A linear guide optimization design method, equipment, medium, and program product.

Abstract

This invention discloses a linear guide optimization design method, device, medium, and program product, including: (1) constructing a simulation model and MaOP design model that can simultaneously optimize stiffness, modality, and weight based on the linear guide structure and static load analysis; (2) generating an elite population based on Latin hypercube and diversity criteria, obtaining the target values ​​of the elite population and establishing a database, and constructing a Gaussian process function model; (3) designing a hybrid mutation operation based on OCC to generate a set of offspring guides; (4) designing a DEP-driven DPM evolution strategy to generate a set of candidate guides and selecting the optimal candidate guide; (5) obtaining the target values ​​of the optimal candidate guide, updating the database and Gaussian process function model, returning to step (3), until all optimization targets meet the requirements, and outputting the optimal parameter values. This invention can effectively balance the MaOP process for stiffness, modality, and weight of linear guides, achieving higher accuracy and better overall performance.

Description

Technical Field

[0001] This invention relates to the fields of general artificial intelligence technology and swarm intelligence, and more specifically, to a linear guide rail MaOP (Many-Objective Optimization) design method, device, medium, and program product based on OCC (Objective Classification Collaboration) and DEP (Dimension Effect Probability). Background Technology

[0002] Linear guides, as core transmission and positioning components in precision mechanical systems, are widely used in high-precision equipment fields such as CNC machine tools, industrial robots, and automated production lines. Their performance directly affects the positioning accuracy, dynamic response characteristics, operational stability, and service life of the entire machine. As the high-end equipment manufacturing industry develops towards higher speed, higher precision, and higher reliability, more stringent requirements are placed on the structural design of linear guides. While ensuring sufficient rigidity and good dynamic characteristics (modal characteristics), they must be as lightweight as possible to reduce motion inertia, decrease energy consumption, and improve system efficiency.

[0003] Traditional linear guide design methods often rely on engineers' experience, trial and error, or sequential optimization strategies based on finite element analysis. These methods tend to focus on optimizing a single performance metric, such as optimizing only stiffness or only reducing weight, making it difficult to find a globally optimal balance among multiple conflicting objectives such as stiffness, modal dynamics, and weight. Furthermore, traditional optimization processes heavily depend on time-consuming finite element simulations for iterative verification, resulting in high computational costs and lengthy design cycles.

[0004] In recent years, machine learning technology has demonstrated significant advantages in the field of engineering optimization. It can learn complex nonlinear mapping relationships between design variables and performance indicators through data-driven approaches, and establish high-precision surrogate models. Compared with traditional methods, machine learning-assisted optimization strategies can significantly reduce reliance on expensive simulations, quickly approximate optimal solutions in complex design spaces, and significantly improve the automation level and overall efficiency of the optimization process.

[0005] However, existing optimization techniques still have significant shortcomings when dealing with multi-objective optimization problems involving stiffness, modality, and weight of linear guides. Existing methods typically fail to deeply integrate DEP-driven and DPM evolutionary strategies, and also fail to systematically construct a hybrid mutation framework based on the OCC mechanism. This makes it difficult to efficiently and reliably obtain Pareto optimal solution sets that meet comprehensive performance requirements when dealing with complex engineering optimization problems involving conflicting objectives. Summary of the Invention

[0006] In view of the above limitations of existing technologies, and considering the design requirements of linear guides for three optimization objectives of stiffness, modality and weight, this invention proposes a linear guide optimization design method, equipment, medium and program product.

[0007] To achieve the above objectives, the first aspect of the present invention provides a linear guide rail optimization design method, the method comprising the steps of:

[0008] S1 uses the slider, raceway, ball bearings and guide rail dimensions of the linear guide as design parameters. Based on the structural characteristics of the linear guide and combined with static load analysis, a simulation model and MaOP design model that can simultaneously optimize the three optimization objectives of stiffness, modality and weight are constructed.

[0009] S2, construct the design space according to the range of design parameters, generate an elite population based on the Latin hypercube and diversity criteria, obtain the target values ​​by simulation evaluation of the elite population, establish a database and construct a Gaussian process function model.

[0010] S3, combining the target classification, select the first type of individual set and the second type of individual set from the database, and use the OCC-based hybrid mutation operation to generate the first type of offspring guide rail set and the second type of offspring guide rail set;

[0011] S4. Combining the prediction of the Gaussian process function model, the first target set of the first type of the first generation of guide rail sets and the second target set of the second type of the second generation of guide rail sets are selected. The DEP-driven DPM evolution strategy is used to generate candidate guide rail sets and the optimal candidate guide rail is selected.

[0012] S5: Perform simulation evaluation on the optimal candidate guide rail to obtain the target values ​​of each optimal candidate guide rail, update the database and Gaussian process function model, return to step S3 until all targets meet the requirements, and output the optimal parameter values.

[0013] Optionally, step S1 specifically includes the following steps:

[0014] S1.1, taking into account the structural characteristics of linear guide rails, the slider length, slider width, slider height, raceway curvature radius, raceway center distance, raceway groove depth, ball diameter, guide rail length, guide rail width, and guide rail height are used as design parameters.

[0015] S1.2, Based on the load conditions of the linear guide structure and the material selected for the linear guide, a three-dimensional model is constructed using three-dimensional modeling software and parameterized to obtain a parameterized model.

[0016] S1.3, import the parametric model, the load conditions of the linear guide structure and the key boundary conditions into the finite element analysis pre- and post-processing software for finite element analysis to obtain the finite element analysis model;

[0017] S1.4, using the solver of structural optimization and multiphysics simulation software, static load analysis is performed on the finite element analysis model to obtain the stiffness, modal and weight simulation model of the linear guide rail.

