Multi-objective mixed integer programming layout optimization method based on intelligent orthogonal constraints

Abstract

This invention discloses a multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints, relating to the field of component layout optimization technology. The method includes: establishing a multi-objective layout optimization model based on mixed-integer linear programming; decomposing the multi-objective layout optimization model into two single-objective optimization models, and solving the two single-objective optimization models using mixed-integer programming algorithms respectively; processing the solution results of the two single-objective optimization models using an intelligent orthogonal constraint method to obtain the intelligent Pareto solution set corresponding to the multi-objective layout optimization model; wherein, when establishing the multi-objective layout optimization model, the finite rectangle method is used to decompose non-rectangular components into multiple orthogonal rectangular components, and for the square term in the moment of inertia, a piecewise linearization technique is used to approximate the square term. This invention can embed the multi-objective layout optimization problem into a mixed-integer linear programming framework, significantly improving the solution efficiency and engineering practicality of component layout optimization.

Description

Technical Field

[0001] This invention relates to the field of component layout optimization technology, and in particular to a multi-objective mixed integer programming layout optimization method based on intelligent orthogonal constraints. Background Technology

[0002] Satellite layout plays a crucial role in determining its on-orbit performance and functionality. The purpose of satellite layout design is to arrange electronic components or equipment in appropriate locations within the satellite to meet various system performance requirements, such as mass characteristics and thermal control. As a vital part of the overall satellite design, satellite layout design directly determines the overall performance, development cost, design cycle, and design level of the satellite system.

[0003] As satellite design becomes increasingly complex, optimizing the layout of its internal components becomes a typical multi-objective, multi-constraint combinatorial optimization problem. Optimization objectives typically include reducing system rotational inertia, improving temperature field uniformity, and satisfying center-of-mass constraints. These objectives often conflict with each other, necessitating the search for a set of balanced Pareto optimal solutions to provide decision-makers with multiple options.

[0004] Existing multi-objective optimization methods mainly include weighted methods and Epsilon constraint methods. Among them, the weighted method is highly subjective, and the weight allocation directly affects the final solution, making it difficult to obtain a uniformly distributed Pareto solution set. The Epsilon constraint method requires preset grid parameters, the distribution of the solution set is limited by the grid density, and the computational complexity increases exponentially with the objective dimension, making it difficult to handle high-dimensional problems.

[0005] In the field of satellite layout optimization, Chinese patent document CN110362909A, entitled "Multi-objective Satellite Layout Optimization Design Method," proposes a multi-objective satellite layout optimization design method. This method utilizes Pareto optimality theory and orthogonal constraint methods to decompose the multi-objective problem into a series of single-objective problems for solution, and employs an accelerated particle swarm optimization algorithm to generate an intelligent Pareto solution set, thus improving the solution effect of multi-objective optimization to a certain extent. However, this method still has the following shortcomings in practical applications:

[0006] Limitations of the solution algorithm: The accelerated particle swarm optimization algorithm used is a metaheuristic algorithm. Although it has strong applicability, the solution results are random, and convergence and optimality of the solution are difficult to guarantee. Especially when facing complex engineering problems with high precision and strong constraints, the solution efficiency and quality are significantly insufficient. In contrast, the mixed integer programming (MIP) method can strictly guarantee the optimality of the solution, and its linearized variant—mixed integer linear programming (MILP) method—further improves the solution efficiency. However, the MILP method requires that the objective function and constraints are both linear, while the rotational inertia in layout optimization involves the square of the distance from the component's centroid to the rotation center, which is a nonlinear expression. The existing MILP modeling framework has not yet achieved effective linearization of this type of nonlinear term.

[0007] Insufficient ability to model complex geometric constraints: It failed to effectively solve the problem of modeling geometric non-interference constraints between circular components. The distance calculation between circular components involves nonlinear terms, which are difficult to directly integrate into the optimization model, resulting in obstacles to the coordinated optimization of geometric constraints and thermal, mechanical and other objectives. Summary of the Invention

[0008] To address some or all of the technical problems existing in the prior art, this invention provides a multi-objective mixed integer programming layout optimization method based on intelligent orthogonal constraints.

[0009] The technical solution of the present invention is as follows:

[0010] A multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints is provided, including:

[0011] Using component layout region constraints, component non-interference constraints, and system centroid constraints as constraints, and minimizing rotational inertia and maximizing the temperature field uniformity of the component layout region as optimization objectives, a multi-objective layout optimization model based on mixed integer linear programming is established.

[0012] The multi-objective layout optimization model is decomposed into two single-objective optimization models, and the two single-objective optimization models are solved using a mixed integer programming algorithm to obtain the solution results of the two single-objective optimization models.

[0013] The solution results of the two single-objective optimization models are processed using the intelligent orthogonal constraint method to obtain the intelligent Pareto solution set corresponding to the multi-objective layout optimization model.

[0014] In establishing the multi-objective layout optimization model, for non-rectangular components, the finite rectangle method is used to decompose the non-rectangular components into multiple orthogonal rectangular components, and the component non-interference constraint is established based on the Phi function. For the square term in the moment of inertia, the piecewise linearization technique is used to approximate the square term.

[0015] Furthermore, in some embodiments, the method further includes:

[0016] An approximate description of the component layout area and components is made, and a simplified structural model of the component layout scheme is established. Based on the simplified structural model, a multi-objective layout optimization model based on mixed integer linear programming is established.

[0017] Furthermore, in some embodiments, the approximate description of the component layout area and the component includes:

[0018] The component layout area is approximated as a rectangular area, the component is approximated as a rectangular component or a circular component, and the component mass is set to be evenly distributed and the centroid coincides with the centroid.

[0019] Specifically, the component is approximated as a rectangular component or a circular component based on the minimum outer envelope shape of the component. If the minimum outer envelope shape of the component is circular, the component is approximated as a circular component; if the minimum outer envelope shape of the component is rectangular, the component is approximated as a rectangular component.

