A multi-objective dimensionality reduction optimization and optimal solution evaluation method for relays

Abstract

A relay multi-objective dimensionality reduction optimization and optimal solution evaluation method belongs to the field of relay technology. Determine a relay multi-objective optimization tolerance hierarchical sequence dimensionality reduction method; set the relay optimal solution evaluation weight; consider the best and worst optimization situations, and determine the weight-based relay optimal solution evaluation method: quantitatively describe the importance of each target to be optimized by weight, combine the weight with weighted summation and other methods to evaluate the solutions in the optimal solution set, give an evaluation value for each optimal solution, and assist the user in selecting the final optimization solution. The present invention reduces the dimension of the frontier, solves the problem of slow convergence of the optimization algorithm caused by too many targets and the difficulty in describing and evaluating the optimal solution set, reduces the influence of the dimensions and orders of magnitude of each target to be optimized on the optimization results, can comprehensively consider subjective experience and objective laws, and help users quickly screen out a satisfactory final optimization solution from a huge optimal solution set.

Description

Technical Field

[0001] The invention relates to a relay multi-objective dimension reduction optimization and optimal solution evaluation method, belonging to the technical field of relays. Background Art

[0002] The optimization design of relays requires accurate calculations of relay performance and the use of optimization algorithms to improve it. However, because most relay performance parameters lack fixed expressions and are difficult to differentiate, traditional gradient optimization algorithms are difficult to effectively apply to relay optimization design. While optimization methods such as orthogonal experiments can improve relay performance to a certain extent, they are often limited by their search mechanisms and struggle to find the global optimal solution. Intelligent optimization algorithms, such as genetic algorithms and particle swarm optimization, possess superior global search capabilities because they do not require gradient information, making them more suitable for relay optimization design.

[0003] Relay optimization is essentially a multi-objective optimization problem, involving the simultaneous optimization of multiple performance indicators. A common solution for this type of problem is to transform the multi-objective optimization problem into a single-objective one using methods such as weighted summation. This problem is then solved using a single-objective intelligent optimization algorithm to obtain the final optimal solution. Another strategy involves directly employing a multi-objective intelligent optimization algorithm to obtain an optimal solution set. The final optimal solution is then selected from this set through evaluation methods.

[0004] However, when the number of optimization objectives exceeds three, the convergence rate of intelligent optimization algorithms slows significantly. Furthermore, the high-dimensional Pareto front surface is difficult to visualize (e.g., images), and the optimization algorithm struggles to provide a sufficient number of optimal solutions to describe the Pareto front. These issues make it difficult for users to select the final optimization solution from the set of optimal solutions.

[0005] To address these issues, one feasible solution is to perform dimensionality reduction on the optimization problem before multi-objective optimization. The hierarchical sequence method (HSM) is a commonly used dimensionality reduction method, but previous studies have primarily focused on situations with a small number of optimization objectives, typically retaining only a single objective. When the number of optimization objectives increases, the HSM may be unable to find a feasible solution due to the excessive number of constraints. Therefore, further improvements and optimizations are needed, combined with multi-objective intelligent optimization algorithms to balance dimensionality reduction effectiveness with optimization difficulty.

[0006] Furthermore, existing optimal solution evaluation methods have limitations. Some rely solely on subjective experience and lack objective evidence, while others are based solely on objective laws and ignore the user's actual needs and preferences. Therefore, it is necessary to develop an optimal solution evaluation method that takes both subjective and objective factors into account to help users select the final optimization solution from the optimal solution set, thereby completing the multi-objective optimization design of relays. Summary of the Invention

[0007] In order to solve the problems existing in the background technology, the present invention provides a relay multi-objective dimensionality reduction optimization and optimal solution evaluation method.

