Pressure vessel design method, device and medium based on multi-strategy improved corner exid algorithm

Abstract

The invention discloses a pressure vessel design method, device and medium based on a multi-strategy improved kenen algorithm, and relates to the technical field of pressure vessel design. The method comprises the steps that modeling is conducted on a pressure vessel design problem, the range and constraint conditions of design variables are determined, and a target function of the pressure vessel design problem is obtained with the purpose of enabling the manufacturing cost of a pressure vessel to be minimum under the constraint conditions; multi-strategy improvement is carried out on the original angle ski algorithm to obtain an angle ski algorithm based on multi-strategy improvement; and solving the target function based on a multi-strategy improved angle exendin optimization algorithm to obtain an optimal solution of the pressure vessel design. According to the method, a hybrid strategy method is adopted to improve the Kerr's algorithm, better design parameters can be obtained, and the design cost of the pressure vessel is effectively reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of pressure vessel design, and more specifically, to a pressure vessel design method, device and medium based on a multi-strategy improved horned lizard algorithm. Background Art

[0002] Pressure vessel design is one of the engineering design problems. Its essence is an optimization problem, which aims to reduce the design cost of pressure vessels. It has a large number of local optimal points and has multi-constraint and nonlinear characteristics. Existing algorithms to solve this problem include Grey Wolf Optimization (GWO) and Sine Cosine Algorithm (SCA), but the design solutions obtained by the optimization of the above algorithms need to be further optimized.

[0003] The Horned Lizard Optimization Algorithm (HLOA) is a novel swarm intelligence optimization algorithm proposed in 2024. It is inspired by the hiding, blood spraying, and escape behaviors of horned lizards. Compared with other intelligent optimization algorithms, HLOA has three major characteristics: first, the algorithm is easy to implement; second, it has a high convergence speed; third, it is applicable to multiple optimization problems with different characteristics. However, like other swarm intelligence optimization algorithms, it has the defect of being easily trapped in the local optimum in the later stage of optimization, and it is difficult to adapt to various complex optimization problems. Summary of the invention

[0004] In view of the technical problems that the production cost of the pressure vessel is high and the original horned lizard algorithm (HLOA) is prone to fall into the local optimal solution, the present invention provides a pressure vessel design method, device and medium based on a multi-strategy improved horned lizard algorithm. The horned lizard algorithm is improved by a mixed strategy method, which can obtain better design parameters and effectively reduce the design cost of the pressure vessel.

[0005] In a first aspect, the present invention provides a pressure vessel design method based on a multi-strategy improved horned lizard algorithm, the method comprising:

[0006] Model the pressure vessel design problem, determine the range of design variables and constraints, take minimizing the pressure vessel manufacturing cost under the constraints as the goal, and obtain the objective function of the pressure vessel design problem;

[0007] The original horned lizard algorithm is improved by multiple strategies to obtain the horned lizard algorithm based on multiple strategies;

[0008] The objective function is solved based on the multi-strategy improved horned lizard optimization algorithm to obtain the optimal solution for the pressure vessel design;

[0009] The original horned lizard algorithm is improved by multiple strategies to obtain the horned lizard algorithm based on multiple strategies, including:

[0010] The population is initialized using a fusion strategy of cubic chaos mapping and refraction reverse learning;

[0011] The water wave dynamic adaptive factor is added to the position update formula of the blood-shot horned lizard, and the search step size and direction are adjusted using the uncertainty of water wave dynamic changes.

[0012] Incorporating Brownian motion and Lévy flight strategy into the position update formula for horned lizards’ escape behavior;

[0013] After the position of the horned lizard is updated, the position of the population is perturbed using the adaptive t distribution, and the dynamic selection probability p is used to adjust the use of the adaptive t distribution mutation operator.

[0014] Furthermore, the pressure vessel design problem is modeled, the range of design variables and constraints are determined, and the objective is to minimize the pressure vessel manufacturing cost under the constraints. The objective function of the pressure vessel design problem is obtained, including:

[0015] Determine the mathematical model of the pressure vessel, expressed as:

[0016] X=[T s ,T h ,R,L]=[x 1 ,x 2 ,x 3 ,x 4 ]

[0017] In the formula, X represents a set of design solutions consisting of four design variables, T s Indicates the container wall thickness, T h represents the thickness of the head, R represents the inner radius, L represents the length of the container, and x 1 、x 2 、x 3 and x 4 represents the design variables for the pressure vessel design;

[0018] The objective function of pressure vessel design is set as:

[0019]

[0020] Where f(x) represents the objective function;

[0021] The constraints of the mathematical model of the pressure vessel are g 1 (x)~g 4 (x), expressed as:

[0022] g 1 (x) = -x 1+0.0193x 3 ≤0;

[0023] g 2 (x) = -x 2 +0.00954x 3 ≤0;

[0024]

[0025] g 4 (x) = x 4 -240≤0;

[0026] In the formula, g 1 (x) indicates that the wall thickness of the vessel is at least 0.0193 times the inner radius of the vessel, thereby ensuring that the wall thickness of the pressure vessel is large enough to withstand the pressure inside the vessel;

[0027] g 2 (x) indicates that the thickness of the head is at least 0.00954 times the inner radius of the vessel, thereby ensuring that the wall thickness of the head of the pressure vessel is large enough to withstand the pressure at the head of the vessel;

[0028] g 3 (x) indicates that the overall volume of the pressure vessel must be greater than the limit value of 1296000mm 3 ;

[0029] g 4 (x) indicates that the length of the pressure vessel shall not exceed the limit value of 240 mm.

