, α is the sensitivity coefficient, defining the exploration accuracy, with a value of 5.

[0023] In the exploitation stage, the update of the population is completed by addition and subtraction in basic arithmetic operations. Individuals are updated using addition and subtraction, and the movement range of individuals decreases, enabling individuals to conduct local searches. The individual update formula in the exploitation stage is as follows:

[0024]

[0025] in, r 3 is a random number belonging to the range [0,1].

[0026] Step 4: Follow the golden sine strategy to guide the population individuals entering the exploration phase to update their positions, and follow the addition and subtraction strategy to update their positions.

[0027] Step 5: Determine whether the fitness value of an individual in the population after the update is less than the current best value. If so, update the current best value and update the best individual in the population at the same time; otherwise, do not update.

[0028] Step 6: Substitute the current optimal solution into the Runge-Kutta algorithm's Enhanced Solution Query (ESQ) mechanism to improve solution quality;

[0029] Step 7: Calculate the fitness value of individuals in the enhanced population. If it is less than the fitness value of the optimal solution before enhancement, the enhancement is successful, and the optimal solution and the optimal population individual are updated; otherwise, the enhancement fails, the optimal solution remains unchanged, and the number of iterations is recorded.

[0030] Step 8: If the number of iterations is less than the maximum number of iterations, substitute the obtained optimal solution into step 3 and execute step 3;

[0031] Step 9: Once all iterations are completed, the optimization ends, and the global optimum is output.

[0032] This invention is based on arithmetic optimization algorithms and improves upon existing problems in these algorithms. Arithmetic optimization algorithms are a type of swarm intelligence optimization algorithm, inspired by the characteristics of basic arithmetic operations, and perform global search and local development. The multi-strategy improved arithmetic optimization algorithm primarily improves the comparison method of its mathematical accelerator optimization function MOA, the search method in the exploration phase, and the inclusion of a phase that enhances the quality of individuals in the population.

[0033] In the preferred embodiment, in step 3, the mathematical optimizer acceleration function MOA and the sinusoidally improved r1 are compared using the sinusoidally improved r1 with MOA. This allows individuals in the population to enter the exploration phase in the early stage of iteration and the development phase in the later stage of iteration, enhancing the algorithm's global search capability in the early stage of iteration and its local development capability in the later stage of iteration. The expression for the sinusoidally improved r1 is shown below:

[0034]

[0035] in t This represents the current iteration number. T max This represents the maximum number of iterations.

[0036] In the preferred embodiment, during the exploration phase described in steps 3 and 4, the golden sine strategy is used to guide the population individuals in updating their positions. The golden sine algorithm is a novel intelligent algorithm that combines the special relationship between the sine function and the unit circle with the golden ratio to improve optimization performance. Since the contraction steps of the golden ratio are fixed, each step only requires one iteration. Therefore, combining the golden ratio and the sine function improves the convergence speed while avoiding getting trapped in local optima. The expression for guiding the population individuals in updating their positions using the golden sine is as follows:

[0037]

[0038] in, t This represents the current iteration number. R 1 and R 2 are random numbers in the ranges [0, 2p] and [0, p], respectively. P i t The position of the current optimal individual. x 1 and x 2 The golden ratio is used to narrow the search space and guide individuals to converge toward the optimal value in the space. Its definition is:

[0039]

[0040] in, a and b This is the search interval, with a value of 0.618. τ It is the golden ratio.

[0041] In the preferred approach, step 6 includes a population quality improvement phase after each iteration to enhance the search quality of individual populations and prevent them from getting trapped in local optima. The Runge-Kutta algorithm's Enhanced Solution Quality (ESQ) mechanism is used to optimize the current best individual generated after each iteration, thereby enhancing its search ability and enabling the population to move closer to the optimal value more quickly.

[0042] Its mathematical expression is:

[0043]

[0044]

[0045] in, r It can be any value among 1, 0, or -1. β It is a random number belonging to the range [0,1]. c and w It is a random constant. x new1It is a new solution generated by combining the average of three random numbers with the current best value.

[0046] Compared with existing technologies, this method has the following advantages:

[0047] 1. This invention improves r1 by using a sinusoidal factor and compares it with the mathematical optimizer acceleration function MOA, so that a large number of individuals in the population enter the exploration stage in the early stage of iteration and a large number enter the development stage in the later stage of iteration. This balances the global search capability and local development capability of the algorithm and solves the problem that the algorithm has poor global development capability in the early stage of iteration and is difficult to converge in the later stage of iteration.