[0020] Furthermore, in some embodiments, when the non-rectangular component is a circular component, the finite rectangle method is used to decompose the non-rectangular component into multiple orthogonal rectangular components. The multiple orthogonal rectangular components obtained from the decomposition satisfy the following constraints:

[0021] ;

[0022] in, Indicates the first The first circular component was decomposed to obtain the... A rectangular component is parallel to the coordinate system. Length in the axial direction, Indicates the first The first circular component was decomposed to obtain the... A rectangular component is parallel to the coordinate system. Length in the axial direction, Indicates the first The first circular component was decomposed to obtain the... The center coordinates of the rectangular components Indicates the first The width of the rectangular component obtained by decomposing the circular component. Indicates the first The radius of each circular component, Indicates the first The center coordinates of the circular components Indicates the first The number of rectangular components obtained by decomposing a circular component. As variables, .

[0023] Furthermore, in some implementations, the establishment of component non-interference constraints based on the Phi function includes:

[0024] The Phi function is used to determine the formula for calculating the interference between any two rectangular components. Indicator variables are introduced and the large number method is combined to linearize the formula for calculating the interference, and component non-interference constraints are established.

[0025] The rectangular component includes: an initially determined rectangular component and a rectangular component obtained by decomposing the non-rectangular component.

[0026] Furthermore, in some implementations, the temperature field uniformity of the component layout area is maximized by modeling the amount of interference that minimizes the thermally effective area of ​​the component.

[0027] Furthermore, in some implementations, the optimization objective of maximizing the temperature field uniformity in the component layout area is expressed as:

[0028] ;

[0029] in, The optimization objective value is to maximize the temperature field uniformity in the component layout area. For preset positive numbers, Indicates the first The center coordinates of each component Indicates the first The thermally effective area of ​​each component is parallel to the coordinate system. Length in the axial direction, Indicates the first The thermally effective area of ​​each component is parallel to the coordinate system. Length in the axial direction, Indicates the first The center coordinates of each component Indicates the first The thermally effective area of ​​each component is parallel to the coordinate system. Length in the axial direction, Indicates the first The thermally effective area of ​​each component is parallel to the coordinate system. Length in the axial direction, As an indicator variable, Indicates the number of components.

[0030] Furthermore, in some embodiments, the size of the thermally effective region of the component is determined using the following method:

[0031] ;

[0032] in, Indicates the first Each component is parallel to the coordinate system. Length in the axial direction, Indicates the first Each component is parallel to the coordinate system. Length in the axial direction, Indicates the first The thermally effective area of ​​each component.

[0033] Furthermore, in some implementations, the optimization objective of minimizing the moment of inertia is expressed as:

[0034] ;

[0035] in, This represents the moment of inertia of the component system. Indicates the component layout scheme. , , and Indicates the first The center of each component is On the axis On the axis and Coordinates on the axis Indicates the number of components. Represents the component system relative to the global coordinate system Approximate value corresponding to the translational rotational moment of inertia of the axis. Represents the component system relative to the global coordinate system Approximate value corresponding to the translational rotational inertia of the axis. Represents the component system relative to the global coordinate system Approximate value corresponding to the translational rotational inertia of the axis. Indicates the first The quality of each component Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first The corresponding component of the first Segmentation points Axis coordinates Indicates the first The corresponding component of the first Segmentation points Axis coordinates Indicates the first The corresponding component of the first Segmentation points Axis coordinates This indicates the number of segments or intervals into which the coordinate space is divided. and Indicates the first Each component The lower and upper bounds of the axial coordinates, and Indicates the first Each component The lower and upper bounds of the axial coordinates, and Indicates the first Each component The lower and upper bounds of the axial coordinates, Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point.

[0036] Furthermore, in some embodiments, the step of using the intelligent orthogonal constraint method to process the solution results of the two single-objective optimization models to obtain the intelligent Pareto solution set corresponding to the multi-objective layout optimization model includes the following steps:

[0037] Step 301: Use the solution results of the two single-objective optimization models as positioning points, set an intelligent Pareto solution set with empty initial elements, set the positioning points as Pareto optimal solutions, and store the positioning points as elements in the intelligent Pareto solution set.

[0038] Step 302: Use the location point as the vertex of the Pareto front to construct an ideal approximate line;

[0039] Step 303: Generate multiple uniformly distributed Pareto approximation points on the ideal approximation line;

[0040] Step 304: Remove Pareto approximations that do not meet the set requirements from among multiple Pareto approximations;

[0041] Step 305: Calculate the smart distance between each of the remaining Pareto approximation points and all known Pareto optimal solutions.

[0042] Step 306: Select two Pareto approximation points that are located on both sides of and adjacent to the Pareto approximation point corresponding to the maximum intelligent distance, establish two linear orthogonal constraints, and construct the corresponding single-objective optimization problem based on the two linear orthogonal constraints;

[0043] Step 307: Solve the single-objective optimization problem using a mixed-integer programming algorithm to generate a Pareto solution;

[0044] Step 308: Determine whether the Pareto solution belongs to the Smart Pareto solution set. If yes, store the Pareto solution as an element in the Smart Pareto solution set and designate it as one of the Pareto optimal solutions; otherwise, delete the Pareto solution.

[0045] Step 309: Determine if there are any remaining Pareto approximation points that can generate Pareto solutions. If yes, return to step 302; otherwise, output the smart Pareto solution set.

[0046] The main advantages of the technical solution of this invention are as follows:

[0047] The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints of this invention achieves accurate linearization modeling of the geometric interference of non-rectangular components by using the finite rectangle method, and combines piecewise linearization technology to handle the nonlinear square term in the moment of inertia. It can completely embed the complex multi-objective layout optimization problem into the mixed-integer linear programming framework. By decomposing the multi-objective layout optimization problem into a series of single-objective optimization problems dynamically guided by intelligent orthogonal constraints and directly solvable by mixed-integer programming algorithms, it can ensure the uniformity and diversity of the solution set distribution, and significantly improve the efficiency and engineering practicality of component layout optimization. Attached Figure Description

[0048] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and constitute a part of this invention, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0049] Figure 1 A flowchart of a multi-objective mixed integer programming layout optimization method based on intelligent orthogonal constraints provided in an embodiment of the present invention;

[0050] Figure 2 A schematic plan view of a component layout area and some components arranged thereon, provided for an embodiment of the present invention;

[0051] Figure 3 This is a schematic diagram illustrating the principle of decomposing a circular component using the finite rectangle method, as provided in an embodiment of the present invention.