[0030] The value ranges of the four variables are:

[0031] 0mm≤x 1 ≤100mm,0mm≤x 2 ≤100mm,10mm≤x 3 ≤200mm,10mm≤x 4 ≤200mm.

[0032] Furthermore, the population is initialized using a cubic chaos map and refraction reverse learning fusion strategy, including:

[0033] The cubic chaotic sequence is mapped to the horned lizard individuals. The reverse solution population of the population after cubic chaotic mapping is solved through the refraction reverse learning mechanism. The cubic chaotic mapping population and the reverse solution population are merged and sorted according to their fitness values. The horned lizard individuals with the top N fitness values ​​are selected as the initial population. The calculation process is expressed as:

[0034]

[0035] In the formula, y iis the cubic chaotic sequence at the i-th iteration; y i+1 is the cubic chaotic sequence at the i+1th iteration; x ub and x lb are the upper and lower bounds of the search space respectively; x i,j represents the population of forward solutions after cubic chaos mapping; For x i,j The refraction reverse solution population; a j and b j are the minimum and maximum values ​​of the j-th dimension in the search space respectively; k is the scaling factor.

[0036] Furthermore, the water wave dynamic adaptive factor is expressed as:

[0037] λ=1-sin(πt / 2T+2π)

[0038] Where λ is the water wave dynamic adaptive factor, t is the current iteration number, and T is the maximum iteration number.

[0039] Furthermore, Brownian motion and Levy flight strategy are incorporated into the position update formula of the horned lizard's escape behavior.

[0040] The step length formula for standard Brownian motion is:

[0041]

[0042] In the formula, randn represents a random number that obeys the standard normal distribution; Represents the time step.

[0043] The step length formula of Levy flight is:

[0044] levy=x / |y| 1 / β

[0045] Where: β is a constant; x and y are two normally distributed variables.

[0046] The reference point position update formula that incorporates Brownian motion and Levy flight is:

[0047]

[0048] In the formula, x best (t) is the optimal horned lizard position found at the tth iteration; x i (t) is the position of the i-th horned lizard at the t-th iteration; walk is a random number generated between -1 and 1; ε is a random number following the Cauchy distribution; t is the current iteration number; T is the maximum iteration number; x i (t+1) is the position of the i-th horned lizard at the t+1th iteration.

[0049] Furthermore, after the position of the horned lizard is updated, the position of the population is disturbed by using the adaptive t distribution, and the calculation process of using the dynamic selection probability p to adjust the use of the adaptive t distribution mutation operator is expressed as:

[0050]

[0051] Where t(iter) is the adaptive t distribution function with the number of population iterations as the degree of freedom parameter; w 1 Determines the upper limit of the dynamic selection probability; w 2 Determines the change range of dynamic selection probability; p is the dynamic selection probability.

[0052] Furthermore, the objective function is solved based on the multi-strategy improved horned lizard optimization algorithm to obtain the optimal solution for the pressure vessel design, including:

[0053] The population of horned lizards was initialized by using cubic chaotic mapping and refraction reverse learning fusion strategy;

[0054] The objective function of the pressure vessel design is used as the fitness function to determine the locations of hiding, ejecting, and escaping horned lizards;

[0055] Check whether the range of the updated solution exceeds the value range of the design variable, and if so, replace the solution that exceeds the range with the boundary value of the design variable;

[0056] Determine whether the current number of iterations t is less than the maximum number of iterations T. If so, continue to use the objective function of the pressure vessel design as the fitness function to determine the positions of the hidden, ejected, and escaped horned lizards. Otherwise, output the minimum value of the objective function as the minimum design cost of the pressure vessel, and the currently found solution is used as the optimal pressure vessel design solution.

[0057] Furthermore, the objective function of the pressure vessel design is used as the fitness function to determine the positions of hiding, ejecting, and escaping horned lizards, including:

[0058] Update the hidden horned lizard position using the following formula:

[0059]

[0060] In the formula, δ is a constant, c 1 and c 2 are all random numbers drawn from a standardized palette, and c 1 ≠c 2 , σ is a random binary value, r 1 、r 2 、r 3 and r 4 is a random integer generated between 1 and the maximum population size N, and r 1≠r 2 ≠r 3 ≠r 4 , x r1 (t), x r2 (t), x r3 (t) and x r4 (t) is the selected rth 1 、r 2 、r 3 and r 4 Horned lizard;

[0061] Update the position of the bloodshot horned lizard using the following formula:

[0062] x i (t+1)=[v 0 cos(αt / T)+ξ]x best (t)+λ·[v 0 sin(α-αt / T)-g+ξ]x i (t)

[0063] In the formula, v 0 is the initial velocity, α is the angle parameter, λ is the water wave dynamic adaptive factor, ξ is a constant used to avoid division by zero, and g is the earth's gravitational acceleration;

[0064] Update the position of the escaping horned lizard using the following formula:

[0065]

[0066] Where walk is a random number generated between -1 and 1, and ε is a random number following the Cauchy distribution.

[0067] In a second aspect, the present invention provides a pressure vessel design device based on a multi-strategy improved horned lizard algorithm, the device comprising:

[0068] An objective function determination unit is configured to model the pressure vessel design problem, determine the range of design variables and constraints, take minimizing the pressure vessel manufacturing cost under the constraints as the goal, and obtain an objective function of the pressure vessel design problem;

[0069] The horned lizard algorithm improvement unit is configured to initialize the population using cubic chaos mapping and refraction reverse learning fusion strategy; add water wave dynamic adaptive factors to the position update formula of the blood-shot horned lizard, and use the uncertainty of water wave dynamic changes to adjust the search step size and direction; integrate Brownian motion and Levy flight strategy into the position update formula of the horned lizard's escape behavior; after the horned lizard's position is updated, the position of the population is disturbed using adaptive t distribution, and the dynamic selection probability p is used to adjust the use of the adaptive t distribution mutation operator;

[0070] The objective function solving unit is configured to solve the objective function based on the multi-strategy improved horned lizard optimization algorithm to obtain the optimal solution for the pressure vessel design.