[0008] To achieve the above object, the present invention adopts the following technical solution: a relay multi-objective dimensionality reduction optimization and optimal solution evaluation method, the method comprising the following steps:

[0009] S1: Determine the relay multi-objective optimization tolerance hierarchical sequence dimensionality reduction method;

[0010] S101: Use the hierarchical sequence method to sort the optimization objectives in descending order of importance as f1(X), f2(X)...f i (X);

[0011] S102: For m op The multi-objective optimization problem in which the objective functions to be optimized are minimized at the same time, assuming that the first n op There are n objectives to be optimized as constraints, op <m op , then the optimization function is as follows:

[0012]

[0013] In formula (1):

[0014] F(X) means containing m op The objective function of the target to be optimized;

[0015] f1(X),f2(X)...f i (X) represents the targets to be optimized, which are ranked in descending order of importance;

[0016] Represents the expected value of each target to be optimized;

[0017] f p (X) indicates the first n numbers sorted in descending order of importance. op The pth target to be optimized among the targets to be optimized;

[0018] g j (X) represents the jth equality constraint;

[0019] h k (X) represents the kth inequality constraint;

[0020] m e 、m u They are all counting units and have no special meaning;

[0021] X=[x1,x2...x n ] represents n-dimensional decision variables;

[0022] D represents the n-dimensional decision space;

[0023] S103: Optimize the most important target to be optimized, and obtain the optimal solution, which is recorded as f1 * :

[0024]

[0025] S104: The optimal solution f1 * As a constraint, the next target to be optimized is recorded and optimized, and since the optimal solution is the only solution, which means that the subsequent optimization will not be able to find other feasible solutions, so the optimal solution Perform tolerance processing, that is, give a tolerance value ε1 to ensure that the result is consistent with the optimal solution The phase difference tolerance value ε1 can also meet the optimization requirements, and we can get:

[0026]

[0027] S105: confirm whether the remaining target number meets the user's requirements. If not, repeat S204 until the remaining target number meets the user's requirements.

[0028] S106: When the number of remaining targets meets the user's requirements, an intelligent algorithm is used to perform optimization design to obtain a Pareto optimal solution set, thereby achieving the purpose of reducing the number of targets to be optimized simultaneously.

[0029] S2: Set the evaluation weight of the relay optimal solution;

[0030] S201: Standardize each target to be optimized to eliminate the impact of dimension and magnitude differences:

[0031]

[0032] In formula (4):

[0033] Represents the standardized target value, i=1,…,n p ; j = 1,…,m op ;

[0034] m op is the number of objectives to be optimized in the Pareto optimal solution set;

[0035] n p is the number of optimal solutions in the Pareto optimal solution set;

[0036] Y ij represents the jth objective value of the i-th optimal solution in the Pareto optimal solution;

[0037] S302: Calculate the empirical distribution of the target value of each optimal solution

[0038]

[0039] S203: Calculate the information entropy E of each target to be optimized j :

[0040]

[0041] S204: Assuming that there is only one target to be optimized and the target values for all solutions are the same, then the target does not contain any information and its information entropy is 1. At this time, the corresponding weight of the target is 0. Therefore, the entropy weight τ is defined as Sj as follows:

[0042]

[0043] S205: Calculate the entropy weight corresponding to each target to be optimized;

[0044] S206: Formula (7) only considers the objective laws of the data and ignores the subjective preferences of users. Therefore, the objective importance obtained by the entropy weight method is introduced into the hierarchical analysis method. The hierarchical analysis method is used to obtain the weights, and the importance is compared between each two targets. The evaluation scale is clearly given, which is suitable for quantitatively determining the weights to achieve the purpose of taking into account the influence of both subjective and objective data.

[0045] S20601: Based on the analytic hierarchy process, the relay optimization problem is divided into the target layer, the criterion layer and the solution layer;

[0046] S20602: Build a pairwise comparison relationship matrix A based on the mutual relationships between the targets to be optimized at the criterion layer, and obtain the relative weights between all the targets to be optimized:

[0047]

[0048] In formula (8):

[0049] a ij Represents the value of the i-th row and j-th column of the relationship matrix A;

[0050] S20603: Normalize by column to obtain a normalized matrix

[0051]

[0052] S20604: Calculate weight

[0053]

[0054] In formula (11):

[0055] W i Represents the conversion value;

[0056] S20605: Since the relationship matrix obtained by comparing any two optimization targets may not necessarily satisfy consistency:

[0057] a ij ·a jk =a ik (12)

[0058] Therefore, the consistency ratio CR is used to verify whether the relationship matrix meets the consistency and determine whether the weight setting is reasonable:

[0059]

[0060] In formulas (13)-(16):

[0061] λ max and CI are converted values and have no special meaning;

[0062] RI is the coefficient value

[0063] S30606: Consistency determination:

[0064] If the consistency ratio CR is less than 0.1, it means that the relationship matrix is consistent, the weight setting meets the requirements, and the relationship matrix describes the importance relationship between the objectives to be optimized;

[0065] If the consistency ratio CR>0.1, the relationship matrix is deemed to have poor consistency, and the criterion layer relationship matrix and weights are adjusted to be qualified.