[0052] Figure 4 A schematic diagram illustrating the relationship between a positioning point and an ideal approximate line, provided in an embodiment of the present invention;

[0053] Figure 5 This is a schematic diagram illustrating the relationship between a Pareto approximation point and a linear orthogonal constraint, provided as an embodiment of the present invention. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0055] The technical solutions provided by the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0056] refer to Figure 1 This invention provides a multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints, which includes the following steps:

[0057] Step 1: Using component layout area constraints, component non-interference constraints, and system centroid constraints as constraints, and minimizing rotational inertia and maximizing the uniformity of temperature field in component layout area as optimization objectives, a multi-objective layout optimization model based on mixed integer linear programming is established.

[0058] Step 2: Decompose the multi-objective layout optimization model into two single-objective optimization models, and solve the two single-objective optimization models using the mixed integer programming algorithm to obtain the solution results of the two single-objective optimization models;

[0059] Step 3: Using the intelligent orthogonal constraint method, process the solution results of the two single-objective optimization models to obtain the intelligent Pareto solution set corresponding to the multi-objective layout optimization model;

[0060] In establishing the multi-objective layout optimization model, for non-rectangular components, the finite rectangle method is used to decompose the non-rectangular components into multiple orthogonal rectangular components, and the component non-interference constraint is established based on the Phi function. For the square term in the moment of inertia, the piecewise linearization technique is used to approximate the square term.

[0061] In this embodiment of the invention, the component layout area constraint means that the component must be placed within the component layout area, the component non-interference constraint means that no two components interfere with each other, and the system centroid constraint means that the distance between the centroid position of the system composed of all components and the desired centroid position does not exceed the preset centroid deviation.

[0062] In this embodiment of the invention, the moment of inertia represents the moment of inertia of the system consisting of all components.

[0063] The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints provided in this invention achieves accurate linearization modeling of the geometric interference of non-rectangular components by using the finite rectangle method, and combines piecewise linearization technology to handle the nonlinear square term in the moment of inertia. It can completely embed the complex multi-objective layout optimization problem into the mixed-integer linear programming framework. By decomposing the multi-objective layout optimization problem into a series of single-objective optimization problems dynamically guided by intelligent orthogonal constraints and directly solvable by mixed-integer programming algorithms, it can ensure the uniformity and diversity of the solution set distribution, and significantly improve the efficiency and engineering practicality of component layout optimization.

[0064] Furthermore, considering the actual situation of component layout optimization, in order to improve the efficiency of component layout optimization solution, in this embodiment of the invention, the component layout area and components are first approximated, a simplified structural model of the component layout scheme is established, and based on the simplified structural model, a multi-objective layout optimization model based on mixed integer linear programming is established.

[0065] In this embodiment of the invention, the approximate description of the component layout area and the component further includes:

[0066] The component layout area is approximated as a rectangular area, and the components are approximated as rectangular or circular components. The component mass is set to be evenly distributed and the centroid coincides with the centroid.

[0067] Specifically, the component is approximated as a rectangular component or a circular component based on the minimum outer envelope shape of the component. If the minimum outer envelope shape of the component is circular, the component is approximated as a circular component; if the minimum outer envelope shape of the component is rectangular, the component is approximated as a rectangular component.

[0068] It should be noted that, based on the above approximate description method, non-rectangular components are represented by circular components.

[0069] In this embodiment of the invention, by approximating the component layout area and components in the above manner, a simplified structural model of the component layout scheme is established, which can improve the efficiency of component layout optimization and ensure the feasibility of the obtained solution set.

[0070] refer to Figure 2 Furthermore, in this embodiment of the invention, the center point of the component layout area is taken as the origin of the global coordinate system. Use either the length or width direction of the component layout area as the global coordinate system. The axis direction is used as the global coordinate system, with the other of the length or width directions of the component layout area as the coordinate system. The axis direction is defined as the direction perpendicular to the plane of the component layout area and pointing upwards, serving as the global coordinate system. Establish a global coordinate system along the axis. Based on the established global coordinate system, a multi-objective layout optimization model based on mixed integer linear programming is established.

[0071] It should be noted that, since components are placed directly on the component layout area during component layout optimization, after determining the system coordinate system, the center of each component is located in the coordinate system when placed in the component layout area. Since the coordinate positions on the axes are fixed, when modeling subsequent constraints on component layout areas, component non-interference constraints, system centroid constraints, and maximizing the uniformity of the temperature field in the component layout area, the position of the component center in the coordinate system is not considered. The coordinate position on the axis.

[0072] Furthermore, in this embodiment of the invention, based on the aforementioned global coordinate system, when establishing a multi-objective layout optimization model based on mixed-integer linear programming, the component layout region constraint is expressed as:

[0073] ;

[0074] in, and Indicates the first The center of each component is On the axis and Coordinates on the axis Indicates the first Each component is parallel to the global coordinate system. Length in the axial direction, Indicates the first Each component is parallel to the global coordinate system. Length in the axial direction, Indicates the component layout area in the global coordinate system Length in the axial direction, Indicates the component layout area in the global coordinate system Length in the axial direction, Indicates the number of components.

[0075] refer to Figure 3 Furthermore, in this embodiment of the invention, in order to achieve linear modeling of non-interference constraints of components, for non-rectangular components, the finite rectangle method is used to decompose the non-rectangular components into multiple orthogonal rectangular components.