[0071] In a third aspect, the present invention provides a readable storage medium, wherein the readable storage medium stores one or more programs, and the one or more programs can be executed by one or more processors to implement the method as described above.

[0072] The present invention has at least the following beneficial effects:

[0073] The present invention makes up for the shortcoming that the original horned lizard algorithm (HLOA) is prone to fall into local optimum in the late stage of optimization, and applies the improved algorithm to the pressure vessel design optimization problem, which greatly reduces the design cost of the pressure vessel. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 A flow chart of a pressure vessel design method based on a multi-strategy improved horned lizard algorithm according to an embodiment of the present invention is shown.

[0075] Figure 2 A schematic diagram of the structure of a pressure vessel provided in an embodiment of the present invention.

[0076] Figure 3 The improved horned lizard algorithm proposed in this invention is compared with other optimization algorithms in F 1 Convergence comparison diagram on functions;

[0077] Figure 4 The improved horned lizard algorithm proposed in this invention is compared with other optimization algorithms in F 2 Convergence comparison diagram on functions;

[0078] Figure 5 The improved horned lizard algorithm proposed in this invention is compared with other optimization algorithms in F 3 Convergence comparison diagram on functions;

[0079] Figure 6 The improved horned lizard algorithm proposed in this invention is compared with other optimization algorithms in F 4 Convergence comparison diagram on functions;

[0080] Figure 7 A structural diagram of a pressure vessel design device based on a multi-strategy improved horned lizard algorithm according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0081] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings and specific embodiments, but are not intended to limit the present invention. For the various steps described herein, if there is no necessity for a causal relationship between each other, the order in which they are described as examples herein should not be regarded as a limitation, and those skilled in the art should know that they can be adjusted in order, as long as the logic between them is not destroyed, resulting in the inability to implement the entire process.

[0082] The embodiment of the present invention provides a pressure vessel design method based on a multi-strategy improved horned lizard algorithm, such as Figure 1 FIG. 1 is a flow chart of a pressure vessel design method based on a multi-strategy improved horned lizard algorithm. The pressure vessel design method based on a multi-strategy improved horned lizard algorithm includes steps S10 to S30, which are described in detail as follows.

[0083] S10: Model the pressure vessel design problem, determine the range of design variables and constraints, take minimizing the pressure vessel manufacturing cost under the constraints as the goal, and obtain the objective function of the pressure vessel design problem;.

[0084] In some embodiments, see Figure 2 , is a schematic diagram of the pressure vessel structure. The mathematical model of the pressure vessel is defined as: X = [T s ,T h ,R,L]=[x 1 ,x 2 ,x 3 ,x 4 ], where the pressure vessel includes four parameters: the thickness of the vessel wall T s , Head thickness T h , inner radius R and container length L (excluding the head), where T s and T h is an integer multiple of 0.0625, and R and L are continuous variables. Both ends of the pressure vessel are capped with lids, and the cap at the head end is hemispherical. These four parameters are used as design variables for pressure vessel design, such as Figure 2 As shown, denoted by x 1 ,x 2 ,x 3 ,x 4 ; X represents a set of design schemes consisting of four design variables.

[0085] The objective function of pressure vessel design is set as:

[0086]

[0087] Where f(x) represents the objective function;

[0088] The constraints of the mathematical model of the pressure vessel are g 1 (x)~g 4 (x), expressed as:

[0089] g 1 (x) = -x 1 +0.0193x 3 ≤0;

[0090] g 2 (x) = -x 2 +0.00954x 3 ≤0;

[0091]

[0092] g 4 (x) = x 4 -240≤0;

[0093] In the formula, g 1 (x) indicates that the wall thickness of the vessel is at least 0.0193 times the inner radius of the vessel, thereby ensuring that the wall thickness of the pressure vessel is large enough to withstand the pressure inside the vessel;

[0094] g 2 (x) indicates that the thickness of the head is at least 0.00954 times the inner radius of the vessel, thereby ensuring that the wall thickness of the head of the pressure vessel is large enough to withstand the pressure at the head of the vessel;

[0095] g 3 (x) indicates that the overall volume of the pressure vessel must be greater than the limit value of 1296000mm 3 ;

[0096] g 4 (x) indicates that the length of the pressure vessel shall not exceed the limit value of 240 mm.

[0097] The value ranges of the four variables are:

[0098] 0mm≤x 1 ≤100mm,0mm≤x 2 ≤100mm,10mm≤x 3 ≤200mm,10mm≤x 4 ≤200mm.

[0099] S20: Perform multi-strategy improvements on the original horned lizard algorithm to obtain a horned lizard algorithm based on multi-strategy improvements.

[0100] Specifically, step S20 is implemented by the following steps S21 to S24.

[0101] S21. Initialize the population using cubic chaos mapping and refraction reverse learning fusion strategy.

[0102] In this embodiment, a cubic chaos map and refraction reverse learning fusion strategy is used to initialize the population. This strategy combines the ergodicity of the cubic chaos map and the diversity of the refraction reverse learning mechanism, increases the diversity of the initial population, and improves the global search capability of the optimization algorithm. When there are more local optimal solutions, it is easier to search for the global optimal solution.