[0066] S3: Considering the best and worst optimization situations, determine the weight-based evaluation method for the relay optimal solution: quantitatively describe the importance of each target to be optimized through weights, and combine the weights with weighted summation to evaluate the solutions in the Pareto optimal solution set. Give an evaluation value for each optimal solution to assist users in selecting the final optimization plan.

[0067] S301: Define the evaluation value of the minimization optimization problem:

[0068]

[0069] In formula (17):

[0070] τ j Represents the weight of each target to be optimized;

[0071] S302: Theoretically, the evaluation value pw i is the desired final optimization solution, but due to the evaluation value pw i Ignoring the characteristics of each target to be optimized, the optimal value of some targets to be optimized is greater than the worst value of the other targets to be optimized. Therefore, the minimum case of each target to be optimized is introduced.

[0072]

[0073] In formula (18):

[0074] Indicates the minimum situation of each target to be optimized;

[0075] S303: Since the minimum case of each target to be optimized is the set of optimization results of each target to be optimized without considering the influence of other targets, there is no optimal solution that can reach the minimum case in the actual optimization process. Therefore, the optimal solution closest to the minimum case is the optimal solution with the best performance. Considering the different importance of each target to be optimized, weighted distance is used instead of Euclidean distance, and the evaluation value of the minimization optimization problem becomes:

[0076]

[0077] S304: Determine the maximum value of each target to be optimized by setting the Pareto optimal solution And satisfy formula (19):

[0078]

[0079] S305: Replace the weighted distance in equation (19) with the new distance D through the fuzzy membership function i :

[0080]

[0081] If the expected value of the optimization target is large, the maximum value and the minimum value are swapped;

[0082] S306: The evaluation value of the minimization optimization problem becomes:

[0083]

[0084] Compared with the prior art, the present invention has the following beneficial effects:

[0085] The present invention transforms the complex relay multi-objective optimization problem into a more tractable constrained optimization problem through a tolerant hierarchical sequence dimensionality reduction method for relay multi-objective optimization, reduces the dimension of the Pareto frontier, and solves the problems of slow convergence of the optimization algorithm and difficulty in describing and evaluating the optimal solution set due to the excessive number of objectives. Secondly, the concept of fuzzy membership is introduced to reduce the influence of the dimension and order of magnitude of each target to be optimized on the optimization result. Furthermore, a weight-based evaluation value calculation method is proposed, which can comprehensively consider subjective experience and objective laws, and provide users with a scientific and quantifiable evaluation standard, thereby helping users to quickly screen out a satisfactory final optimization solution from a huge set of optimal solutions. Finally, compared with traditional constrained optimization methods, the tolerant hierarchical sequence multi-objective optimization method proposed in the present invention not only avoids the problem of difficulty in determining the expected value, but also fully considers the optimal and worst cases, ensuring the optimization effect of each target, so that the final optimization solution is more in line with actual needs and has higher practicality and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 is a flow chart of S1 of the present invention;

[0087] Figure 2 It is a flow chart of the weight-based relay optimal solution evaluation method;

[0088] Figure 3 This is a schematic diagram of a typical rotary relay structure;

[0089] Figure 4 This is a schematic diagram of the optimal solution set of Example 1. DETAILED DESCRIPTION

[0090] The technical solutions of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0091] A relay multi-objective dimensionality reduction optimization and optimal solution evaluation method, the method comprising the following steps:

[0092] S1: Determine the relay multi-objective optimization tolerance hierarchical sequence dimensionality reduction method;

[0093] S101: In order to avoid the problem that the expected value is difficult to determine in the process of processing the optimization problem by the commonly used constraint method, and the problem that the optimization algorithm may not be able to find a feasible solution when the expected value is set unreasonably, the present invention uses a hierarchical sequence method to sort the optimization objectives in descending order of importance as f1(X), f2(X)...f i (X);

[0094] S102: For m op The multi-objective optimization problem in which the objective functions to be optimized are minimized at the same time, assuming that the first n op There are n objectives to be optimized as constraints, op <m op , then the optimization function is as follows:

[0095]

[0096] In formula (1):

[0097] F(X) means containing m op The objective function of the target to be optimized;