[0076] Specifically, based on the above-mentioned approximate description method, non-rectangular components include circular components. In this embodiment of the invention, the circular component is decomposed into multiple orthogonal rectangular components using the finite rectangle method. The multiple orthogonal rectangular components obtained from the decomposition satisfy the following constraints:

[0077] ;

[0078] in, Indicates the first The first circular component was decomposed to obtain the... A rectangular component is parallel to the global coordinate system. Length in the axial direction, Indicates the first The first circular component was decomposed to obtain the... A rectangular component is parallel to the global coordinate system. Length in the axial direction, and Indicates the first The first circular component was decomposed to obtain the... The center of each rectangular component is at On the axis and Coordinates on the axis Indicates the first The width of the rectangular component obtained by decomposing the circular component. Indicates the first The radius of each circular component, and Indicates the first The center of each circular component is at On the axis and Coordinates on the axis Indicates the first The number of rectangular components obtained by decomposing a circular component. As variables, .

[0079] It should be noted that when the circular component is decomposed into multiple orthogonal rectangular components using the finite rectangle method, the resulting multiple rectangular components have the same width.

[0080] Furthermore, in this embodiment of the invention, establishing component non-interference constraints based on the Phi function further includes:

[0081] The Phi function is used to determine the formula for calculating the interference between any two rectangular components. Indicator variables are introduced and the large number method is used to linearize the formula for calculating the interference, thus establishing non-interference constraints between the components.

[0082] In this embodiment of the invention, when establishing non-interference constraints for components, the rectangular component includes: an initially determined rectangular component and a rectangular component obtained by decomposing the non-rectangular component.

[0083] Specifically, in the embodiments of the present invention, the following is defined: the first The first rectangular component and the first The interference between the rectangular components is To ensure that there is no interference between components, the interference amount The following conditions must be met:

[0084] .

[0085] In this embodiment of the invention, the Phi function method is used to calculate the interference between any two rectangular components.

[0086] Specifically, the two rectangular components are respectively the first... The first rectangular component and the first Taking two rectangular components as an example, the formula for calculating the interference between two rectangular components is as follows:

[0087] ;

[0088] in, and Indicates the first The center of each rectangular component is at On the axis and Coordinates on the axis Indicates the first A rectangular component is parallel to the global coordinate system. Length in the axial direction, Indicates the first A rectangular component is parallel to the global coordinate system. Length in the axial direction, and Indicates the first The center of each rectangular component is at On the axis and Coordinates on the axis Indicates the first A rectangular component is parallel to the global coordinate system. Length in the axial direction, Indicates the first A rectangular component is parallel to the global coordinate system. Length in the axial direction, This indicates the number of rectangular components, including the initially determined rectangular components and the rectangular components obtained by decomposing the non-rectangular components.

[0089] Expanding the absolute value operation in the above formula for calculating the interferometric amount, the formula for calculating the interferometric amount can be equivalently transformed into:

[0090] .

[0091] Furthermore, indicator variables are introduced. By linearizing the above interference calculation formula using the method of large numbers, we obtain the following equivalent constraint form, namely the component non-interference constraint:

[0092] ;

[0093] in, For preset positive numbers, The specific settings should be adjusted according to the actual situation, for example... The requirement is that all inequalities in the constraint expression corresponding to the non-interference constraint of the above components must be satisfied simultaneously.

[0094] In the above component non-interference constraints, when At that time, Can be converted If the inequality If true, it means that the component non-interference constraint is satisfied; when At that time, It can degenerate into ,because Since it is a positive constant, this inequality applies regardless of whether interference occurs between components. It is always true; through constraints It is required that at least one of the four indicator variables is equal to 1, thereby satisfying the component non-interference constraint.

[0095] Furthermore, in this embodiment of the invention, based on the aforementioned approximate description method and global coordinate system, the system centroid constraint is expressed as:

[0096] ;

[0097] in, and Indicates that the system's center of mass is at On the axis and Coordinates on the axis Indicates the first The quality of each component and Indicates the expected center of mass is at On the axis and Coordinates on the axis and Indicates the preset centroid deviation is at Axial direction and The component along the axial direction.

[0098] Furthermore, in this embodiment of the invention, the temperature field uniformity of the component layout area is maximized by modeling the interference amount of minimizing the thermally effective region of the component, wherein the thermally effective region of the component is modeled based on the size of the component layout area and the average operating power of the component.

[0099] Specifically, the area of ​​the component layout region is defined as follows: , No. The average operating power of each component is The average heat flux of the component layout area can then be expressed as:

[0100] ;

[0101] This represents the average heat flux over the component layout area.

[0102] In order for each component to achieve an average heat flux, each component must distribute heat uniformly over an area proportional to its power. Therefore, the thermally effective area of ​​a component can be expressed as:

[0103] ;

[0104] Indicates the first The effective thermal area of ​​each component.

[0105] It can be seen that the sum of the thermally effective areas of all components equals the area of ​​the component layout region, specifically:

[0106] .

[0107] Furthermore, based on approximating the components as rectangular or circular components, in order to achieve linearized modeling that maximizes the uniformity of the temperature field in the component layout area, the thermally effective region of the component is modeled as square. Simultaneously, to ensure that the thermally effective region of the component can be adapted to the structural dimensions of the component, the dimensions of the thermally effective region of the component are determined using the following method:

[0108] ;

[0109] in, Indicates the first The thermally active area of ​​each component is parallel to the global coordinate system. Length in the axial direction, Indicates the first The thermally active area of ​​each component is parallel to the global coordinate system. Length in the axial direction, Indicates the first Each component is parallel to the global coordinate system. Length in the axial direction, Indicates the first Each component is parallel to the global coordinate system. Length along the axial direction.

[0110] Based on the definitions of the thermally effective area and thermally effective region of the component, maximizing the uniformity of the temperature field in the component layout area is equivalent to minimizing the interference of the thermally effective region of the component.

[0111] Furthermore, in this embodiment of the invention, the interference amount of the thermally effective region of the component is modeled based on the Phi function. Based on the modeling result of the interference amount of the thermally effective region of the component, the interference amount of minimizing the thermally effective region of the component is modeled, that is, the optimization objective of maximizing the uniformity of the temperature field in the component layout area is modeled.