[0018] S1.5, Based on the stiffness, modal and weight simulation model of the linear guide, the MaOP design model of the linear guide is constructed with three optimization objectives: stiffness, modal and weight. The specific expressions are as follows:

[0019] ,

[0020] ,

[0021] ,

[0022] In the above formula, This indicates the search for the optimal solution to the design parameters. This indicates the design parameters of the linear guide. Indicates the length of the slider. Indicates the height of the slider. Indicates the width of the slider. Indicates the radius of curvature of the raceway. Indicates the center distance of the raceways. Indicates the groove depth of the raceway. Indicates the length of the guide rail. Indicates the height of the guide rail. Indicates the width of the guide rail. Indicates the diameter of the ball. This represents maximizing the stiffness and first natural frequency of the linear guide. This indicates the design parameters of the linear guide. The corresponding stiffness, This indicates the design parameters of the linear guide. The corresponding stiffness function, This indicates the design parameters of the linear guide. The corresponding first natural frequency, This indicates the design parameters of the linear guide. The corresponding first-order natural frequency function, This indicates minimizing the total weight of the linear guide. This indicates the total weight of the linear guide. Indicates design parameters The linear guide is divided into The total weight function of the linear guide rail obtained by summing the components. This indicates the density of the linear guide rail. Indicates design parameters The volume of the linear guide rail corresponding to the time.

[0023] Optionally, step S2 specifically includes the following steps:

[0024] S2.1 Determine the range of design parameters based on design requirements and material properties, and construct the design space based on the range of values;

[0025] S2.2, using Latin hypercube to generate multiple candidate populations within the design space;

[0026] S2.3, Combine the diversity criterion to calculate the scalar value discriminant function value of each candidate population, and take the candidate population with the smallest scalar value discriminant function value as the elite population;

[0027] S2.4. Using the simplex method, a uniformly distributed reference vector is generated in the target space composed of three optimization objectives: stiffness, mode and weight. The linear guide stiffness function, first natural frequency function and total weight function are used to simulate and evaluate the elite population. The obtained linear guide stiffness, first natural frequency and total weight are used as real sample data to establish a database.

[0028] S2.5 uses all individual vectors in the database to establish a Gaussian process function model for the stiffness function, first-order natural frequency function, and total weight function of the linear guide rail.

[0029] Optionally, the specific calculation steps for the scalar discriminant function value are as follows:

[0030] S2.3.1, calculate the pairwise Euclidean distance between all individual vectors in each candidate population;

[0031] S2.3.2 Construct the scalar value discriminant function and calculate the scalar value discriminant function value for each candidate population. The specific formula is as follows:

[0032] ,

[0033] In the above formula, It is the scalar discriminant function value of the candidate population. This represents the scalar value discriminant function. Indicates candidate populations, This represents the number of different Euclidean distances calculated for the candidate population. Indicates that the Euclidean distance is equal to The corresponding logarithm of the individual vector at time, Indicates the first Euclidean distance.

[0034] Optionally, step S3 specifically includes the following steps:

[0035] S3.1, the three optimization objectives of stiffness, modality, and weight are combined in pairs to form three objective sets: stiffness and modality, stiffness and weight, and modality and weight. Each objective set considers two optimization objectives simultaneously. For each objective value of the elite population, for each objective set, firstly, all individual vectors in the elite population are sorted in ascending order according to the objective value corresponding to that objective set to obtain the sorted value; then, the objective sets corresponding to individual vector sorted values ​​less than half the size of the elite population are selected and classified as the first type of objective set; then, the objective sets corresponding to sorted values ​​greater than half the size of the elite population are selected and classified as the second type of objective set.

[0036] S3.2, for each target set in the first type of target set, select targets from the database whose values ​​are greater than [a certain value] after ascending sorting. The individual vectors are used to construct the first type of individual set; for each target set in the second type of target set, select targets from the database whose sorted values ​​are less than [a certain value]. The individual vectors are used to construct the second type of individual set; where, Indicates the size of the elite population. This represents the number of optimization objectives in the first type of objective set. This indicates the number of optimization objectives in the second set of objectives;

[0037] S3.3, Design a hybrid mutation operation based on OCC, which includes a first type of cooperative mutation operation and a second type of cooperative mutation operation. The hybrid mutation operation is performed on each individual vector in the elite population to generate a first type of temporary offspring individual vector and a second type of temporary offspring individual vector. The formula for the hybrid mutation operation is as follows:

[0038] ,

[0039] ,

[0040] In the above formula, This represents a type I cooperative mutation operation. This indicates a type II cooperative mutation operation. This indicates the first type of cooperative mutation operation that produces the [missing information]. A first-class temporary child individual vector This indicates the type II cooperative mutation operation that produces the first... A second-class temporary offspring individual vector, This represents the vector of the first individual randomly selected from the set of individuals of the first class. This represents the vector of the second individual randomly selected from the set of individuals of the first class. This represents the vector of the third individual randomly selected from the set of individuals of the first class. This represents the vector of the fourth individual randomly selected from the set of individuals of the first class. This represents the vector of the fifth individual randomly selected from the set of individuals of the first class. This represents the vector of the first individual randomly selected from the set of individuals of the second class. This represents the vector of the second individual randomly selected from the set of individuals of the second type. This represents the vector of the third individual randomly selected from the set of individuals of the second type. This represents the vector of the fourth individual randomly selected from the set of individuals of the second type. This represents the vector of the fifth individual randomly selected from the set of individuals of the second class. This represents the first mutator of the second type of cooperative mutation operation. This represents the second mutation factor in a type II cooperative mutation operation. This represents the first mutator of the first type of cooperative mutation operation. This represents the second mutation factor in a type I cooperative mutation operation;

[0041] S3.4 Using the Gaussian process function model, the stiffness, first natural frequency, and weight of the first and second temporary offspring individual vectors are predicted to obtain the target values ​​of the first and second temporary offspring individual vectors.

[0042] S3.5, construct Chebyshev aggregation function using ideal reference vector and nadir reference vector, calculate fitness values ​​of first-class temporary offspring individual vector and second-class temporary offspring individual vector, perform non-dominated sorting based on each target value and fitness value of first-class temporary offspring individual vector and second-class temporary offspring individual vector, and obtain non-dominated ranking levels of first-class temporary offspring individual vector and second-class temporary offspring individual vector respectively.

[0043] The Chebyshev aggregation functions, constructed based on the ideal reference vector and the nadir reference vector respectively, are as follows:

[0044] ,

[0045] ,

[0046] In the above formula, It is a Chebyshev aggregation function constructed based on an ideal reference vector. It is a Chebyshev aggregation function constructed based on the nadir reference vector. It is a temporary offspring individual vector. It is a reference vector. Indicates the reference vector at the th The weight of each goal This indicates that the ideal reference vector in the database is at the th... Minimum value on each objective This indicates that the nadir reference vector in the database is at the [missing information - likely a specific position or location]. The maximum value on each target For the temporary offspring individual vector in the th... The target value on each target;

[0047] S3.6 According to the ascending order principle, the calculated fitness value is used as the screening index, and combined with the obtained non-dominated ranking level, the first type of temporary offspring individual vectors and the second type of temporary offspring individual vectors with higher non-dominated ranking levels and smaller fitness values ​​are selected to form the first type of offspring guide set and the second type of offspring guide set.