[0098] f1(X),f2(X)...f i (X) represents the targets to be optimized, which are ranked in descending order of importance;

[0099] Represents the expected value of each target to be optimized;

[0100] f p (X) indicates the first n numbers sorted in descending order of importance. op The pth target to be optimized among the targets to be optimized;

[0101] g j (X) represents the jth equality constraint;

[0102] h k (X) represents the kth inequality constraint;

[0103] m e 、m u They are all counting units and have no special meaning;

[0104] X=[x1,x2...x n ] represents n-dimensional decision variables;

[0105] D represents the n-dimensional decision space;

[0106] S103: Optimize the most important target to be optimized and obtain the optimal solution, which is recorded as

[0107]

[0108] S104: The optimal solution f1 * As a constraint, the next target to be optimized is recorded and optimized, and since the optimal solution is the only solution, which means that the subsequent optimization will not be able to find other feasible solutions, so the optimal solution Perform tolerance processing, that is, give a tolerance value ε1 to ensure that the result is consistent with the optimal solution The phase difference tolerance value ε1 can also meet the optimization requirements, and we can get:

[0109]

[0110] S105: confirm whether the remaining target number meets the user's requirements. If not, repeat S204 until the remaining target number meets the user's requirements.

[0111] S106: When the number of remaining targets meets the user's requirements, an intelligent algorithm is used to perform optimization design to obtain a Pareto optimal solution set, thereby achieving the purpose of reducing the number of targets to be optimized simultaneously.

[0112] S2: Set the evaluation weight of the relay optimal solution;

[0113] S201: Standardize each target to be optimized to eliminate the impact of dimension and magnitude differences:

[0114]

[0115] In formula (4):

[0116] Represents the standardized target value, i=1,…,n p ; j = 1,…,m op ;

[0117] m op is the number of objectives to be optimized in the Pareto optimal solution set;

[0118] n p is the number of optimal solutions in the Pareto optimal solution set;

[0119] Y ij represents the jth objective value of the i-th optimal solution in the Pareto optimal solution;

[0120] S302: Calculate the empirical distribution of the target value of each optimal solution

[0121]

[0122] S203: Calculate the information entropy E of each target to be optimizedj :

[0123]

[0124] S204: Assuming that there is only one target to be optimized and the target values for all solutions are the same, then the target does not contain any information and its information entropy is 1. At this time, the corresponding weight of the target is 0. Therefore, the entropy weight τ is defined as Sj as follows:

[0125]

[0126] S205: Calculate the entropy weight corresponding to each target to be optimized;

[0127] S206: Formula (7) only considers the objective laws of the data and ignores the subjective preferences of users. Therefore, the objective importance obtained by the entropy weight method is introduced into the hierarchical analysis method. The hierarchical analysis method is used to obtain the weights, and the importance is compared between each two targets. The evaluation scale is clearly given, which is suitable for quantitatively determining the weights to achieve the purpose of taking into account the influence of both subjective and objective data.

[0128] S20601: Based on the analytic hierarchy process, the relay optimization problem is divided into the target layer (to achieve relay optimization design), the criterion layer (each target to be optimized), and the solution layer (optimization result solution);

[0129] S20602: Build a pairwise comparison relationship matrix A based on the mutual relationships between the targets to be optimized at the criterion layer, and obtain the relative weights between all the targets to be optimized:

[0130]

[0131] In formula (8):

[0132] a ij Represents the value of the i-th row and j-th column of the relationship matrix A;

[0133] S20603: Normalize by column to obtain a normalized matrix

[0134]

[0135] S20604: Calculate weight

[0136]

[0137] In formula (11):

[0138] W i Represents the conversion value;

[0139] S20605: Since the relationship matrix obtained by comparing any two optimization targets may not necessarily satisfy consistency:

[0140] a ij ·a jk =a ik (12)

[0141] Therefore, the consistency ratio CR is used to verify whether the relationship matrix meets the consistency and determine whether the weight setting is reasonable:

[0142]

[0143] In formulas (13)-(16):

[0144] λ max and CI are converted values and have no special meaning;

[0145] RI is the coefficient value, the specific value can be found in Table 1, which is the average random consistency of the relationship matrix at different orders.