[0112] Specifically, in this embodiment of the invention, based on the above settings, the following definition is made: the first The thermally effective area of ​​the first component is related to the first... The interference between the thermally effective regions of each component is The two components are respectively the first The component and the first Taking one component as an example, the formula for calculating the interference between the thermally effective regions of two components is as follows:

[0113] ;

[0114] in, and Indicates the first The center of each component is On the axis and Coordinates on the axis Indicates the first The thermally active area of ​​each component is parallel to the global coordinate system. Length in the axial direction, Indicates the first The thermally active area of ​​each component is parallel to the global coordinate system. Length along the axial direction.

[0115] Among them, when If this is the case, it indicates that there is a certain distance between the two effective thermal regions. The value can roughly measure the distance between the two, by reducing This allows the two to move closer to each other; when When this occurs, it indicates that interference has occurred between the two effective thermal regions. The value can roughly measure the amount of interference between the two, by increasing... It can separate the two.

[0116] Expanding the absolute value operation in the above formula for calculating the interference between thermally effective regions, the formula for calculating the interference between thermally effective regions can be equivalently transformed into:

[0117] .

[0118] In this embodiment of the invention, since maximizing the temperature field uniformity of the component layout area is equivalent to minimizing the interference of the thermally effective area of ​​the component, the optimization objective of maximizing the temperature field uniformity of the component layout area can be expressed as the following maximum-minimum form:

[0119] .

[0120] Introducing indicator variables By linearizing the calculation formula for interference between the above-mentioned thermally effective regions using the method of large numbers, and combining this linearized formula, the optimization objective of maximizing the uniformity of the temperature field in the component layout area can be further transformed into the following form:

[0121] ;

[0122] in, The optimization objective value is to maximize the temperature field uniformity in the component layout area. For preset positive numbers, The specific values ​​are set according to the actual situation. In the above optimization objective expression, all inequalities must be satisfied simultaneously to ensure that the interference amount of the thermally effective region of the component is minimized.

[0123] Furthermore, in this embodiment of the invention, based on the aforementioned approximate description method and global coordinate system, the moment of inertia is defined as the sum of the moments of inertia of the component system relative to each principal axis of mass, specifically expressed as:

[0124] ;

[0125] in, This represents the moment of inertia of the component system. Indicates the relative centroid of the component system Moment of inertia of the shaft Indicates the relative centroid of the component system Moment of inertia of the shaft Indicates the relative centroid of the component system Moment of inertia of the shaft Indicates the component layout scheme. , , and Indicates the first The center of each component is On the axis On the axis and Coordinates on the axis.

[0126] Among them, the centroid The axis passes through the centroid of the component system and is parallel to the global coordinate system. The axis of the shaft, the center of mass The axis passes through the centroid of the component system and is parallel to the global coordinate system. The axis of the shaft, the center of mass The axis passes through the centroid of the component system and is parallel to the global coordinate system. The axis of the shaft.

[0127] In this embodiment of the invention, the moment of inertia of the component system relative to each principal axis of mass can be expressed as:

[0128] ;

[0129] in, , and Indicates the first Each component relative to its own coordinate system axis, shaft and Moment of inertia of the shaft , and Indicates the first The center of each component is On the axis On the axis and Coordinates on the axis , and Indicates that the system's center of mass is at On the axis On the axis and Coordinates on the axis Indicates the first The quality of each component Indicates the first The rotation angle of each component Indicates the number of components.

[0130] In this context, the origin of the component's own coordinate system is the center of the component, and the coordinate system of the component itself... The axis passes through the component center and is parallel to the global coordinate system. The axis of the axis, the component's own coordinate system. The axis passes through the component center and is parallel to the global coordinate system. The axis of the axis, the component's own coordinate system. The axis passes through the component center and is parallel to the global coordinate system. The axis of the shaft.

[0131] For a circular component, the component's coordinates relative to its own coordinate system axis, shaft and The moment of inertia of the shaft is expressed as:

[0132] ;

[0133] in, Indicates the quality of the component. Indicates the radius of the component. Indicates the height of the component.

[0134] For a rectangular component, the component's coordinates relative to its own coordinate system axis, shaft and The moment of inertia of the shaft is expressed as:

[0135] ;

[0136] in, Indicates the quality of the component. This indicates that the component is parallel to the global coordinate system. Length in the axial direction, This indicates that the component is parallel to the global coordinate system. Length in the axial direction, Indicates the height of the component.

[0137] Based on the aforementioned approximate description, since the components are all rigid bodies with known shapes and sizes, and their angles are kept fixed during the layout process (i.e., the rotation angle of the component remains 0), the component's coordinates relative to its own coordinate system remain constant during component layout optimization. axis, shaft and The moments of inertia of the shafts are all constants and can be considered as constants.

[0138] For correction terms involving the centroid coordinates of the component system, the specific items include: , and Directly modeling the aforementioned correction terms introduces highly nonlinear coupling terms, significantly increasing the complexity and computational cost of linearization, thus hindering efficient optimization. Considering the introduction of strict system centroid constraints, the overall centroid of the component system is limited to a very small range of fluctuation. In the final optimized component layout scheme, the centroid always strictly satisfies the preset constraints. Therefore, the change in rotational inertia caused by small centroid deviations is controllable, and the magnitude of this change can be continuously reduced by further tightening the system centroid constraint range until the system centroid completely coincides with the desired centroid. Furthermore, compared to the movement of components throughout the layout space, the impact of small changes in the position of the overall centroid of the component system on the objective function is negligible during the optimization process.

[0139] Based on the above analysis, in order to balance computational efficiency and optimized solution accuracy, in this embodiment of the invention, the correction term involving the centroid coordinates of the component system is approximated as a constant error term. Therefore, the moment of inertia of the component system can be simplified as:

[0140] ;

[0141] in, Represents the component system relative to the global coordinate system Translational moment of inertia of the axis Represents the component system relative to the global coordinate system Translational moment of inertia of the axis Represents the component system relative to the global coordinate system Translational moment of inertia of the axis , , , , , These are preset constant terms.

[0142] in, , , , , , , , , .

[0143] Based on the above settings, the optimization objective of minimizing rotational inertia can be mathematically transformed into minimizing the sum of translational rotational inertia determined by the distribution of the centroid positions of each component.