[0048] Optionally, step S4 specifically includes the following steps:

[0049] S4.1, using the Gaussian process function model, the stiffness, first natural frequency, and weight of the first and second child guide rail sets are predicted to obtain the target values ​​of the first and second child guide rail sets. The first and second child guide rail sets are merged with the database to form a temporary library. For the three target sets of stiffness and mode, stiffness and weight, and first natural frequency and weight, according to the target values ​​of the child guide rail sets, for each target set, all individual vectors in the temporary library are sorted in ascending order to obtain the sorted value.

[0050] S4.2 For each child individual vector in the first type of child guide track set, select the target set corresponding to the child individual vector sorting value that is less than half the size of the temporary library to form the first type of target set. For each child individual vector in the second type of child guide track set, select the target set corresponding to the child individual vector sorting value that is less than half the size of the temporary library to form the second type of target set.

[0051] S4.3, for each child individual vector in the first type of child guide track set, the gradients of all design parameters of the child individual vector on the first type of target set are calculated using the Gaussian process function model, and a first gradient matrix is ​​constructed. Then, the dimensionality effect probability of all design parameters is calculated. For each child individual vector in the second type of child guide track set, the gradients of all design parameters of the child individual vector on the second type of target set are calculated using the Gaussian process function model, and a second gradient matrix is ​​constructed. Then, the dimensionality effect probability of all design parameters is calculated. The formula for calculating the dimensionality effect probability is as follows:

[0052] ,

[0053] ,

[0054] In the above formula, It is the first in the first type of descendant guide rail set The first generation of individual vectors The dimensionality effect probability of each design parameter. It is the first in the first type of descendant guide rail set Individual vectors of each offspring express The first type of target set, express The Each design parameter value, express In the Gradient on each target, It is the first in the second type of offspring guide rail set The first generation of individual vectors The dimensionality effect probability of each design parameter. It is the first in the second type of offspring guide rail set Individual vectors of each offspring express The second type of target set, express The Each design parameter value, express In the Gradient over each objective;

[0055] S4.4, randomly select a child individual vector from the first type of child guide rail set as the reference point based on a uniformly distributed random number. For each design parameter, combine the uniformly distributed random number; if the uniformly distributed random number is less than... Then, the DPM evolutionary strategy is executed to generate the first type of candidate individual vector; similarly, a child individual vector is randomly selected from the second type of child guide set as a reference point. For each design parameter, combined with a uniformly distributed random number, if the uniformly distributed random number is less than... Then, the DPM evolution strategy is executed to generate a second type of candidate individual vector; all first type of candidate individual vectors and second type of candidate individual vectors are merged to form a candidate guide set;

[0056] S4.5 uses a Gaussian process function model to predict the stiffness, first natural frequency, and weight of the candidate guide rail set, obtaining the predicted values ​​of stiffness, first natural frequency, and weight for all candidate individual vectors. A scalarization function for the PBI method is constructed using an ideal reference vector, and the fitness values ​​of the candidate individual vectors are calculated. Non-dominated ranking is then performed based on the target values ​​and fitness values ​​of the candidate individual vectors, yielding the non-dominated ranking hierarchy for all candidate individual vectors. The scalarization function for the PBI method is as follows:

[0057] ,

[0058] ,

[0059] ,

[0060] In the above formula, It is the scalarization function of the PBI method. Represents the candidate individual vector. Represents the reference vector. This represents the minimum value of the ideal reference vector in the database. This represents the convergence distance of the candidate individual vectors. Indicates the penalty parameter. Represents the diversity distance of candidate individual vectors. The objective function value vector represents the candidate individual vectors;

[0061] S4.6, based on the ascending order principle, using the calculated fitness value as the screening index, and combined with the obtained non-dominated ranking level, the candidate individual vector with the smallest fitness value is selected from the first level of the non-dominated ranking as the optimal candidate guide.

[0062] Optionally, step S5 specifically includes the following steps:

[0063] S5.1, The simulation model is used to simulate and evaluate the optimal candidate guide rail to obtain the target values ​​corresponding to the optimal candidate guide rail, namely the linear guide rail stiffness, first natural frequency and weight.

[0064] S5.2, store the optimal candidate guide rail and its corresponding target values ​​into the database, and update the Gaussian process function model based on all individual vectors in the database;

[0065] S5.3 Determine whether the three optimization objectives of stiffness, modality and weight corresponding to the current optimal candidate guide rail meet the requirements respectively; if they do, output the optimal parameter values; otherwise, return to step S3 to continue iterative optimization until all objectives meet the requirements and output the optimal parameter values.

[0066] Secondly, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the aforementioned linear guide optimization design method.

[0067] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the aforementioned linear guide optimization design method.

[0068] Fourthly, the present invention provides a computer program product, including a computer program, which, when executed by a processor, implements the steps of the aforementioned linear guide optimization design method.

[0069] In summary, compared with the prior art, the technical solutions conceived in this invention have the following main advantages:

[0070] 1. To address the limitations of existing technologies that cannot systematically integrate the OCC mechanism with the hybrid mutation framework, making it difficult to achieve MaOP for linear guides, this invention designs a hybrid mutation operation based on OCC, based on the classification of targets during the optimization process. During optimization, this hybrid mutation operation accelerates convergence to the optimal region while maintaining exploration of unexplored regions, thus effectively balancing the convergence and exploration processes.

[0071] 2. To address the limitations of traditional methods in efficiently and reliably obtaining Pareto optimal solution sets that meet comprehensive performance requirements when dealing with complex engineering optimization problems involving conflicting objectives, this invention designs a DEP-driven DPM evolution strategy and combines it with a Gaussian process function model for prediction. While ensuring accuracy, it effectively achieves global balance among conflicting objectives, obtaining a Pareto solution set with better comprehensive performance.