[0103] In some embodiments, the specific process of initializing the population by the cubic chaos mapping and refraction reverse learning fusion strategy is: first, the cubic chaos sequence is mapped to the horned lizard individuals, then the reverse solution population of the population after the cubic chaos mapping is solved through the refraction reverse learning mechanism, and finally the cubic chaos mapping population and the reverse solution population are merged, sorted according to their fitness values, and the first N horned lizard individuals with better fitness values ​​are selected as the initial population. Its mathematical model is:

[0104]

[0105] In the formula, y i is the cubic chaotic sequence at the i-th iteration; y i+1 is the cubic chaotic sequence at the i+1th iteration; x ub and x lb are the upper and lower bounds of the search space respectively; x i,j represents the population of forward solutions after cubic chaos mapping; For x i,j The refraction reverse solution population; a j and b j are the minimum and maximum values ​​of the j-th dimension in the search space respectively; k is the scaling factor.

[0106] S22. Add a water wave dynamic adaptive factor to the position update formula of the blood-shot horned lizard, and use the uncertainty of the dynamic changes of the water waves to adjust the search step size and direction.

[0107] In this embodiment, a water wave dynamic adaptive factor is added to the position update formula of the blood-throwing horned lizard, and the uncertainty of the dynamic changes of water waves is used to adjust the search step size and direction, thereby improving the ability of the algorithm to jump out of the local optimum.

[0108] In some embodiments, the water wave dynamic adaptive factor λ is introduced into the position update formula of the blood-jetting horned lizard, and its mathematical model is:

[0109] λ=1-sin(πt / 2T+2π)

[0110] Among them, t is the current iteration number; T is the maximum iteration number.

[0111] S23. Incorporate Brownian motion and Levy flight strategy into the position update formula of the horned lizard's escape behavior.

[0112] In this embodiment, Brownian motion and Levy flight strategy are integrated into the position update formula of the horned lizard's escape behavior, which not only balances the need for optimization, but also improves the algorithm's ability to escape from the local optimum.

[0113] In some embodiments, Brownian motion and Levy flight strategy are incorporated into the position update formula of the horned lizard's escape behavior.

[0114] The step length formula for standard Brownian motion is:

[0115]

[0116] In the formula, randn represents a random number that obeys the standard normal distribution; Represents the time step.

[0117] The step length formula of Levy flight is:

[0118] levy=x / |y| 1 / β

[0119] Where: β is usually taken as 1.5; x and y are two normally distributed variables.

[0120] The reference point position update formula that incorporates Brownian motion and Levy flight is:

[0121]

[0122] Among them, x best (t) is the optimal horned lizard position found at the tth iteration; x i (t) is the position of the i-th horned lizard at the t-th iteration; walk is a random number generated between -1 and 1; ε is a random number following the Cauchy distribution.

[0123] S24. After the position of the horned lizard is updated, the position of the population is disturbed using the adaptive t distribution, and the dynamic selection probability p is used to adjust the use of the adaptive t distribution mutation operator.

[0124] In this embodiment, after the position of the horned lizard is updated, the position of the population is disturbed using an adaptive t distribution. At the same time, in order to avoid indiscriminate use of all individuals in each iteration, a dynamic selection probability p is used to adjust the use of the adaptive t distribution mutation operator, thereby reducing the calculation time of the algorithm and improving the convergence speed of the algorithm.

[0125] In some embodiments, the position of the population is disturbed by using an adaptive t distribution and a dynamic selection strategy, and the dynamic selection probability p is selected to adjust the use of the adaptive t distribution mutation operator, and its mathematical model is:

[0126]

[0127] Among them, t(iter) is the adaptive t distribution function with the number of population iterations as the degree of freedom parameter; w 1 Determines the upper limit of the dynamic selection probability; w 2 Determines the magnitude of change in the dynamic selection probability.

[0128] In order to prove the effectiveness of the improved horned lizard algorithm (IHLOA), four benchmark functions are used to conduct optimization experiments. The parameters of the four benchmark functions are shown in Table 1. The experimental results are compared with the grey wolf algorithm (GWO), the sine-cosine algorithm (SCA) and the original horned lizard algorithm (HLOA). Figure 3-Figure 6 shown.

[0129] Table 1 Four benchmark functions

[0130]

[0131] S30: Solving the objective function based on the multi-strategy improved horned lizard optimization algorithm to obtain the optimal solution for the pressure vessel design.

[0132] In some embodiments, step S30 is implemented by the following steps S31 to S34.

[0133] S31: The population is initialized by using cubic chaos mapping and refraction reverse learning fusion strategy to initialize the population of horned lizards so that the population distribution is uniform, which provides conditions for later optimization and escaping from local optimality;

[0134] S32: Using the objective function of the pressure vessel design as the fitness function, determine the positions of the hiding, ejecting, and escaping horned lizards.

[0135] In this embodiment, the formula for updating the position of the hidden horned lizard is as follows:

[0136]

[0137] Among them, δ is a constant with a value of 2, c 1 、c 2 is a random number drawn from a standardized palette, and c 1 ≠c 2 , σ is a random binary value, r 1 , r 2 , r 3 and r 4 is a random integer generated between 1 and the maximum population size N, and r 1 ≠r 2 ≠r 3 ≠r4 , x r1 (t), x r2 (t), x r3 (t) and x r4 (t) is the selected rth 1 、r 2 、r 3 、r 4 A horned lizard.