[0048] 2. This invention improves the convergence speed and accuracy by using the golden sine strategy to guide the population individuals into the exploration stage, thereby greatly increasing the optimization ability of the population individuals.

[0049] 3. This invention introduces the Enhanced Solution Quality (ESQ) mechanism of the Runge-Kutta algorithm to improve the quality of the current optimal solution in each iteration. This further improves the convergence accuracy while preventing the algorithm from getting trapped in local optima, and ensures that the algorithm can maintain the historical optimal value after each iteration.

[0050] In summary, this invention provides a method for engineering optimization based on a multi-strategy improved arithmetic optimization algorithm, enabling a fast and convenient pressure vessel design method. First, the improved r1 using a sine factor is compared with the mathematical optimizer acceleration function MOA to reconstruct the search phase of the arithmetic optimization algorithm, thereby balancing the proportion of the exploration and development phases. Then, the golden sine strategy is used to guide individuals to approach the optimal solution, achieving refined search. The Runge-Kutta algorithm's Enhanced Solution Quality (ESQ) mechanism further improves the quality of the current optimal solution, enabling it to escape local optima and find the optimal solution. The algorithm is applied to benchmark functions and engineering optimization problem examples. Experimental results show that the improved algorithm has strong search capabilities, high convergence accuracy, fast convergence speed, and performs well in practical engineering optimization problems. Attached Figure Description

[0051] Figure 1 The flowchart of a multi-strategy improved arithmetic optimization algorithm proposed in this invention is shown below.

[0052] Figure 2 This is a schematic diagram comparing the convergence of the improved algorithm and the arithmetic optimization algorithm proposed in this invention on the F1 function;

[0053] Figure 3 This is a schematic diagram comparing the convergence of the improved algorithm proposed in this invention and the arithmetic optimization algorithm on the F2 function;

[0054] Figure 4Schematic diagram of the convergence comparison between the improved algorithm proposed in this invention and the arithmetic optimization algorithm on the F3 function. Detailed implementation manners

[0055] To enable researchers and technicians in this field to better understand the technical solution of this invention, the technical solution of this invention will be further clearly and detailedly described below in conjunction with the attached drawings and embodiments.

[0056] In order to reduce the workload of ordinary technicians, improve the solution efficiency of pressure vessel design problems, improve the solution accuracy, and reduce the design cost, this invention has developed a method for realizing engineering optimization based on an arithmetic optimization algorithm improved by multiple strategies.

[0057] The arithmetic optimization algorithm is a new type of metaheuristic algorithm proposed by Laith Abualigah in 2021. This algorithm is based on the four basic arithmetic operation rules in arithmetic. By multiplication and division operations, it improves the dispersion of global search, and uses addition and subtraction operations to improve the accuracy of local search of the algorithm. This algorithm has a certain solution accuracy and stability. However, when facing gradually complex optimization problems, due to the increase in the amount of calculation in the later stage of iteration, the convergence speed of the algorithm becomes slower, and it is easy to fall into local optimum, which leads to the fact that the algorithm cannot converge to the optimal value, greatly affecting the use effect of the algorithm.

[0058] Based on the basic rules of the arithmetic optimization algorithm, this invention proposes a multi-strategy improved arithmetic optimization algorithm to solve the existing problems of the arithmetic optimization algorithm. As Figure 1 shown is the flowchart of a multi-strategy improved arithmetic optimization algorithm proposed in this invention.

[0059] Refer to the attached Figure 1 drawings, a multi-strategy improved arithmetic optimization algorithm proposed in this invention includes the following steps:

[0060] Step 1: Randomly generate an initial population. There are m individuals in the population, and the dimension of each individual is n ;

[0061] Step 2: Set the fitness function, calculate the fitness values of the population individuals, obtain the optimal solution of the initial population, and start to enter the iteration;

[0062] Step 3: Calculate the mathematical optimizer acceleration function MOA, the mathematical optimizer probability function MOP, and the value of r1 improved by the sine factor, and compare the value of r1 with the value of MOA. If r1 < MOA, the population individuals will enter the exploration stage, otherwise they will enter the exploitation stage;

[0063] Step 4: Guide the population individuals entering the exploration stage to update their positions according to the golden sine strategy, and the population individuals entering the exploitation stage will update their positions according to the addition and subtraction strategy;

[0064] Step 5: Determine whether the fitness value of an individual in the population after the update is less than the current best value. If so, update the current best value and update the best individual in the population at the same time; otherwise, do not update.