[0072] In summary, this invention can optimize multi-objective problems involving complex simulations, adapt to target conflicts caused by complex simulations, and achieve higher accuracy and better overall performance. It simultaneously optimizes three objectives of a linear guide to achieve overall optimality, and also provides a usable algorithmic structure for the MaOP design of other complex structures. Attached Figure Description

[0073] Figure 1 A simplified flowchart of a linear guide optimization design method provided by the present invention. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0075] Please see Figure 1 This invention provides a linear guide optimization design method, applicable to multi-objective optimization design of linear guides. Specifically, the method includes steps S1 to S5.

[0076] S1 uses the slider, raceway, ball bearings, and guide rail dimensions of the linear guide as design parameters. Based on the structural characteristics of the linear guide and combined with static load analysis, a simulation model and MaOP design model are constructed that can simultaneously optimize three optimization objectives: stiffness, modal dynamics, and weight.

[0077] The specific steps of step S1 are as follows:

[0078] S1.1, taking into account the structural characteristics of linear guide rails, the slider length, slider width, slider height, raceway curvature radius, raceway center distance, raceway groove depth, ball diameter, guide rail length, guide rail width, and guide rail height are used as design parameters.

[0079] S1.2, Based on the load conditions of the linear guide structure and the material selected for the linear guide, a three-dimensional model is constructed using three-dimensional modeling software and parameterized to obtain a parameterized model.

[0080] S1.3, import the parametric model, the load conditions of the linear guide structure, and the key boundary conditions into the finite element analysis pre- and post-processing software for finite element analysis to obtain the finite element analysis model.

[0081] S1.4. Using the solver of structural optimization and multiphysics simulation software, static load analysis is performed on the finite element analysis model to obtain the stiffness, modal and weight simulation model of the linear guide rail.

[0082] S1.5, Based on the stiffness, modal and weight simulation model of the linear guide, the MaOP design model of the linear guide is constructed with three optimization objectives: stiffness, modal and weight. The specific expressions are as follows:

[0083] ,

[0084] ,

[0085] ,

[0086] In the above formula, This indicates the search for the optimal solution to the design parameters. This indicates the design parameters of the linear guide. Indicates the length of the slider. Indicates the height of the slider. Indicates the width of the slider. Indicates the radius of curvature of the raceway. Indicates the center distance of the raceways. Indicates the groove depth of the raceway. Indicates the length of the guide rail. Indicates the height of the guide rail. Indicates the width of the guide rail. Indicates the diameter of the ball. This represents maximizing the stiffness and first natural frequency of the linear guide. This indicates the design parameters of the linear guide. The corresponding stiffness, This indicates the design parameters of the linear guide. The corresponding stiffness function, This indicates the design parameters of the linear guide. The corresponding first natural frequency, This indicates the design parameters of the linear guide. The corresponding first-order natural frequency function, This indicates minimizing the total weight of the linear guide. This indicates the total weight of the linear guide. Indicates design parameters The linear guide is divided into The total weight function of the linear guide rail obtained by summing the components. This indicates the density of the linear guide rail. Indicates design parameters The volume of the linear guide rail corresponding to the time.

[0087] S2. Construct a design space based on the range of design parameters, generate an elite population based on the Latin hypercube and diversity criteria, simulate and evaluate the elite population to obtain the target values, establish a database and construct a Gaussian process function model.

[0088] The specific steps of step S2 are as follows:

[0089] S2.1 Determine the range of design parameters based on design requirements and material properties, and construct the design space based on the range of values.

[0090] S2.2, using Latin hypercube to generate multiple candidate populations within the design space.

[0091] S2.3, Combine the diversity criterion to calculate the scalar discriminant function value of each candidate population, and select the candidate population with the smallest scalar discriminant function value as the elite population.

[0092] The specific calculation steps for the scalar discriminant function are as follows:

[0093] S2.3.1, calculate the pairwise Euclidean distance between all individual vectors in each candidate population;

[0094] S2.3.2 Construct the scalar value discriminant function and calculate the scalar value discriminant function value for each candidate population. The specific formula is as follows:

[0095] ,

[0096] In the above formula, It is the scalar discriminant function value of the candidate population. This represents the scalar value discriminant function. Indicates candidate populations, This represents the number of different Euclidean distances calculated for the candidate population. Indicates that the Euclidean distance is equal to The corresponding logarithm of the individual vector at time, Indicates the first Euclidean distance.

[0097] S2.4. Using the simplex method, a uniformly distributed reference vector is generated in the target space composed of three optimization objectives: stiffness, mode, and weight. The linear guide stiffness function, first-order natural frequency function, and total weight function are used to simulate and evaluate the elite population. The obtained linear guide stiffness, first-order natural frequency, and total weight are used as real sample data to establish a database.

[0098] S2.5 uses all individual vectors in the database to establish a Gaussian process function model for the stiffness function, first-order natural frequency function, and total weight function of the linear guide rail.

[0099] S3, combining the target classification, select the first type of individual set and the second type of individual set from the database, and use OCC-based hybrid mutation operation to generate the first type of offspring guide rail set and the second type of offspring guide rail set.

[0100] The specific steps of step S3 are as follows:

[0101] S3.1, the three optimization objectives of stiffness, modality, and weight are combined in pairs to form three objective sets: stiffness and modality, stiffness and weight, and modality and weight. Each objective set considers two optimization objectives simultaneously. For each objective value of the elite population, for each objective set, all individual vectors in the elite population are first sorted in ascending order according to the objective value corresponding to that objective set to obtain the sorted value. Then, the objective sets corresponding to individual vector sorted values ​​less than half the size of the elite population are selected and classified as the first type of objective set. Then, the objective sets corresponding to sorted values ​​greater than half the size of the elite population are selected and classified as the second type of objective set.

[0102] S3.2, for each target set in the first type of target set, select targets from the database whose values ​​are greater than [a certain value] after ascending sorting. The individual vectors are used to construct the first type of individual set; for each target set in the second type of target set, select targets from the database whose sorted values ​​are less than [a certain value]. The individual vectors are used to construct the second type of individual set; where, Indicates the size of the elite population. This represents the number of optimization objectives in the first type of objective set. This represents the number of optimization objectives in the second set of objectives.