[0138] The formula for updating the position of the bloodshot horned lizard is as follows:

[0139] x i (t+1)=[v 0 cos(αt / T)+ξ]x best (t)+λ·[v 0 sin(α-αt / T)-g+ξ]x i (t)

[0140] Among them, v 0 is the initial velocity, which is 1, α is the angle parameter, which is π / 2, λ is the water wave dynamic adaptive factor, and ξ is used to avoid division by zero or very small numerical calculation problems, which is 1×10 -6 , g is the earth's gravitational acceleration, set to 9.8m / s 2 .

[0141] The formula for updating the position of the fleeing horned lizard is as follows:

[0142]

[0143] Where walk is a random number generated between -1 and 1, and ε is a random number following the Cauchy distribution.

[0144] S33: Check whether the range of the updated solution exceeds the value range of the design variable. If so, replace the solution that exceeds the range with the boundary value of the design variable.

[0145] S34: Determine whether the current number of iterations t is less than the maximum number of iterations T. If so, return to step 3.2; otherwise, output the minimum value of the objective function as the minimum design cost of the pressure vessel, and the currently found solution is used as the optimal pressure vessel design solution.

[0146] Exemplarily, the process of solving the objective function based on the multi-strategy improved horned lizard optimization algorithm is as follows:

[0147] Input: horned lizard population size N, maximum number of iterations T;

[0148] Output: optimal solution x best (t), the optimal fitness value f(x best );

[0149] 1. Initialize the horned lizard population using cubic chaos mapping and refraction reverse learning mechanism;

[0150] 2. t = 1;

[0151] 3. whilet <T;

[0152] 4. Randomly generate a number between 0 and 1

[0153] 5.

[0154] 6. Update the position according to the hidden horned lizard position update formula;

[0155] 7.else;

[0156] 8.if(mod(t,2));

[0157] 9. Update the position according to the bloodshot horned lizard position update formula;

[0158] 10.else;

[0159] 11. Update the position according to the escaped horned lizard position update formula;

[0160] 12.end if;

[0161] 13.end if;

[0162] 14.for i=1:N;

[0163] 15. Use adaptive t distribution and dynamic selection strategy to perturb the location of horned lizard population;

[0164] 16.end for;

[0165] 17. Compare the fitness value of the current optimal position with the fitness value of the global optimal position. If the current new position is better than the original optimal position, retain this position to form a new global optimal position.

[0166] 18.t=t+1;

[0167] 19.end while.

[0168] In this embodiment, a simulation experiment of the method is carried out with the help of MATLAB under the Intel(R)Core(TM)i5-11320H CPU 3.20GHz and 16.00GB memory, and Windows11 operating environment. The experimental results show that the method results of this embodiment are better than the experimental results of other algorithms.

[0169] In this embodiment, the multi-strategy improved horned lizard optimization algorithm (IHLOA) is used to perform the minimum cost design of the pressure vessel, and the design effect is compared with the gray wolf algorithm (GWO), the sine-cosine algorithm (SCA), and the original horned lizard algorithm (HLOA). The data results are shown in Table 2, where the best optimal solution, optimal value, average value and standard deviation of all algorithms are bolded.

[0170] In this embodiment, each parameter is set to a population size of 30, a maximum number of iterations of 1000, the program is repeated 50 times, and the output results are shown in Table 2. From the results in Table 2, the pressure vessel design method based on the multi-strategy improved horned lizard optimization algorithm (IHLOA) can obtain the best optimal value among all methods, and each design variable can obtain the optimal solution, which shows that this embodiment can reduce the design cost of the pressure vessel in actual design. Moreover, compared with other algorithms, IHLOA has the best average value and the smallest standard deviation, which proves that this embodiment has better robustness.

[0171] Table 2 Optimization results and comparison table of pressure vessel design problems

[0172]

[0173] The embodiment of the present invention also provides a pressure vessel design device based on the multi-strategy improved horned lizard algorithm, such as Figure 7 As shown, the device comprises:

[0174] The objective function determination unit 701 is configured to model the pressure vessel design problem, determine the range of design variables and constraints, take minimizing the pressure vessel manufacturing cost under the constraints as the goal, and obtain the objective function of the pressure vessel design problem;

[0175] The horned lizard algorithm improvement unit 702 is configured to initialize the population by using cubic chaos mapping and refraction reverse learning fusion strategy; add water wave dynamic adaptive factor to the position update formula of the blood-shot horned lizard, and adjust the search step size and direction by using the uncertainty of the dynamic change of water waves; integrate Brownian motion and Levy flight strategy into the position update formula of the horned lizard's escape behavior; after the horned lizard's position is updated, use adaptive t distribution to perturb the position of the population, and use dynamic selection probability p to adjust the use of adaptive t distribution mutation operator;

[0176] The objective function solving unit 703 is configured to solve the objective function based on the multi-strategy improved horned lizard optimization algorithm to obtain the optimal solution for the pressure vessel design.