[0065] Step 6: Substitute the current optimal solution into the Runge-Kutta algorithm's Enhanced Solution Query (ESQ) mechanism to improve solution quality;

[0066] Step 7: Calculate the fitness value of individuals in the enhanced population. If it is less than the fitness value of the optimal solution before enhancement, the enhancement is successful, and the optimal solution and the optimal population individual are updated; otherwise, the enhancement fails, the optimal solution remains unchanged, and the number of iterations is recorded.

[0067] Step 8: If the number of iterations is less than the maximum number of iterations, substitute the obtained optimal solution into step 3 and execute step 3;

[0068] Step 9: Once all iterations are completed, the optimization ends, and the global optimum is output.

[0069] As can be seen from the above steps, the multi-strategy improved arithmetic optimization algorithm proposed in this invention mainly includes five stages: initialization stage, mathematical optimizer acceleration function MOA individual allocation stage, exploration stage, development stage, and population individual quality improvement stage.

[0070] In step 3 of a multi-strategy improved arithmetic optimization algorithm, the mathematical optimizer acceleration function MOA allocates individuals. A sine factor is used to improve r1, which is compared with MOA. This allows individuals to enter the exploration phase in the early iterations and the development phase in the later iterations, enhancing the algorithm's global search capability in the early iterations and its local development capability in the later iterations. The expression for improving r1 using the sine factor is shown below:

[0071]

[0072] in t This represents the current iteration number. T max This represents the maximum number of iterations.

[0073] The specific steps for comparing r1 with MOA using the sinusoidal factor improvement are as follows:

[0074] Step 1: Use formula (10) to calculate r1 and compare it with the MOA value of the current iteration number;

[0075] Step 2: When the r1 improved by the sine factor is less than the MOA value of the current iteration number, the population enters the exploration phase;

[0076] Step 3: When the improved r1 by the sine factor is greater than the MOA value of the current iteration, the population enters the development stage.

[0077] In steps 3 and 4 of a multi-strategy improved arithmetic optimization algorithm, the golden sine strategy is used to guide the population individuals entering the exploration phase to update their positions. The golden sine algorithm is a novel intelligent algorithm that combines the special relationship between the sine function and the unit circle with the golden ratio to improve optimization performance. Since the contraction steps of the golden ratio are fixed, each step only requires one iteration. Therefore, combining the golden ratio and the sine function improves the convergence speed while avoiding getting trapped in local optima. The expression for guiding the population individuals to update their positions using the golden sine is as follows:

[0078]

[0079] in, t This represents the current iteration number. R 1 and R 2 The random numbers are in the ranges [0, 2p] and [0, p], respectively. P i t The position of the current optimal individual. x 1 and x 2 The golden ratio is used to narrow the search space and guide individuals to converge toward the optimal value in the space. Its definition is:

[0080]

[0081]

[0082] in, a and b This is the search interval, with a value of 0.618. τ It is the golden ratio.

[0083] The specific implementation steps for using the golden sine wave strategy to guide the position updates of individuals in a population are as follows:

[0084] Step 1: When the r1 improved by the sine factor is less than the MOA value of the current iteration number, the population enters the exploration phase;

[0085] Step 2: Update the position of individuals in the population using the golden sine formula (11).

[0086] In step 6 of a multi-strategy improved arithmetic optimization algorithm, the enhancement of solution quality is achieved by adding a population individual quality improvement stage after each iteration update to improve the search quality of individual individuals and prevent them from getting trapped in local optima. The Runge-Kutta algorithm's ESQ mechanism is used to optimize the current best individual generated after each iteration, thereby enhancing its optimization ability and enabling the population individuals to move towards the optimal value more quickly. Its mathematical expression is:

[0087]

[0088] in, r It can be any value among 1, 0, or -1. β It is a random number belonging to the range [0,1]. c and w It is a random constant. x new1 It is a new solution generated by combining the average of three random numbers with the current best value.

[0089] The specific steps for improving the quality of the current optimal solution using the ESQ mechanism of the Runge-Kutta algorithm are as follows:

[0090] Step 1: Obtain the optimal solution for the current iteration number;

[0091] Step 2: Calculate the relevant ESQ parameter values ​​using formulas (16) to (18);

[0092] Step 3: Calculate the enhanced optimal solution using formula (15). ;

[0093] Step 4: Compare the enhanced optimal solution with the current optimal solution The solution is compared, and if it is less than the current optimal solution, the position is updated.