[0146] Table 1 RI changes with the number of relay optimization targets

[0147]

[0148] S30606: Consistency determination:

[0149] If the consistency ratio CR is less than 0.1, it means that the relationship matrix is consistent, the weight setting meets the requirements, and the relationship matrix describes the importance relationship between the objectives to be optimized;

[0150] If the consistency ratio CR>0.1, the relationship matrix is deemed to have poor consistency, and the criterion layer relationship matrix and weights are adjusted to be qualified.

[0151] S3: Consider the best and worst optimization situations, such as Figure 2 As shown in the figure, a weight-based evaluation method for relay optimal solutions is determined: the importance of each target to be optimized is quantitatively described by weight, and the solutions in the Pareto optimal solution set can be evaluated by combining the weight with weighted summation. An evaluation value is given for each optimal solution to assist users in selecting the final optimization solution.

[0152] S301: Define the evaluation value of the minimization optimization problem:

[0153]

[0154] In formula (17):

[0155] τ j Represents the weight of each target to be optimized;

[0156] S302: Theoretically, the evaluation value pw i is the desired final optimization solution, but due to the evaluation value pw i Ignoring the characteristics of each target to be optimized, the optimal value of some targets to be optimized is greater than the worst value of the other targets to be optimized. Therefore, the minimum case of each target to be optimized is introduced.

[0157]

[0158] In formula (18):

[0159] Indicates the minimum situation of each target to be optimized;

[0160] S303: Since the minimum case of each target to be optimized is the set of optimization results of each target to be optimized without considering the influence of other targets, there is no optimal solution that can reach the minimum case in the actual optimization process. Therefore, the optimal solution closest to the minimum case is the optimal solution with the best performance. Considering the different importance of each target to be optimized, weighted distance is used instead of Euclidean distance, and the evaluation value of the minimization optimization problem becomes:

[0161]

[0162] S304: Due to the different units and orders of magnitude between the targets to be optimized, the above evaluation method is extremely disadvantageous for targets with small orders of magnitude. For example, the electromagnetic force of a relay can reach tens or even hundreds of Newtons, while its pull-in time is only milliseconds or even lower. Therefore, the orders of magnitude of each target are unified through calculation, and the maximum value of each target to be optimized is determined by determining the Pareto optimal solution set. And satisfy formula (19):

[0163]

[0164] S305: Replace the weighted distance in equation (19) with the new distance D through the fuzzy membership function i :

[0165]

[0166] If the expected value of the optimization target is large, the maximum value and the minimum value are swapped;

[0167] S306: The evaluation value of the minimization optimization problem becomes:

[0168]

[0169] Denominator term in fuzzy membership function This method effectively solves the problem of different units and orders of magnitude among the objectives to be optimized. Therefore, the judgment effect of this method is better than the above-mentioned direct weighted summation method and the method of using the minimum case alone.

[0170] Example 1:

[0171] Take a typical rotary relay as an example (such as Figure 3 The effectiveness of the proposed multi-objective dimensionality reduction optimization and optimal solution evaluation method for relays was verified. The optimization design was performed using a five-objective optimization problem involving electromagnetic torque, closing speed, closing time, coil power, and initial reed pressure as an example.

[0172] First, the dimensionality of the optimization problem is reduced using a hierarchical sequence method. Based on the importance of the objectives, single-objective optimization is performed for the most important objective, the pull-in speed, and the less important objective, the electromagnetic torque. The optimization results of these two objectives are then set as constraints, and multi-objective optimization is performed on the remaining objectives, ultimately obtaining a Pareto optimal solution set.

[0173] Figure 4 The optimal solution set was obtained. The optimal closing speed was 446 rad / s, a 5.51% improvement over the current state of the art. The optimal electromagnetic force was 1.90 N×mm, a 6.15% improvement over the current state of the art. Secondary objectives included: closing time was 1.18 ms, a 2.5% improvement over the current state of the art. The optimal coil power was 0.439 W, a 6.00% improvement over the current state of the art. The optimal initial pressure of the reaction spring was 0.014 N, a 16.67% improvement over the current state of the art. Since it was impossible to achieve optimality for all objectives simultaneously, the final optimization result was selected based on the optimal solution evaluation method.

[0174] In order to evaluate the optimal solution and select the final optimization scheme, according to the method described in the present invention, the entropy weight of each optimization target must first be calculated. For the optimal solution in the optimal solution set obtained by optimization, according to formulas (8) to (11), the entropy weight of the pull-in time is 0.16, the entropy weight of the coil power is 0.69, and the entropy weight of the initial pressure is 0.14. Therefore, the importance of the coil power is higher than the pull-in time and the initial pressure when objectively analyzed based on the entropy weight method alone.