[0177] In some embodiments, the objective function determination unit is further configured to:

[0178] Determine the mathematical model of the pressure vessel, expressed as:

[0179] X=[T s ,T h ,R,L]=[x 1 ,x 2 ,x 3 ,x 4 ]

[0180] In the formula, X represents a set of design solutions consisting of four design variables, T s Indicates the container wall thickness, T h represents the thickness of the head, R represents the inner radius, L represents the length of the container, and x 1 、x 2 、x 3 and x 4 represents the design variables for the pressure vessel design;

[0181] The objective function of pressure vessel design is set as:

[0182]

[0183] Where f(x) represents the objective function;

[0184] The constraints of the mathematical model of the pressure vessel are g 1 (x)~g 4 (x), expressed as:

[0185] g 1 (x) = -x 1 +0.0193x 3 ≤0;

[0186] g 2 (x) = -x 2 +0.00954x 3 ≤0;

[0187]

[0188] g 4 (x) = x 4 -240≤0;

[0189] In the formula, g 1 (x) indicates that the wall thickness of the vessel is at least 0.0193 times the inner radius of the vessel, thereby ensuring that the wall thickness of the pressure vessel is large enough to withstand the pressure inside the vessel;

[0190] g 2 (x) indicates that the thickness of the head is at least 0.00954 times the inner radius of the vessel, thereby ensuring that the wall thickness of the head of the pressure vessel is large enough to withstand the pressure at the head of the vessel;

[0191] g 3(x) indicates that the overall volume of the pressure vessel must be greater than the limit value of 1296000mm 3 ;

[0192] g 4 (x) indicates that the length of the pressure vessel shall not exceed the limit value of 240 mm.

[0193] The value ranges of the four variables are:

[0194] 0mm≤x 1 ≤100mm,0mm≤x 2 ≤100mm,10mm≤x 3 ≤200mm,10mm≤x 4 ≤200mm.

[0195] In some embodiments, the horned lizard algorithm improvement unit is further configured to:

[0196] The cubic chaotic sequence is mapped to the horned lizard individuals. The reverse solution population of the population after cubic chaotic mapping is solved through the refraction reverse learning mechanism. The cubic chaotic mapping population and the reverse solution population are merged and sorted according to their fitness values. The horned lizard individuals with the top N fitness values ​​are selected as the initial population. The calculation process is expressed as:

[0197]

[0198] In the formula, y i is the cubic chaotic sequence at the i-th iteration; y i+1 is the cubic chaotic sequence at the i+1th iteration; x ub and x lb are the upper and lower bounds of the search space respectively; x i,j represents the population of forward solutions after cubic chaos mapping; For x i,j The refraction reverse solution population; a j and b j are the minimum and maximum values ​​of the j-th dimension in the search space respectively; k is the scaling factor.

[0199] In some embodiments, the water wave dynamic adaptive factor is expressed as:

[0200] λ=1-sin(πt / 2T+2π)

[0201] Where λ is the water wave dynamic adaptive factor, t is the current iteration number, and T is the maximum iteration number.

[0202] In some embodiments, the horned lizard algorithm improvement unit is further configured to incorporate Brownian motion and Levy flight strategy into the position update formula of the horned lizard's escape behavior.

[0203] The step length formula for standard Brownian motion is:

[0204]

[0205] In the formula, randn represents a random number that obeys the standard normal distribution; Represents the time step.

[0206] The step length formula of Levy flight is:

[0207] levy=x / |y| 1 / β

[0208] Where: β is usually taken as 1.5; x and y are two normally distributed variables.

[0209] The reference point position update formula that incorporates Brownian motion and Levy flight is:

[0210]

[0211] In the formula, x best (t) is the optimal horned lizard position found at the tth iteration; x i (t) is the position of the i-th horned lizard at the t-th iteration; walk is a random number generated between -1 and 1; ε is a random number following the Cauchy distribution; t is the current iteration number; T is the maximum iteration number; x i (t+1) is the position of the i-th horned lizard at the t+1th iteration.

[0212] In some embodiments, the horned lizard algorithm improvement unit is further configured to use adaptive t distribution to perturb the position of the population after the position of the horned lizard is updated, and the calculation process of using the dynamic selection probability p to adjust the use of the adaptive t distribution mutation operator is expressed as:

[0213]

[0214] Where t(iter) is the adaptive t distribution function with the number of population iterations as the degree of freedom parameter; w 1 Determines the upper limit of the dynamic selection probability; w 2 Determines the change range of dynamic selection probability; p is the dynamic selection probability.

[0215] In some embodiments, the objective function solving unit is further configured to:

[0216] The population of horned lizards was initialized by using cubic chaotic mapping and refraction reverse learning fusion strategy;

[0217] The objective function of the pressure vessel design is used as the fitness function to determine the locations of hiding, ejecting, and escaping horned lizards;

[0218] Check whether the range of the updated solution exceeds the value range of the design variable, and if so, replace the solution that exceeds the range with the boundary value of the design variable;

[0219] Determine whether the current number of iterations t is less than the maximum number of iterations T. If so, continue to use the objective function of the pressure vessel design as the fitness function to determine the positions of the hidden, ejected, and escaped horned lizards. Otherwise, output the minimum value of the objective function as the minimum design cost of the pressure vessel, and the currently found solution is used as the optimal pressure vessel design solution.

[0220] In some embodiments, the objective function solving unit is further configured to:

[0221] Update the hidden horned lizard position using the following formula:

[0222]

[0223] In the formula, δ is a constant with a value of 2, c 1 and c 2 are all random numbers drawn from a standardized palette, and c 1 ≠c 2 , σ is a random binary value, r 1 、r 2 、r 3 and r 4 is a random integer generated between 1 and the maximum population size N, and r 1 ≠r 2 ≠r 3 ≠r 4 , x r1 (t), x r2 (t), x r3 (t) and x r4 (t) is the selected rth 1 、r 2 、r 3 and r 4 Horned lizard;

[0224] Update the position of the bloodshot horned lizard using the following formula:

[0225] x i (t+1)=[v 0 cos(αt / T)+ξ]x best (t)+λ·[v 0 sin(α-αt / T)-g+ξ]x i (t)

[0226] In the formula, v 0is the initial velocity, α is the angle parameter, λ is the water wave dynamic adaptive factor, and ξ is used to avoid division by zero or very small numerical calculation problems, and its value is 1×10 -6 , g is the acceleration of gravity of the earth;

[0227] Update the position of the escaping horned lizard using the following formula:

[0228]

[0229] Where walk is a random number generated between -1 and 1, and ε is a random number following the Cauchy distribution.