[0094] Example:

[0095] 1. Test Methods

[0096] To demonstrate the effectiveness of the improved algorithm proposed in this invention, experiments were conducted using three benchmark test functions and a pressure vessel design problem example. The experimental results were then compared with the original arithmetic optimization algorithm. The experimental environment was a 64-bit Windows 10 operating system, and the software used was Matlab 2020a.

[0097] The specific implementation steps for conducting the experiment using three benchmark test functions are as follows:

[0098] Step 1: Three benchmark test functions were used to conduct optimization experiments. The detailed parameters of the three benchmark test functions are shown in Table 1.

[0099] Step 2: Use the multi-strategy improved arithmetic optimization algorithm proposed in this invention to conduct optimization experiments on the three benchmark functions and solve for the optimal value;

[0100] Step 3: Use the original arithmetic optimization algorithm to find the optimal values ​​of the three benchmark functions;

[0101] Step 4: Compare the experimental data obtained in Step 2 and Step 3. The experimental results are shown in the appendix. Figure 2-4 As shown;

[0102] Table 1 Three benchmark functions

[0103]

[0104] The engineering optimization problem example is the pressure vessel design problem described in the specification. The pressure vessel design problem is a typical engineering optimization problem, with the design objective of minimizing the material, welding, and forming costs required for the manufacture of the pressure vessel. This engineering problem involves four optimization variables: the length of the cylindrical portion of the vessel... L ( x 1) Diameter of the inner wall of the cylinder R ( x 2) Container wall thickness T s ( x 3) and the thickness of the top cover wall T h ( x 4), its mathematical model is shown in equation (19):

[0105]

[0106] The constraints are as follows:

[0107]

[0108] The specific implementation steps are as follows:

[0109] Step 1: Conduct optimization experiments using the pressure vessel design problem, inputting the constraints into the multi-strategy improved arithmetic optimization algorithm and the original arithmetic optimization algorithm;

[0110] Step 2: Use the multi-strategy improved arithmetic optimization algorithm proposed in this invention to conduct optimization experiments on the three benchmark functions and solve for the optimal value;

[0111] Step 3: Use the original arithmetic optimization algorithm to find the optimal values ​​of the three benchmark functions;

[0112] Step 4: Compare the experimental data obtained in Step 2 and Step 3. The experimental results are shown in Table 2.

[0113] Table 2. Experimental Results of Pressure Vessel Design Issues

[0114]

[0115] 2. Experimental Conclusions

[0116] The experimental results show that the multi-strategy improved arithmetic optimization algorithm proposed in this invention has higher optimization accuracy and fewer iterations, can quickly achieve the global optimum, and performs well in engineering optimization problems, proving that the multi-strategy improved arithmetic optimization algorithm proposed in this invention has good optimization effect and optimization performance.

[0117] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method of implementing engineering optimization based on a multi-strategy improved arithmetic optimization algorithm, the engineering optimization comprising: The pressure vessel design problem is characterized by comprising the following steps: S1, for the pressure vessel design problem, the optimization parameters include the cross section length of the pressure vessel cylinder part L , the inner wall diameter of the cylinder part R , the wall thickness of the cylinder part T s , the head wall thickness T l ; at this time, n=4, represent the m candidate values of the optimization parameters {L, R, Ts, Tl}, m represents the number of candidate values, is a self-defined numerical value, and the algorithm selects the optimal value from the m candidate values through multiple iterations. S2, optimization is performed by using a multi-strategy improved arithmetic optimization algorithm, comprising the following sub-steps: Step 1: in the initialization stage, an initialization population matrix is generated by the following equation: wherein, X to initialize the population matrix, represents a population individual; respectively represent the maximum and minimum values of the individual dimension, and self-defined values are used to constrain the value range of the population individual; and rand(0, 1) is a random number in [0, 1]. Step 2: set the fitness function, calculate the population individual fitness value, and obtain the initialization population optimal solution to start iteration; Step 3: calculate the mathematical optimizer acceleration function MOA, the mathematical optimizer probability function MOP, and the value of r1 improved by the sine factor, and compare r1 with the value of MOA; if r1 < MOA, the population individual enters the exploration stage, otherwise, the population individual enters the development stage; The mathematical optimizer acceleration function MOA is as follows: wherein, t is the current iteration number, T max is the maximum iteration number, MOA max and MOA min are the maximum value 1 and minimum value 0.2, respectively, of the mathematical optimizer acceleration function; Step 4: according to the golden sine strategy, the population individual entering the exploration stage is guided to update the position, and the population individual entering the development stage is guided to update the position according to the addition and subtraction strategy; Step 5: judge whether the fitness value of the updated population individual is less than the current optimal value; if yes, update the current optimal value and the optimal population individual, otherwise, do not update; Step 6: the current optimal solution is substituted into the enhanced solution mechanism ESQ of the Runge-Kutta algorithm to enhance the solution quality; Step 7: calculate the fitness value of the enhanced population individual; if it is less than the fitness value of the optimal solution before enhancement, the enhancement is successful, and the optimal solution and the optimal population individual are updated; otherwise, the enhancement fails, the optimal solution remains unchanged, and the iteration number is recorded; Step 8: if the iteration number is less than the maximum iteration number, the optimal solution obtained is substituted into step 3, and step 3 is executed; Step 9: if the iteration number is greater than or equal to the maximum iteration number, all iterations are completed, and the optimization is ended, and the global optimal value is output.