[0144] Specifically, in this embodiment of the invention, the optimization objective of minimizing the moment of inertia can be expressed as:

[0145] .

[0146] Furthermore, considering that the above-mentioned optimization objective expression for minimizing the moment of inertia contains a square term, in order to achieve linear modeling of the optimization objective, in this embodiment of the invention, a piecewise linearization technique is used to approximate the square term in the moment of inertia.

[0147] Specifically, for functions In other words, by using differentiation, any segment of a curve on a function can be differentiated into a straight line, and then for the function... In other words, the differentiated function is a piecewise linear function. Piecewise linear functions can be linearized so that they can be modeled using integer programming techniques.

[0148] Suppose a piecewise linear function exist for There are segmentation points at this point. To set a value, for a given value , , For piecewise linear functions The number of segment points is: Therefore, for a given value , , can Notation:

[0149] ;

[0150] Due to piecewise linear functions for It is linear, so we can divide it into piecewise linear functions. Notation:

[0151] .

[0152] Based on the above analysis, in this embodiment of the invention, a piecewise linear approximation method based on binary variables (PLA method) is used to approximate the square term in the moment of inertia. This is achieved by dividing the coordinate space into multiple intervals and constructing an interpolation structure using a set of weight variables and binary variables.

[0153] Specifically, in this embodiment of the invention, regarding the translational rotational inertia... It can be approximated using the following linearized form:

[0154] ;

[0155] For translational rotational inertia It can be approximated using the following linearized form:

[0156] ;

[0157] For translational rotational inertia It can be approximated using the following linearized form:

[0158] ;

[0159] in, express The corresponding approximate value, express The corresponding approximate value, express The corresponding approximate value, Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first The corresponding component of the first Segmentation points Axis coordinates Indicates the first The corresponding component of the first Segmentation points Axis coordinates Indicates the first The corresponding component of the first Segmentation points Axis coordinates This indicates the number of segments in the coordinate space.

[0160] Based on the principle of the piecewise linear approximation method using binary variables, the parameters in the linearized form of the translational rotational inertia formula described above satisfy the following constraints:

[0161] ;

[0162] in, and Indicates the first Each component The lower and upper bounds of the axial coordinates, and Indicates the first Each component The lower and upper bounds of the axial coordinates, and Indicates the first Each component The lower and upper bounds of the axial coordinates, Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point.

[0163] Among them, binary variables Used to control the activation segment interval, ensuring that only one is active at any given time. Or at most adjacent and Non-zero.

[0164] Based on the above analysis, in this embodiment of the invention, the optimization objective of minimizing the moment of inertia can be transformed into the following linearized form:

[0165] .

[0166] Furthermore, based on the modeling results of the component layout region constraints, component non-interference constraints, and system centroid constraints, as well as the modeling results of minimizing rotational inertia and maximizing the temperature field uniformity of the component layout region, the multi-objective layout optimization model based on mixed-integer linear programming is expressed as follows:

[0167] ;

[0168] in, The objective function represents the uniformity of the temperature field in the component layout area.

[0169] Furthermore, in this embodiment of the invention, the above-mentioned multi-objective layout optimization model based on mixed-integer linear programming is decomposed into two single-objective optimization models based on mixed-integer linear programming. The single-objective optimization models based on mixed-integer linear programming are solved using mixed-integer programming algorithms respectively, and the solution results of the two single-objective optimization models are obtained, that is, the component layout schemes corresponding to the two single-objective optimization models.

[0170] In this approach, existing mathematical programming solvers that integrate mixed-integer programming algorithms can be directly used to solve single-objective optimization models based on mixed-integer linear programming. Examples of mathematical programming solvers include the SCIP optimization solver and the CPLEX optimization solver.

[0171] Furthermore, in this embodiment of the invention, the solution results of two single-objective optimization models are processed using an intelligent orthogonal constraint method to obtain the intelligent Pareto solution set corresponding to the multi-objective layout optimization model, including the following steps 301-309:

[0172] Step 301: Use the solution results of the two single-objective optimization models as positioning points, set an intelligent Pareto solution set with empty initial elements, set the positioning points as Pareto optimal solutions, and store the positioning points as elements in the intelligent Pareto solution set.

[0173] Step 302: Use the location point as the vertex of the Pareto front to construct an ideal approximate line;

[0174] Specifically, based on the two optimization objectives set above, two positioning points are connected to construct an ideal approximate line;

[0175] It should be noted that for optimization problems with more than two objectives, an ideal approximation surface is constructed; the ideal approximation line (or ideal approximation surface) can be calculated using the following formula:

[0176] ;

[0177] in, Represents an ideal approximation line vector. Indicates the first j The location points corresponding to each optimization objective. Indicates the first The location points corresponding to each optimization objective. This represents the number of optimization objectives, from which we can generate... An ideal approximation line.

[0178] Step 303: Generate multiple uniformly distributed Pareto approximation points on the ideal approximation line;

[0179] Specifically, the Pareto approximation point generated on the ideal approximation line can be calculated using the following formula:

[0180] ;

[0181] in, Indicates the first i Pareto approximation points It is a scalar parameter and satisfies the following constraints: and , This indicates the number of optimization objectives.

[0182] Corresponding optimization objectives In this case, the relationship between the positioning point, the ideal approximation line, and the Pareto approximation point is shown in the appendix. Figure 4 As shown, in the appendix Figure 4 In the diagram, the points marked with triangles represent location points. The solid black dot represents the Pareto approximation point. The line connecting two positioning points represents the utopia line, and the curve represents the normal constraint line.

[0183] Step 304: Remove Pareto approximations that do not meet the set requirements from among multiple Pareto approximations;

[0184] Specifically, the requirements include: the Pareto approximation point is not within the defined restrictive region and is not within the PIT region of all known Pareto optimal solutions.