[0230] It should be noted that the structures of the pressure vessel design devices based on the multi-strategy improved horned lizard algorithm described in this embodiment belong to the same technical concept as the pressure vessel design method based on the multi-strategy improved horned lizard algorithm described previously, and achieve the same beneficial effects through the same principles, which will not be repeated here.

[0231] An embodiment of the present invention further provides a readable storage medium, which stores one or more programs. The one or more programs can be executed by one or more processors to implement the method described in any of the above embodiments.

[0232] In addition, although exemplary embodiments have been described herein, the scope includes any and all embodiments based on the present invention with equivalent elements, modifications, omissions, combinations (e.g., various embodiments intersecting schemes), adaptations or changes. The elements in the claims will be interpreted broadly based on the language adopted in the claims, and are not limited to the examples described in this specification or during the implementation of this application, and the examples will be interpreted as non-exclusive. Therefore, this specification and examples are intended to be considered as examples only, and the true scope and spirit are indicated by the following claims and the full scope of their equivalents.

[0233] The above description is intended to be illustrative rather than restrictive. For example, the above examples (or one or more of them) can be used in combination with each other. For example, those of ordinary skill in the art can use other embodiments when reading the above description. In addition, in the above-mentioned specific embodiments, various features can be grouped together to simplify the present invention. This should not be interpreted as a feature of an invention that is not claimed for protection being necessary for any claim. On the contrary, the subject matter of the present invention may be less than all the features of the embodiments of a specific invention. Thus, the following claims are incorporated into the specific embodiments as examples or embodiments, wherein each claim is independently used as a separate embodiment, and it is considered that these embodiments can be combined with each other in various combinations or arrangements. The scope of the present invention should be determined with reference to the full scope of the equivalent forms of the attached claims and these claims.

Claims

1. A pressure vessel design method based on a multi-strategy improved horned lizard algorithm, characterized in that: The method comprises: Model the pressure vessel design problem, determine the range of design variables and constraints, take minimizing the pressure vessel manufacturing cost under the constraints as the goal, and obtain the objective function of the pressure vessel design problem; The original horned lizard algorithm is improved by multiple strategies to obtain the horned lizard algorithm based on multiple strategies; The objective function is solved based on the multi-strategy improved horned lizard optimization algorithm to obtain the optimal solution for the pressure vessel design; The original horned lizard algorithm is improved by multiple strategies to obtain the horned lizard algorithm based on multiple strategies, including: The population is initialized using a fusion strategy of cubic chaos mapping and refraction reverse learning; The water wave dynamic adaptive factor is added to the position update formula of the blood-shot horned lizard, and the search step size and direction are adjusted using the uncertainty of water wave dynamic changes. Incorporating Brownian motion and Lévy flight strategy into the position update formula for horned lizards’ escape behavior; After the position of the horned lizard is updated, the position of the population is perturbed using the adaptive t distribution, and the dynamic selection probability p is used to adjust the use of the adaptive t distribution mutation operator.

2. The pressure vessel design method based on the multi-strategy improved horned lizard algorithm according to claim 1 is characterized in that: The pressure vessel design problem is modeled, the range of design variables and constraints are determined, and the goal is to minimize the pressure vessel manufacturing cost under the constraints. The objective function of the pressure vessel design problem is obtained, including: Determine the mathematical model of the pressure vessel, expressed as: X=[T s ,T h ,R,L]=[x1,x2,x3,x4] In the formula, X represents a set of design solutions consisting of four design variables, T s Indicates the container wall thickness, T h represents the thickness of the head, R represents the inner radius, L represents the length of the vessel, and x1, x2, x3 and x4 represent the design variables of the pressure vessel design; The objective function of pressure vessel design is set as: Where f(x) represents the objective function; The constraints of the mathematical model of the pressure vessel are g1(x)~g4(x), expressed as: g1(x)=-x1+0.0193x3≤0; g2(x)=-x2+0.00954x3≤0; g4(x)=x4-240≤0; In the formula, g1(x) means that the thickness of the container wall is at least 0.0193 times the inner radius of the container, thus ensuring that the wall thickness of the pressure vessel is large enough to withstand the pressure inside the container; g2(x) indicates that the thickness of the head is at least 0.00954 times the inner radius of the vessel, thereby ensuring that the wall thickness of the head of the pressure vessel is large enough to withstand the pressure at the head of the vessel; g3(x) indicates that the overall volume of the pressure vessel must be greater than the limit value of 1296000mm 3 ; g4(x) means that the length of the pressure vessel shall not exceed the limit value of 240mm. The value ranges of the four variables are: 0mm≤x1≤100mm,0mm≤x2≤100mm,10mm≤x3≤200mm,10mm≤x4≤200mm.