[0175] Combined with subjective experience, here we define the pull-in time as target 1, the coil power entropy weight as target 2, and the initial pressure entropy weight as target 3 according to the hierarchical analysis method, and compare these targets pairwise. Since the initial pressure is directly related to the mechanical resistance of the relay, the higher the better, and the margin between coil power and pull-in time is large, it is judged from experience that the initial pressure is more important than the pull-in time and coil power. In the tolerance hierarchical analysis method, a 31 ,a 32It should be 5. Compared with the pull-in time, the coil power is difficult to judge subjectively. The coil power judged by the entropy weight is more important. To ensure that the consistency ratio meets the requirements, a is set here. 31 is 5, a 32 is 5, a 21 is 2, and the final relationship matrix is:

[0176]

[0177] Based on this relationship matrix, the weights of the comprehensive subjective experience and objective analysis calculated using equations (13) to (15) are: 0.12 for pull-in time, 0.18 for coil power, and 0.70 for initial pressure. The consistency ratio (CR) of this relationship matrix calculated using equations (7) to (10) is 0.05, satisfying CR < 0.1. The above weight settings are reasonable. This matrix reflects both subjective and objective factors and describes the importance relationship between each objective.

[0178] The final optimization scheme here selects the optimal solution with the smallest evaluation value as shown in Table 2, and the optimization effect is shown in Table 3, where the armature height is h1, the core diameter is r, the number of coil turns N, and the initial pressure f c1 , static pressure f c2 .

[0179] Table 2 Optimized relay parameter levels

[0180]

[0181] Table 3 Current results of each target of the relay after optimization by the method of the present invention

[0182]

[0183] After optimization, the primary objectives of closing speed and electromagnetic torque increased by 4.45% and 3.41%, respectively. The issue of optimizing one primary objective while degrading the others was resolved. Meanwhile, secondary objectives such as coil power and reed initial pressure increased by 5.80% and 13.33%, respectively. This result is superior to directly optimizing the relay's five-objective problem, demonstrating that this patented method is more suitable for multi-objective relay optimization.

[0184] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the invention can be embodied in other forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the invention is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