[0103] S3.3, Design a hybrid mutation operation based on OCC, which includes a first type of cooperative mutation operation and a second type of cooperative mutation operation. The hybrid mutation operation is performed on each individual vector in the elite population to generate a first type of temporary offspring individual vector and a second type of temporary offspring individual vector. The formula for the hybrid mutation operation is as follows:

[0104] ,

[0105] ,

[0106] In the above formula, This represents a type I cooperative mutation operation. This indicates a type II cooperative mutation operation. This indicates the first type of cooperative mutation operation that produces the [missing information]. A first-class temporary child individual vector This indicates the type II cooperative mutation operation that produces the first... A second-class temporary offspring individual vector, This represents the vector of the first individual randomly selected from the set of individuals of the first class. This represents the vector of the second individual randomly selected from the set of individuals of the first class. This represents the vector of the third individual randomly selected from the set of individuals of the first class. This represents the vector of the fourth individual randomly selected from the set of individuals of the first class. This represents the vector of the fifth individual randomly selected from the set of individuals of the first class. This represents the vector of the first individual randomly selected from the set of individuals of the second class. This represents the vector of the second individual randomly selected from the set of individuals of the second type. This represents the vector of the third individual randomly selected from the set of individuals of the second type. This represents the vector of the fourth individual randomly selected from the set of individuals of the second type. This represents the vector of the fifth individual randomly selected from the set of individuals of the second class. This represents the first mutator of the second type of cooperative mutation operation. This represents the second mutation factor in a type II cooperative mutation operation. This represents the first mutator of the first type of cooperative mutation operation. This represents the second mutation factor in the first type of cooperative mutation operation.

[0107] S3.4. Using the Gaussian process function model, the stiffness, first natural frequency, and weight of the first and second temporary offspring individual vectors are predicted to obtain the target values ​​of the first and second temporary offspring individual vectors.

[0108] S3.5 Construct a Chebyshev aggregation function using the ideal reference vector and the nadir reference vector, calculate the fitness values ​​of the first-class temporary offspring individual vector and the second-class temporary offspring individual vector, and perform non-dominated sorting based on the target values ​​and fitness values ​​of the first-class temporary offspring individual vector and the second-class temporary offspring individual vector, respectively, to obtain the non-dominated ranking levels of the first-class temporary offspring individual vector and the second-class temporary offspring individual vector.

[0109] The Chebyshev aggregation functions, constructed based on the ideal reference vector and the nadir reference vector respectively, are as follows:

[0110] ,

[0111] ,

[0112] In the above formula, It is a Chebyshev aggregation function constructed based on an ideal reference vector. It is a Chebyshev aggregation function constructed based on the nadir reference vector. It is a temporary offspring individual vector. It is a reference vector. Indicates the reference vector at the th The weight of each goal This indicates that the ideal reference vector in the database is at the th... Minimum value on each objective This indicates that the nadir reference vector in the database is at the [missing information - likely a specific position or location]. The maximum value on each target For the temporary offspring individual vector in the th... The target value on each target.

[0113] S3.6 According to the ascending order principle, the calculated fitness value is used as the screening index, and combined with the obtained non-dominated ranking level, the first type of temporary offspring individual vectors and the second type of temporary offspring individual vectors with higher non-dominated ranking levels and smaller fitness values ​​are selected to form the first type of offspring guide set and the second type of offspring guide set.

[0114] S4. Combining the prediction of the Gaussian process function model, the first target set of the first type of offspring guide rail set and the second target set of the second type of offspring guide rail set are selected. The DEP-driven DPM evolution strategy is used to generate candidate guide rail sets and the optimal candidate guide rail is selected.

[0115] The specific steps of step S4 are as follows:

[0116] S4.1, using the Gaussian process function model, the stiffness, first natural frequency, and weight of the first and second generation of child guide rail sets are predicted to obtain the target values ​​for each of the first and second generation of child guide rail sets. The first and second generation of child guide rail sets are merged with the database to form a temporary library. For the three target sets of stiffness and mode, stiffness and weight, and first natural frequency and weight, according to the target values ​​of each generation of child guide rail sets, for each target set, all individual vectors in the temporary library are sorted in ascending order to obtain the sorted value.

[0117] S4.2 For each child individual vector in the first type of child guide set, select the target set corresponding to the child individual vector sorting value that is less than half the size of the temporary library to form the first type of target set. For each child individual vector in the second type of child guide set, select the target set corresponding to the child individual vector sorting value that is less than half the size of the temporary library to form the second type of target set.

[0118] S4.3, for each child individual vector in the first type of child guide track set, the gradients of all design parameters of the child individual vector on the first type of target set are calculated using the Gaussian process function model, and a first gradient matrix is ​​constructed. Then, the dimensionality effect probability of all design parameters is calculated. For each child individual vector in the second type of child guide track set, the gradients of all design parameters of the child individual vector on the second type of target set are calculated using the Gaussian process function model, and a second gradient matrix is ​​constructed. Then, the dimensionality effect probability of all design parameters is calculated. The formula for calculating the dimensionality effect probability is as follows:

[0119] ,

[0120] ,

[0121] In the above formula, It is the first in the first type of descendant guide rail set The first generation of individual vectors The dimensionality effect probability of each design parameter. It is the first in the first type of descendant guide rail set Individual vectors of each offspring express The first type of target set, express The Each design parameter value, express In the Gradient on each target, It is the first in the second type of offspring guide rail set The first generation of individual vectors The dimensionality effect probability of each design parameter. It is the first in the second type of offspring guide rail set Individual vectors of each offspring express The second type of target set, express The Each design parameter value, express In the The gradient on each target.

[0122] S4.4, randomly select a child individual vector from the first type of child guide rail set as the reference point based on a uniformly distributed random number. For each design parameter, combine the uniformly distributed random number; if the uniformly distributed random number is less than... Then, the DPM evolutionary strategy is executed to generate the first type of candidate individual vector; similarly, a child individual vector is randomly selected from the second type of child guide set as a reference point. For each design parameter, combined with a uniformly distributed random number, if the uniformly distributed random number is less than... Then, the DPM evolution strategy is executed to generate a second type of candidate individual vector; all first type and second type candidate individual vectors are merged to form a candidate guide set.