[0185] The definition of the restricted region is the same as that defined in step 308; the PIT (Practically Insignificant Trade-off) region of the Pareto optimal solution represents a region enclosed by the Pareto optimal solution as the center, where the intelligent distance from points on the boundary of the region to the Pareto optimal solution is always equal to 1, and the intelligent distance from points inside the boundary of the region to the Pareto optimal solution is less than 1.

[0186] The intelligent distance is calculated using the following formula:

[0187] ;

[0188] in, , Indicates the first i Insignificant changes to the optimization objective The specific details will be provided based on the actual design requirements. This represents the distance vector between two points. Representing vectors Norm, , Indicates the number of optimization objectives. Representing vectors The Middle Line 1 Column elements, Representing vectors The first in One element, The shape corresponding to the PIT region, The specific value should be determined based on the actual situation.

[0189] Step 305: Calculate the smart distance between each of the remaining Pareto approximation points and all known Pareto optimal solutions.

[0190] Specifically, the intelligent distance between each of the remaining Pareto approximation points and all known Pareto optimal solutions is calculated according to the above-mentioned intelligent distance calculation formula.

[0191] Step 306: Select two Pareto approximation points that are located on both sides of and adjacent to the Pareto approximation point corresponding to the maximum intelligent distance, establish two linear orthogonal constraints, and construct the corresponding single-objective optimization problem based on the two linear orthogonal constraints;

[0192] refer to Figure 5 Specifically, select two adjacent Pareto approximation points located on either side of the Pareto approximation point corresponding to the maximum intelligent distance. and Two linear orthogonal constraints are established, and a corresponding single-objective optimization problem is constructed based on these constraints. The corresponding single-objective optimization problem (SOO) can be expressed as:

[0193] (Formula 5)

[0194] in, This represents the design variable vector, i.e., the component layout scheme. and These represent the upper and lower bounds of the corresponding design variables, This represents the objective function to be optimized. and Let represent the inequality constraint vector and the equality constraint vector, respectively. and These represent two adjacent Pareto approximation points located on either side of the Pareto approximation point corresponding to the maximum intelligent distance. Represents an ideal approximation line vector. This represents the vector consisting of all optimization objective functions. This indicates the number of optimization targets, and the superscript T indicates the transpose operation.

[0195] By adding bidirectional linear orthogonal constraints, the Pareto optimal solution obtained from solving the single-objective optimization model can be restricted to the band-shaped design region formed by the linear orthogonal constraints, thereby reducing the generation of dominant and redundant solutions.

[0196] Step 307: Solve the single-objective optimization problem using a mixed-integer programming algorithm to generate a Pareto solution;

[0197] Specifically, after constructing the single-objective optimization problem, a mixed-integer programming algorithm is used to solve the single-objective optimization problem to generate a Pareto solution. .

[0198] Step 308: Determine whether the Pareto solution belongs to the Smart Pareto solution set. If yes, store the Pareto solution as an element in the Smart Pareto solution set and designate it as one of the Pareto optimal solutions; otherwise, delete the Pareto solution.

[0199] Specifically, regarding how to determine the Pareto solution Whether a solution belongs to the intelligent Pareto solution set is determined by the following method provided in this embodiment: when a newly generated Pareto solution... The Pareto solution is given in the following three cases. It does not belong to the intelligent Pareto solution set;

[0200] Case 1: Newly generated Pareto solution Non-dominant solutions belonging to the known set of intelligent Pareto solutions;

[0201] Case 2: Newly generated Pareto solution It lies within the PIT region of the known Pareto optimal solution;

[0202] The newly generated Pareto solution at this time This is a redundant solution;

[0203] Case 3: Newly generated Pareto solution It is not located on the constraint line or constraint region of a two-way linear orthogonal constraint;

[0204] This indicates that when solving other single-objective optimization problems beyond this one, it is possible to generate a Pareto solution similar to this one. The same solution occurs; this also indicates that the design space within the design region of the linear two-way constraint is discontinuous. In this case, the newly generated Pareto solution... The region between the constraint lines of the bidirectional linear orthogonal constraint is set as a restricted region and preserved.

[0205] Step 309: Determine if there are any remaining Pareto approximation points that can generate Pareto solutions. If yes, return to step 302; otherwise, output the smart Pareto solution set.

[0206] Specifically, if there are extra Pareto approximation points that can generate new Pareto solutions, then return to step 302 and perform iterative optimization again to continuously supplement the intelligent Pareto solution set; if there are no extra Pareto approximation points that can generate new Pareto solutions, then output the final intelligent Pareto solution set.

[0207] After solving the intelligent Pareto solution set for the component layout scheme, since each element in the intelligent Pareto solution set (each Pareto optimal solution) is a feasible component layout scheme, the final layout scheme can be determined based on the obtained intelligent Pareto solution set.

[0208] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Additionally, the terms "front," "back," "left," "right," "upper," and "lower" in this document refer to the placement shown in the accompanying drawings.

[0209] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints, characterized in that, The method includes: Using component layout region constraints, component non-interference constraints, and system centroid constraints as constraints, and minimizing rotational inertia and maximizing the temperature field uniformity of the component layout region as optimization objectives, a multi-objective layout optimization model based on mixed integer linear programming is established. The multi-objective layout optimization model is decomposed into two single-objective optimization models, and the two single-objective optimization models are solved using a mixed integer programming algorithm to obtain the solution results of the two single-objective optimization models. The solution results of the two single-objective optimization models are processed using the intelligent orthogonal constraint method to obtain the intelligent Pareto solution set corresponding to the multi-objective layout optimization model. In establishing the multi-objective layout optimization model, for non-rectangular components, the finite rectangle method is used to decompose the non-rectangular components into multiple orthogonal rectangular components, and the component non-interference constraint is established based on the Phi function. For the square term in the moment of inertia, the piecewise linearization technique is used to approximate the square term. Among them, the correction term involving the centroid coordinates of the component system in the optimization objective of minimizing the moment of inertia is approximated as a constant error term. The square term in the moment of inertia is approximated by a piecewise linear approximation method based on binary variables. The coordinate space is divided into multiple intervals, and an interpolation structure is constructed by a set of weight variables and binary variables. The optimization objective of minimizing the moment of inertia is expressed as: ； in, This represents the moment of inertia of the component system. Indicates the component layout scheme. , , and Indicates the first The center of each component is On the axis On the axis and Coordinates on the axis Indicates the number of components. Represents the component system relative to the global coordinate system Approximate value corresponding to the translational rotational inertia of the axis. Represents the component system relative to the global coordinate system Approximate value corresponding to the translational rotational inertia of the axis. Represents the component system relative to the global coordinate system Approximate value corresponding to the translational rotational inertia of the axis. Indicates the first The quality of each component Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first The corresponding component of the first Segmentation points Axis coordinates Indicates the first The corresponding component of the first Segmentation points Axis coordinates Indicates the first The corresponding component of the first Segmentation points Axis coordinates This indicates the number of segments or intervals into which the coordinate space is divided. and Indicates the first Each component The lower and upper bounds of the axial coordinates, and Indicates the first Each component The lower and upper bounds of the axial coordinates, and Indicates the first Each component The lower and upper bounds of the axial coordinates, Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point Indicates the first Each component in The first in the axial direction The weight of each segment point Indicates the first Each component in The first in the axial direction The binary variables corresponding to each segment point.