3. The pressure vessel design method based on the multi-strategy improved horned lizard algorithm according to claim 1 is characterized in that: The population is initialized using cubic chaos mapping and refraction reverse learning fusion strategy, including: The cubic chaotic sequence is mapped to the horned lizard individuals. The reverse solution population of the population after cubic chaotic mapping is solved through the refraction reverse learning mechanism. The cubic chaotic mapping population and the reverse solution population are merged and sorted according to their fitness values. The horned lizard individuals with the top N fitness values ​​are selected as the initial population. The calculation process is expressed as: In the formula, y i is the cubic chaotic sequence at the i-th iteration; y i+1 is the cubic chaotic sequence at the i+1th iteration; x ub and x lb are the upper and lower bounds of the search space respectively; x i,j represents the population of forward solutions after cubic chaos mapping; For x i,j The refraction reverse solution population; a j and b j are the minimum and maximum values ​​of the j-th dimension in the search space respectively; k is the scaling factor.

4. The pressure vessel design method based on the multi-strategy improved horned lizard algorithm according to claim 3 is characterized in that: The water wave dynamic adaptive factor is expressed as: λ=1-sin(πt / 2T+2π) Where λ is the water wave dynamic adaptive factor, t is the current iteration number, and T is the maximum iteration number.

5. The pressure vessel design method based on the multi-strategy improved horned lizard algorithm according to claim 3 is characterized in that: Incorporating Brownian motion and Lévy flight strategy into the position update formula for the escape behavior of horned lizards. The step length formula for standard Brownian motion is: In the formula, randn represents a random number that obeys the standard normal distribution; Represents the time step. The step length formula of Levy flight is: levy=x / y 1β Where: β is a constant; x and y are two normally distributed variables. The reference point position update formula that incorporates Brownian motion and Levy flight is: In the formula, x best (t) is the optimal horned lizard position found at the tth iteration; x i (t) is the position of the i-th horned lizard at the t-th iteration; walk is a random number generated between -1 and 1; ε is a random number following the Cauchy distribution; t is the current iteration number; T is the maximum iteration number; x i (t+1) is the position of the i-th horned lizard at the t+1th iteration.

6. The pressure vessel design method based on the multi-strategy improved horned lizard algorithm according to claim 5 is characterized in that: After the position of the horned lizard is updated, the position of the population is disturbed by using the adaptive t distribution. The calculation process of using the dynamic selection probability p to adjust the use of the adaptive t distribution mutation operator is expressed as: Where t(iter) is an adaptive t-distribution function with the number of population iterations as the degree of freedom parameter; w1 determines the upper limit of the dynamic selection probability; w2 determines the variation range of dynamic selection probability; p is the dynamic selection probability.

7. The pressure vessel design method based on the multi-strategy improved horned lizard algorithm according to claim 6 is characterized in that: The objective function is solved by the multi-strategy improved horned lizard optimization algorithm to obtain the optimal solution for the pressure vessel design, including: The population of horned lizards was initialized by using cubic chaotic mapping and refraction reverse learning fusion strategy; The objective function of the pressure vessel design is used as the fitness function to determine the locations of hiding, ejecting, and escaping horned lizards; Check whether the range of the updated solution exceeds the value range of the design variable, and if so, replace the solution that exceeds the range with the boundary value of the design variable; Determine whether the current number of iterations t is less than the maximum number of iterations T. If so, continue to use the objective function of the pressure vessel design as the fitness function to determine the positions of the hidden, ejected, and escaped horned lizards. Otherwise, output the minimum value of the objective function as the minimum design cost of the pressure vessel, and the currently found solution is used as the optimal pressure vessel design solution.

8. The pressure vessel design method based on the multi-strategy improved horned lizard algorithm according to claim 7 is characterized in that: The objective function of the pressure vessel design is used as the fitness function to determine the positions of hiding, ejecting blood, and escaping horned lizards, including: Update the hidden horned lizard position using the following formula: Where δ is a constant, c1 and c2 are random numbers drawn from a standardized palette, and c1≠c2, σ is a random binary value, r1, r2, r3, and r4 are random integers generated between 1 and the maximum population size N, and r1≠r2≠r3≠r4, and x r1 (t), x r2 (t), x r3 (t) and x r4 (t) are the selected r1, r2, r3 and r4 horned lizards; Update the position of the bloodshot horned lizard using the following formula: x i (t+1)=[v0cos(αt / T)+ξ]x best (t)+λ·[v0sin(α-αt / T)-g+ξ]x i (t) Where v0 is the initial velocity, α is the angle parameter, λ is the water wave dynamic adaptive factor, ξ is a constant used to avoid division by zero, and g is the earth's gravitational acceleration; Update the position of the escaping horned lizard using the following formula: Where walk is a random number generated between -1 and 1, and ε is a random number following the Cauchy distribution.

9. A pressure vessel design device based on a multi-strategy improved horned lizard algorithm, characterized in that: The device comprises: An objective function determination unit is configured to model the pressure vessel design problem, determine the range of design variables and constraints, take minimizing the pressure vessel manufacturing cost under the constraints as the goal, and obtain an objective function of the pressure vessel design problem; The horned lizard algorithm improvement unit is configured to initialize the population using cubic chaos mapping and refraction reverse learning fusion strategy; add water wave dynamic adaptive factors to the position update formula of the blood-shot horned lizard, and use the uncertainty of water wave dynamic changes to adjust the search step size and direction; integrate Brownian motion and Levy flight strategy into the position update formula of the horned lizard's escape behavior; after the horned lizard's position is updated, the position of the population is disturbed using adaptive t distribution, and the dynamic selection probability p is used to adjust the use of the adaptive t distribution mutation operator; The objective function solving unit is configured to solve the objective function based on the multi-strategy improved horned lizard optimization algorithm to obtain the optimal solution for the pressure vessel design. 10 . A non-transitory computer-readable storage medium storing instructions, which, when executed by a processor, perform the method according to claim 1 .

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