[0123] S4.5 uses a Gaussian process function model to predict the stiffness, first natural frequency, and weight of the candidate guide rail set, obtaining the predicted values ​​of stiffness, first natural frequency, and weight for all candidate individual vectors. A scalarization function for the PBI method is constructed using an ideal reference vector, and the fitness values ​​of the candidate individual vectors are calculated. Non-dominated ranking is then performed based on the target values ​​and fitness values ​​of the candidate individual vectors, yielding the non-dominated ranking hierarchy for all candidate individual vectors. The scalarization function for the PBI method is as follows:

[0124] ,

[0125] ,

[0126] ,

[0127] In the above formula, It is the scalarization function of the PBI method. Represents the candidate individual vector. Represents the reference vector. This represents the minimum value of the ideal reference vector in the database. This represents the convergence distance of the candidate individual vectors. Indicates the penalty parameter. Represents the diversity distance of candidate individual vectors. The objective function value vector represents the candidate individual vector.

[0128] S4.6. Based on the ascending order principle, the calculated fitness value is used as the screening index, and combined with the obtained non-dominated ranking level, the candidate individual vector with the smallest fitness value is selected from the first level of the non-dominated ranking as the optimal candidate guide.

[0129] S5: Perform simulation evaluation on the optimal candidate guide rail to obtain the target values ​​of each optimal candidate guide rail, update the database and Gaussian process function model, return to step S3 until all targets meet the requirements, and output the optimal parameter values.

[0130] The specific steps of step S5 are as follows:

[0131] S5.1, The simulation model is used to simulate and evaluate the optimal candidate guide rail, and the target values ​​corresponding to the optimal candidate guide rail are obtained, namely, the stiffness, first natural frequency and weight of the linear guide rail.

[0132] S5.2 Store the optimal candidate guide rail and its corresponding target values ​​into the database, and update the Gaussian process function model based on all individual vectors in the database.

[0133] S5.3 Determine whether the three optimization objectives of stiffness, modality and weight corresponding to the current optimal candidate guide rail meet the requirements respectively; if they do, output the optimal parameter values; otherwise, return to step S3 to continue iterative optimization until all objectives meet the requirements and output the optimal parameter values.

[0134] Example 1 illustrates the optimization performance of the proposed linear guide optimization design method using the benchmark test function DTLZ1. The expression of the benchmark test function DTLZ1, which has three optimization objectives, is as follows:

[0135] ,

[0136] ,

[0137] ,

[0138] ,

[0139] In the above formula, , and These are the first objective function, the second objective function, and the third objective function, respectively. It is an auxiliary constructor. This represents the first design parameter. This represents the second design parameter. These are the remaining design parameters within the design space, excluding the first and second design parameters. It is the first One design parameter, It refers to the number of design parameters.

[0140] The above benchmark test functions are processed through steps S1 to S5 of the linear guide rail optimization design method provided by this invention to obtain experimental results.

[0141] To further illustrate this embodiment, a linear guide optimization design method from this embodiment is compared with another classic and excellent Kriging-assisted reference vector guided evolutionary algorithm. The maximum number of simulation evaluations in this embodiment is set to 300, and the number of design parameters is set to 10. The experimental results are shown in Table 1. With the same number of simulation samples, the method of this embodiment obtains a better backward generation distance (IGD value) and significantly outperforms the Kriging-assisted reference vector guided evolutionary algorithm. It can be considered that the method of this embodiment performs well in the multi-objective design optimization problem of linear guide structure stiffness, modalities, and weight.

[0142] Table 1. Comparison of optimization results of different methods

[0143]

[0144] This invention provides a linear guide optimization design method, which designs a hybrid mutation operation based on OCC and a DEP-driven DPM evolution strategy. It can optimize multi-objective problems involving complex simulations, achieving higher accuracy and better overall performance, and provides a systematic solution for the MaOP design of linear guide structure stiffness, modality and weight.

[0145] In a second aspect, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of a linear guide optimization design method of the foregoing embodiments.

[0146] The memory can be volatile or non-volatile, or a combination of both. Non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memory of this invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0147] The processor can be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in this invention can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0148] The method steps of this invention can be implemented in hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or combinations thereof.

[0149] Software implementation can be achieved by executing functional modules (such as procedures, functions, etc.). Software code can be stored in memory and executed by the processor. Memory can be implemented in the processor or outside the processor.

[0150] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a linear guide optimization design method of the foregoing embodiments.

[0151] Computer storage media can include various media that can store program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0152] Fourthly, the present invention provides a computer program product, including a computer program, which, when executed by a processor, implements the steps of a linear guide optimization design method according to the foregoing embodiments.

[0153] Specifically, computer program products include: data signals and data signals embodied in a carrier wave.

[0154] It should be noted that the technical solutions described in this invention can be combined arbitrarily without conflict.