[0185] In addition, it should be understood that although this specification is described in terms of implementation methods, not every implementation method contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A relay multi-objective dimensionality reduction optimization and optimal solution evaluation method, characterized by: The method comprises the following steps: S1: Determine the relay multi-objective optimization tolerance hierarchical sequence dimensionality reduction method; The S1 comprises the following steps: S101: Use the hierarchical sequence method to sort the optimization objectives in descending order of importance. ; S102: For m op The multi-objective optimization problem in which the objective functions to be optimized are minimized at the same time, assuming that the first n op There are n objectives to be optimized as constraints, op <m op , then the optimization function is as follows: (1) In formula (1): F(X) means containing m op An objective function of a target to be optimized, wherein the target to be optimized includes pull-in speed, electromagnetic torque, pull-in time, coil power, and initial pressure; Indicates the goals to be optimized sorted in descending order of importance; Represents the expected value of each target to be optimized; Indicates the first n items sorted in descending order of importance op The first of the objectives to be optimized A target to be optimized; represents the jth equality constraint; represents the kth inequality constraint; m e 、m u They are all counting units and have no special meaning; represents n-dimensional decision variables; D represents the n-dimensional decision space, including armature height, core diameter, coil turns, initial pressure, and static pressure; S103: Optimize the most important target to be optimized and obtain the optimal solution, which is recorded as : (2) S104: The optimal solution As a constraint, the next target to be optimized is recorded and optimized, and since the optimal solution is the only solution, which means that the subsequent optimization will not be able to find other feasible solutions, so the optimal solution Perform tolerance processing, that is, give a tolerance value ε1 to ensure that the result is consistent with the optimal solution The phase difference tolerance value ε1 can also meet the optimization requirements, and we can get: (3) S105: confirm whether the remaining target number meets the user's requirements. If not, repeat S204 until the remaining target number meets the user's requirements. S106: When the number of remaining targets meets the user's requirements, an intelligent algorithm is used to optimize the design and obtain a Pareto optimal solution set, thereby reducing the number of targets to be optimized simultaneously. S2: Set the evaluation weight of the relay optimal solution; The S2 comprises the following steps: S201: Standardize each target to be optimized to eliminate the impact of dimension and magnitude differences: (4) In formula (4): represents the standardized target value, i=1,…, n p ; j = 1,…, m op ; m op is the number of objectives to be optimized in the Pareto optimal solution set; n p is the number of optimal solutions in the Pareto optimal solution set; represents the jth objective value of the i-th optimal solution in the Pareto optimal solution; S202: Calculate the empirical distribution of the target value of each optimal solution : (5) S203: Calculate the information entropy of each target to be optimized : (6) S204: Assuming that there is only one target to be optimized and the target values for all solutions are the same, then the target does not contain any information and its information entropy is 1. At this time, the corresponding weight of the target is 0. Therefore, the entropy weight is defined as as follows: (7) S205: Calculate the entropy weight corresponding to each target to be optimized; S206: Formula (7) only considers the objective laws of the data and ignores the subjective preferences of users. Therefore, the objective importance obtained by the entropy weight method is introduced into the hierarchical analysis method. The hierarchical analysis method is used to obtain the weights, and the importance is compared between each two targets. The evaluation scale is clearly given, which is suitable for quantitatively determining the weights to achieve the purpose of taking into account the influence of both subjective and objective data. S3: Considering the best and worst optimization situations, determine the weight-based evaluation method for relay optimal solutions: quantitatively describe the importance of each optimization target through weights, combine weights with weighted summation and other methods to evaluate the solutions in the Pareto optimal solution set, and provide an evaluation value for each optimal solution to assist users in selecting the final optimization solution; The S3 comprises the following steps: S301: Define the evaluation value of the minimization optimization problem: (17) In formula (17): Represents the weight of each target to be optimized; S302: Theoretically, the evaluation value pw i is the desired final optimization solution, but due to the evaluation value pw i Ignoring the characteristics of each target to be optimized, the optimal value of some targets to be optimized is greater than the worst value of the other targets to be optimized. Therefore, the minimum case of each target to be optimized is introduced. : (18) In formula (18): Indicates the minimum situation of each target to be optimized; S303: Since the minimum case of each target to be optimized is the set of optimization results of each target to be optimized without considering the influence of other targets, there is no optimal solution that can reach the minimum case in the actual optimization process. Therefore, the optimal solution closest to the minimum case is the optimal solution with the best performance. Considering the different importance of each target to be optimized, weighted distance is used instead of Euclidean distance, and the evaluation value of the minimization optimization problem becomes: (19) S304: Determine the maximum value of each target to be optimized by setting the Pareto optimal solution And satisfy formula (19): (20) S305: Replace the weighted distance in equation (19) with the new distance D through the fuzzy membership function i : ( ) If the expected value of the optimization target is large, the maximum value and the minimum value are swapped; S306: The evaluation value of the minimization optimization problem becomes: ( )。 2. A relay multi-objective dimensionality reduction optimization and optimal solution evaluation method according to claim 1, characterized in that: The S206 includes the following steps: S20601: Based on the analytic hierarchy process, the relay optimization problem is divided into the target layer, the criterion layer and the solution layer; S20602: Build a pairwise comparison relationship matrix A based on the mutual relationships between the targets to be optimized at the criterion layer, and obtain the relative weights between all the targets to be optimized: (8) In formula (8): Represents the value of the i-th row and j-th column of the relationship matrix A; S20603: Normalize by column to obtain a normalized matrix : (9) S20604: Calculate weight : (10) (11) Mode( )middle: Represents the conversion value; S20605: Since the relationship matrix obtained by comparing any two optimization targets may not necessarily satisfy consistency: ( ) Therefore, the consistency ratio CR is used to verify whether the relationship matrix meets the consistency and determine whether the weight setting is reasonable: ( ) ( ) ( ) (16) Mode( )-(16): 、 and CI are converted values and have no special meaning; RI is the coefficient value; S30606: Consistency determination: If the consistency ratio CR is less than 0.1, it means that the relationship matrix is consistent, the weight setting meets the requirements, and the relationship matrix describes the importance relationship between the objectives to be optimized; If the consistency ratio CR>0.1, the relationship matrix is deemed to have poor consistency, and the criterion layer relationship matrix and weights are adjusted to be qualified.

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