2. The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints according to claim 1, characterized in that, The method further includes: An approximate description of the component layout area and components is made, and a simplified structural model of the component layout scheme is established. Based on the simplified structural model, a multi-objective layout optimization model based on mixed integer linear programming is established.

3. The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints according to claim 2, characterized in that, The approximate description of the component layout area and components includes: The component layout area is approximated as a rectangular area, the component is approximated as a rectangular component or a circular component, and the component mass is set to be evenly distributed and the centroid coincides with the centroid. Specifically, the component is approximated as a rectangular component or a circular component based on the minimum outer envelope shape of the component. If the minimum outer envelope shape of the component is circular, the component is approximated as a circular component; if the minimum outer envelope shape of the component is rectangular, the component is approximated as a rectangular component.

4. The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints according to claim 3, characterized in that, When the non-rectangular component is a circular component, the finite rectangle method is used to decompose the non-rectangular component into multiple orthogonal rectangular components. The multiple orthogonal rectangular components obtained by decomposition satisfy the following constraints: ； in, Indicates the first The first circular component was decomposed to obtain the... A rectangular component is parallel to the coordinate system. Length in the axial direction, Indicates the first The first circular component was decomposed to obtain the... A rectangular component is parallel to the coordinate system. Length in the axial direction, Indicates the first The first circular component was decomposed to obtain the... The center coordinates of the rectangular components Indicates the first The width of the rectangular component obtained by decomposing the circular component. Indicates the first The radius of each circular component, Indicates the first The center coordinates of the circular components Indicates the first The number of rectangular components obtained by decomposing a circular component. As variables, .

5. The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints according to claim 1, characterized in that, The component non-interference constraint established based on the Phi function includes: The Phi function is used to determine the formula for calculating the interference between any two rectangular components. Indicator variables are introduced and the large number method is combined to linearize the formula for calculating the interference, and component non-interference constraints are established. The rectangular component includes: an initially determined rectangular component and a rectangular component obtained by decomposing the non-rectangular component.

6. The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints according to claim 1, characterized in that, The temperature field uniformity of the component layout area is maximized by modeling the interference of minimizing the thermally effective area of ​​the component.

7. The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints according to claim 6, characterized in that, The optimization objective of maximizing the temperature field uniformity in the component layout area is expressed as: ； in, The optimization objective value is to maximize the temperature field uniformity in the component layout area. For preset positive numbers, Indicates the first The center coordinates of each component Indicates the first The thermally effective area of ​​each component is parallel to the coordinate system. Length in the axial direction, Indicates the first The thermally effective area of ​​each component is parallel to the coordinate system. Length in the axial direction, Indicates the first The center coordinates of each component Indicates the first The thermally effective area of ​​each component is parallel to the coordinate system. Length in the axial direction, Indicates the first The thermally effective area of ​​each component is parallel to the coordinate system. Length in the axial direction, As an indicator variable, Indicates the number of components.

8. The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints according to claim 7, characterized in that, The dimensions of the thermally effective region of the component are determined using the following methods: ； in, Indicates the first Each component is parallel to the coordinate system. Length in the axial direction, Indicates the first Each component is parallel to the coordinate system. Length in the axial direction, Indicates the first The effective thermal area of ​​each component.

9. The multi-objective mixed-integer programming layout optimization method based on intelligent orthogonal constraints according to claim 1, characterized in that, The process of using the intelligent orthogonal constraint method to process the solution results of the two single-objective optimization models and obtain the intelligent Pareto solution set corresponding to the multi-objective layout optimization model includes the following steps: Step 301: Use the solution results of the two single-objective optimization models as positioning points, set an intelligent Pareto solution set with empty initial elements, set the positioning points as Pareto optimal solutions, and store the positioning points as elements in the intelligent Pareto solution set. Step 302: Use the location point as the vertex of the Pareto front to construct an ideal approximate line; Step 303: Generate multiple uniformly distributed Pareto approximation points on the ideal approximation line; Step 304: Remove Pareto approximations that do not meet the set requirements from among multiple Pareto approximations; Step 305: Calculate the smart distance between each of the remaining Pareto approximation points and all known Pareto optimal solutions. Step 306: Select two Pareto approximation points that are located on both sides of and adjacent to the Pareto approximation point corresponding to the maximum intelligent distance, establish two linear orthogonal constraints, and construct the corresponding single-objective optimization problem based on the two linear orthogonal constraints; Step 307: Solve the single-objective optimization problem using a mixed-integer programming algorithm to generate a Pareto solution; Step 308: Determine whether the Pareto solution belongs to the Smart Pareto solution set. If yes, store the Pareto solution as an element in the Smart Pareto solution set and designate it as one of the Pareto optimal solutions; otherwise, delete the Pareto solution. Step 309: Determine if there are any remaining Pareto approximation points that can generate Pareto solutions. If yes, return to step 302; otherwise, output the smart Pareto solution set.

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