[0155] Those skilled in the art will readily understand that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A linear guide rail optimization design method, characterized in that, The method includes: S1 uses the slider, raceway, ball bearings and guide rail dimensions of the linear guide as design parameters. Based on the structural characteristics of the linear guide and combined with static load analysis, a simulation model and MaOP design model that can simultaneously optimize the three optimization objectives of stiffness, modality and weight are constructed. S2, construct the design space according to the range of design parameters, generate an elite population based on the Latin hypercube and diversity criteria, obtain the target values ​​by simulation evaluation of the elite population, establish a database and construct a Gaussian process function model. S3, combining the target classification, select the first type of individual set and the second type of individual set from the database, and use an OCC-based hybrid mutation operation to generate the first type of offspring guide rail set and the second type of offspring guide rail set, wherein the formula for the hybrid mutation operation is as follows: ， ， In the above formula, This represents a type I cooperative mutation operation. This indicates a type II cooperative mutation operation. This indicates the first type of cooperative mutation operation that produces the [missing information]. A first-class temporary child individual vector This indicates the type II cooperative mutation operation that produces the first... A second-class temporary offspring individual vector, This represents the vector of the first individual randomly selected from the set of individuals of the first class. This represents the vector of the second individual randomly selected from the set of individuals of the first class. This represents the vector of the third individual randomly selected from the set of individuals of the first class. This represents the vector of the fourth individual randomly selected from the set of individuals of the first class. This represents the vector of the fifth individual randomly selected from the set of individuals of the first class. This represents the vector of the first individual randomly selected from the set of individuals of the second class. This represents the vector of the second individual randomly selected from the set of individuals of the second type. This represents the vector of the third individual randomly selected from the set of individuals of the second type. This represents the vector of the fourth individual randomly selected from the set of individuals of the second type. This represents the vector of the fifth individual randomly selected from the set of individuals of the second class. This represents the first mutator of the second type of cooperative mutation operation. This represents the second mutation factor in a type II cooperative mutation operation. This represents the first mutator of the first type of cooperative mutation operation. This represents the second mutation factor in a type I cooperative mutation operation; S4, combining the Gaussian process function model prediction, select the first type of target set of the first type of offspring guide rail set and the second type of target set of the second type of offspring guide rail set. Use a DEP-driven DPM evolutionary strategy to generate a candidate guide rail set and select the optimal candidate guide rail. Specifically, the step of using the DEP-driven DPM evolutionary strategy to generate the candidate guide rail set includes: randomly selecting an offspring individual vector from the first type of offspring guide rail set as a reference point based on a uniformly distributed random number; for each design parameter, combining the uniformly distributed random number, if the uniformly distributed random number is less than... , It is the first in the first type of descendant guide rail set The first generation of individual vectors If the dimensionality effect probability of each design parameter is calculated, the DPM evolutionary strategy is executed to generate a first-class candidate individual vector. Similarly, a child individual vector is randomly selected from the second-class child guide set as a baseline. For each design parameter, combined with a uniformly distributed random number, if the uniformly distributed random number is less than... , It is the first in the second type of offspring guide rail set The first generation of individual vectors If the dimensionality effect probability of each design parameter is calculated, the DPM evolution strategy is executed to generate a second type of candidate individual vector; all first type and second type candidate individual vectors are merged to form a candidate guide set. S5: Perform simulation evaluation on the optimal candidate guide rail to obtain the target values ​​of each optimal candidate guide rail, update the database and Gaussian process function model, return to step S3 until all targets meet the requirements, and output the optimal parameter values.

2. The method as described in claim 1, characterized in that, Step S1 specifically includes: S1.1, taking into account the structural characteristics of linear guide rails, the slider length, slider width, slider height, raceway curvature radius, raceway center distance, raceway groove depth, ball diameter, guide rail length, guide rail width, and guide rail height are used as design parameters. S1.2, Based on the load conditions of the linear guide structure and the material selected for the linear guide, a three-dimensional model is constructed using three-dimensional modeling software and parameterized to obtain a parameterized model. S1.3, import the parametric model, the load conditions of the linear guide structure and the key boundary conditions into the finite element analysis pre- and post-processing software for finite element analysis to obtain the finite element analysis model; S1.4, using the solver of structural optimization and multiphysics simulation software, static load analysis is performed on the finite element analysis model to obtain the stiffness, modal and weight simulation model of the linear guide rail. S1.5, Based on the stiffness, modal and weight simulation model of the linear guide, the MaOP design model of the linear guide is constructed with three optimization objectives: stiffness, modal and weight. The specific expressions are as follows: ， ， ， In the above formula, This indicates the search for the optimal solution to the design parameters. This indicates the design parameters of the linear guide. Indicates the length of the slider. Indicates the height of the slider. Indicates the width of the slider. Indicates the radius of curvature of the raceway. Indicates the center distance of the raceways. Indicates the groove depth of the raceway. Indicates the length of the guide rail. Indicates the height of the guide rail. Indicates the width of the guide rail. Indicates the diameter of the ball. This represents maximizing the stiffness and first natural frequency of the linear guide. This indicates the design parameters of the linear guide. The corresponding stiffness, This indicates the design parameters of the linear guide. The corresponding stiffness function, This indicates the design parameters of the linear guide. The corresponding first natural frequency, This indicates the design parameters of the linear guide. The corresponding first-order natural frequency function, This indicates minimizing the total weight of the linear guide. This indicates the total weight of the linear guide. Indicates design parameters The linear guide is divided into The total weight function of the linear guide rail obtained by summing the components. This indicates the density of the linear guide rail. Indicates design parameters The volume of the linear guide rail corresponding to the time.

3. The method as described in claim 1, characterized in that, Step S2 specifically includes: S2.1 Determine the range of design parameters based on design requirements and material properties, and construct the design space based on the range of values; S2.2, using Latin hypercube to generate multiple candidate populations within the design space; S2.3, Combine the diversity criterion to calculate the scalar value discriminant function value of each candidate population, and take the candidate population with the smallest scalar value discriminant function value as the elite population; S2.

4. Using the simplex method, a uniformly distributed reference vector is generated in the target space composed of three optimization objectives: stiffness, mode and weight. The linear guide stiffness function, first natural frequency function and total weight function are used to simulate and evaluate the elite population. The obtained linear guide stiffness, first natural frequency and total weight are used as real sample data to establish a database. S2.5 uses all individual vectors in the database to establish a Gaussian process function model for the stiffness function, first-order natural frequency function, and total weight function of the linear guide rail.

4. The method as described in claim 3, characterized in that, The specific calculation steps for the scalar discriminant function are as follows: S2.3.1, calculate the pairwise Euclidean distance between all individual vectors in each candidate population; S2.3.2 Construct the scalar value discriminant function and calculate the scalar value discriminant function value for each candidate population. The specific formula is as follows: ， In the above formula, It is the scalar discriminant function value of the candidate population. This represents the scalar value discriminant function. Indicates candidate populations, This represents the number of different Euclidean distances calculated for the candidate population. Indicates that the Euclidean distance is equal to The corresponding logarithm of the individual vector at time, Indicates the first Euclidean distance.