2. The method of claim 1, wherein the arithmetic optimization algorithm based on multi-strategy improvement is implemented for engineering optimization. In step 2, the fitness function is the cost function of the pressure vessel in this problem, and the optimization goal is to minimize the cost of manufacturing the pressure vessel.

3. The method of claim 1, wherein the arithmetic optimization algorithm based on multi-strategy improvement is implemented for engineering optimization. In step 3, in the exploration stage, the population update is completed by multiplication and division in basic four arithmetic operations, the individual is updated by multiplication and division, the individual motion range is increased, the individual performs global search, and the individual update formula in the exploration stage is as follows: wherein, is t the first n dimension value of the best individual in the iteration; r 2 is a random number belonging to [0, 1]; ε is the minimum constant, μ is the optimization process control constant, taking the value 0.499; ub n and lb n denotes the boundary of the individual's first n dimension value; MOP is the mathematical optimizer probability function, whose mathematical model is shown in the formula: wherein, α is the sensitivity coefficient, defining the exploration accuracy, and taking the value 5.

4. The method of claim 1, wherein the arithmetic optimization algorithm based on multi-strategy improvement is implemented for engineering optimization. In step 3, in the development stage, the population update is completed by addition and subtraction in basic four arithmetic operations, the individual is updated by addition and subtraction, the individual motion range is reduced, the individual performs local search, and the individual update formula in the development stage is as follows: wherein, r 3 is a random number belonging to [0, 1].

5. The method of claim 1, wherein the arithmetic optimization algorithm based on multi-strategy improvement is implemented for engineering optimization. In step 3, the mathematical optimizer acceleration function MOA and the r1 improved by the sine factor are compared to make the population individual enter the exploration stage in the early iteration stage and enter the development stage in the late iteration stage, thereby enhancing the global search ability in the early iteration stage and the local development ability in the late iteration stage, and the expression of the r1 improved by the sine factor is as follows: wherein t is the current iteration number, T max is the maximum iteration number.

6. The method of claim 1, wherein the arithmetic optimization algorithm based on multi-strategy improvement is implemented for engineering optimization. In step 3 and step 4, the exploration stage uses the golden sine to guide the population individual to update the position, and the expression is as follows: where, t is the current iteration number, R 1 and R 2 are random numbers in [0, 2p] and [0, p] respectively, P i t is the position of the current optimal individual, x 1 and x 2 is the golden section coefficient, used to reduce the search space and guide the individual to converge to the optimal value in space, which is defined as: wherein, a and b is a search interval, taking a value of 0.618, τ is the golden ratio.

7. The method of claim 1, wherein the arithmetic optimization algorithm based on multi-strategy improvement is implemented for engineering optimization. In step 6, the enhanced solution quality ESQ mechanism of the Runge-Kutta algorithm is used to optimize the current optimal individual generated after each iteration to enhance the optimization ability, so that the population individual can approach the optimal value more quickly; The mathematical expression is as follows: wherein, r is any one of the values 1, 0 or -1, β is a random number belonging to [0, 1], c and w is a random constant, x new1 is a new solution generated by averaging the three random numbers and the current best value.

8. The method of claim 1, wherein the arithmetic optimization algorithm based on multi-strategy improvement is implemented for engineering optimization. The engineering problem to be optimized is unmanned aerial vehicle path planning, computer vision image segmentation, or machine learning feature selection.

Images