5. The method as described in claim 1, characterized in that, Step S3 specifically includes: S3.1, the three optimization objectives of stiffness, modality, and weight are combined in pairs to form three objective sets: stiffness and modality, stiffness and weight, and modality and weight. Each objective set considers two optimization objectives simultaneously. For each objective value of the elite population, for each objective set, firstly, all individual vectors in the elite population are sorted in ascending order according to the objective value corresponding to that objective set to obtain the sorted value; then, the objective sets corresponding to individual vector sorted values ​​less than half the size of the elite population are selected and classified as the first type of objective set; then, the objective sets corresponding to sorted values ​​greater than half the size of the elite population are selected and classified as the second type of objective set. S3.2, for each target set in the first type of target set, select targets from the database whose values ​​are greater than [a certain value] after ascending sorting. The individual vectors are used to construct the first type of individual set; for each target set in the second type of target set, select targets from the database whose sorted values ​​are less than [a certain value]. The individual vectors are used to construct the second type of individual set; where, Indicates the size of the elite population. This represents the number of optimization objectives in the first type of objective set. This indicates the number of optimization objectives in the second set of objectives; S3.3, design a hybrid mutation operation based on OCC, which includes a first type of cooperative mutation operation and a second type of cooperative mutation operation, and perform the hybrid mutation operation on each individual vector in the elite population to generate a first type of temporary offspring individual vector and a second type of temporary offspring individual vector. S3.4 Using the Gaussian process function model, the stiffness, first natural frequency, and weight of the first and second temporary offspring individual vectors are predicted to obtain the target values ​​of the first and second temporary offspring individual vectors. S3.5, construct Chebyshev aggregation function using ideal reference vector and nadir reference vector, calculate fitness values ​​of first-class temporary offspring individual vector and second-class temporary offspring individual vector, perform non-dominated sorting based on each target value and fitness value of first-class temporary offspring individual vector and second-class temporary offspring individual vector, and obtain non-dominated ranking levels of first-class temporary offspring individual vector and second-class temporary offspring individual vector respectively. The Chebyshev aggregation functions, constructed based on the ideal reference vector and the nadir reference vector respectively, are as follows: ， ， In the above formula, It is a Chebyshev aggregation function constructed based on an ideal reference vector. It is a Chebyshev aggregation function constructed based on the nadir reference vector. It is a temporary offspring individual vector. It is a reference vector. Indicates the reference vector at the th The weight of each goal This indicates that the ideal reference vector in the database is at the th... Minimum value on each objective This indicates that the nadir reference vector in the database is at the [missing information - likely a specific position or location]. The maximum value on each target For the temporary offspring individual vector in the th... The target value on each target; S3.6 According to the ascending order principle, the calculated fitness value is used as the screening index, and combined with the obtained non-dominated ranking level, the first type of temporary offspring individual vectors and the second type of temporary offspring individual vectors with higher non-dominated ranking levels and smaller fitness values ​​are selected to form the first type of offspring guide set and the second type of offspring guide set.

6. The method as described in claim 1, characterized in that, Step S4 specifically includes: S4.1, using the Gaussian process function model, the stiffness, first natural frequency, and weight of the first and second child guide rail sets are predicted to obtain the target values ​​of the first and second child guide rail sets. The first and second child guide rail sets are merged with the database to form a temporary library. For the three target sets of stiffness and mode, stiffness and weight, and first natural frequency and weight, according to the target values ​​of the child guide rail sets, for each target set, all individual vectors in the temporary library are sorted in ascending order to obtain the sorted value. S4.2 For each child individual vector in the first type of child guide track set, select the target set corresponding to the child individual vector sorting value that is less than half the size of the temporary library to form the first type of target set. For each child individual vector in the second type of child guide track set, select the target set corresponding to the child individual vector sorting value that is less than half the size of the temporary library to form the second type of target set. S4.3, for each child individual vector in the first type of child guide track set, the gradients of all design parameters of the child individual vector on the first type of target set are calculated using the Gaussian process function model, and a first gradient matrix is ​​constructed. Then, the dimensionality effect probability of all design parameters is calculated. For each child individual vector in the second type of child guide track set, the gradients of all design parameters of the child individual vector on the second type of target set are calculated using the Gaussian process function model, and a second gradient matrix is ​​constructed. Then, the dimensionality effect probability of all design parameters is calculated. The formula for calculating the dimensionality effect probability is as follows: ， ， In the above formula, It is the first in the first type of descendant guide rail set Individual vectors of each offspring express The first type of target set, express The Each design parameter value, express In the Gradient on each target, It is the first in the second type of offspring guide rail set Individual vectors of each offspring express The second type of target set, express The Each design parameter value, express In the Gradient over each objective; S4.4, randomly select a child individual vector from the first type of child guide rail set as the reference point based on a uniformly distributed random number. For each design parameter, combine the uniformly distributed random number; if the uniformly distributed random number is less than... Then, the DPM evolutionary strategy is executed to generate the first type of candidate individual vector; similarly, a child individual vector is randomly selected from the second type of child guide set as a reference point. For each design parameter, combined with a uniformly distributed random number, if the uniformly distributed random number is less than... Then, the DPM evolution strategy is executed to generate a second type of candidate individual vector; all first type of candidate individual vectors and second type of candidate individual vectors are merged to form a candidate guide set; S4.5 uses a Gaussian process function model to predict the stiffness, first natural frequency, and weight of the candidate guide rail set, obtaining the predicted values ​​of stiffness, first natural frequency, and weight for all candidate individual vectors. A scalarization function for the PBI method is constructed using an ideal reference vector, and the fitness values ​​of the candidate individual vectors are calculated. Non-dominated ranking is then performed based on the target values ​​and fitness values ​​of the candidate individual vectors, yielding the non-dominated ranking hierarchy for all candidate individual vectors. The scalarization function for the PBI method is as follows: ， ， ， In the above formula, It is the scalarization function of the PBI method. Represents the candidate individual vector. Represents the reference vector. This represents the minimum value of the ideal reference vector in the database. This represents the convergence distance of the candidate individual vectors. Indicates the penalty parameter. Represents the diversity distance of candidate individual vectors. The objective function value vector represents the candidate individual vectors; S4.

6. Based on the ascending order principle, the calculated fitness value is used as the screening index, and combined with the obtained non-dominated ranking level, the candidate individual vector with the smallest fitness value is selected from the first level of the non-dominated ranking as the optimal candidate guide.

7. The method as described in claim 1, characterized in that, Step S5 specifically includes: S5.1, The simulation model is used to simulate and evaluate the optimal candidate guide rail to obtain the target values ​​corresponding to the optimal candidate guide rail, namely the linear guide rail stiffness, first natural frequency and weight. S5.2, store the optimal candidate guide rail and its corresponding target values ​​into the database, and update the Gaussian process function model based on all individual vectors in the database; S5.3 Determine whether the three optimization objectives of stiffness, modality and weight corresponding to the current optimal candidate guide rail meet the requirements respectively; if they do, output the optimal parameter values; otherwise, return to step S3 to continue iterative optimization until all objectives meet the requirements and output the optimal parameter values.

8. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-7.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-7.

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