Relay multi-target dimension reduction optimization and optimal solution evaluation method

Abstract

The invention discloses a relay multi-target dimension reduction optimization and optimal solution evaluation method, and belongs to the technical field of relays. Determining a relay multi-objective optimization tolerance hierarchical sequence dimension reduction method; setting an optimal solution evaluation weight of the relay; and considering the optimal and worst optimization conditions, determining a relay optimal solution evaluation method based on the weight: quantitatively describing the importance degree of each to-be-optimized target through the weight, combining the weight with weighted summation and the like to evaluate solutions in an optimal solution set, giving an evaluation value for each optimal solution, and assisting a user in selecting a final optimization scheme. According to the method, the leading-edge dimensionality is reduced, the problems of slow convergence of an optimization algorithm and difficulty in describing and evaluating an optimal solution set caused by excessive targets are solved, the influence of the dimension and order of magnitude of each to-be-optimized target on an optimization result is reduced, subjective experience and objective laws can be comprehensively considered, and the optimization efficiency is improved. And a user is helped to quickly screen out a satisfactory final optimization scheme 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] For the optimization design problem of relays, it is necessary to improve the performance of relays through optimization algorithms on the basis of accurately solving the performance of relays. However, since most performance parameters of relays lack fixed expressions and are difficult to perform differential operations, traditional gradient optimization algorithms are difficult to effectively apply to the optimization design of relays. Although optimization methods such as orthogonal experiments can improve the performance of relays to a certain extent, they are often difficult to find the global optimal solution due to their limited search mechanism. Intelligent optimization algorithms, such as genetic algorithms and particle swarm optimization algorithms, have excellent global search capabilities because they do not require gradient information and are more suitable for the optimization design of relays.

[0003] The optimal design of relays is essentially a multi-objective optimization problem, involving the simultaneous optimization of multiple performance indicators. For this type of problem, a common solution strategy is to transform the multi-objective optimization problem into a single-objective optimization problem by weighted summation and other methods, and then use the single-objective intelligent optimization algorithm to solve it and obtain the final optimization solution. Another strategy is to directly use the multi-objective intelligent optimization algorithm for optimization, obtain an optimal solution set, and then select the final optimization solution from the solution set through an evaluation method.

[0004] However, when the number of optimization targets exceeds three, the convergence speed of the intelligent optimization algorithm will be significantly reduced. At the same time, the high-dimensional Pareto front surface is difficult to display through visualization means (pictures), and the optimization algorithm is also difficult to provide a sufficient number of optimal solutions to describe the Pareto front. These problems make it difficult for users to select the final optimization solution from the optimal solution set.

[0005] To solve the above problems, a feasible solution is to reduce the dimensionality of the optimization problem before multi-objective optimization. The hierarchical sequence method is a commonly used dimensionality reduction method, but previous studies have mostly focused on situations with fewer optimization objectives, and usually only one optimization objective is retained. When the number of optimization objectives increases, the hierarchical sequence method may not be able to find a feasible solution due to too many constraints. Therefore, it is necessary to further improve and optimize it and combine it with the multi-objective intelligent optimization algorithm to take into account both the dimensionality reduction effect and the difficulty of optimization.

[0006] In addition, the existing optimal solution evaluation methods also have certain limitations. Some methods rely entirely on subjective experience and lack objective basis; while other methods are completely based on objective laws and ignore the actual needs and preferences of users. Therefore, it is necessary to study an optimal solution evaluation method that takes into account both subjective and objective factors 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 scheme: 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: The optimization objectives are sorted in descending order of importance using the hierarchical sequence method 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 targets to be optimized as constraints. op <m op , then the optimization function is as follows:

[0012]

[0013] In formula (1):

[0014] F(X) means including 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 sorted 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 optimization design is performed through an intelligent algorithm 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 the users. Therefore, the objective importance obtained by the entropy weight method is introduced into the hierarchical analysis method. The weights are obtained by the hierarchical analysis method, 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 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: construct a pairwise comparison relationship matrix A through the mutual relationship between the targets to be optimized in 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 get 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 targets to be optimized 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 conversion values ​​and have no special meaning;

[0062] RI is the coefficient value

[0063] S30606: Consistency determination:

[0064] If the consistency ratio CR < 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 minimization optimization problem evaluation value:

[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 The characteristics of each target to be optimized are ignored. The optimal value of some targets to be optimized is greater than the worst value of 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, the weighted distance is used instead of the Euclidean distance, and the evaluation value of the minimization optimization problem becomes:

[0076]

[0077] S304: Determine the maximum situation of each target to be optimized in the Pareto optimal solution set 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 and minimum values ​​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 relay multi-objective optimization tolerant hierarchical sequence dimensionality reduction method, reduces the dimension of the Pareto frontier, and solves the problem of slow convergence of the optimization algorithm and difficulty in describing and evaluating the optimal solution set due to the excessive number of targets. Secondly, the concept of fuzzy membership is introduced to reduce the influence of the dimensions and 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 optimal solution set. Finally, compared with the traditional constrained optimization method, the tolerant hierarchical sequence multi-objective optimization method proposed in the present invention not only avoids the difficulty of 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 It is a schematic diagram of a typical rotary relay structure;

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

[0090] The technical solution 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 of 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 into 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 targets to be optimized as constraints. op <m op , then the optimization function is as follows:

[0095]

[0096] In formula (1):

[0097] F(X) means including 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 sorted 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, denoted 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 optimization design is performed through an intelligent algorithm 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 the users. Therefore, the objective importance obtained by the entropy weight method is introduced into the hierarchical analysis method. The weights are obtained by the hierarchical analysis method, 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 subjective and objective data.

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

[0129] S20602: construct a pairwise comparison relationship matrix A through the mutual relationship between the targets to be optimized in 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 get 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 targets to be optimized 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 conversion values ​​and have no special meaning;

[0145] RI is the coefficient value, and the specific value can be found in Table 1. It 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 < 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 and other methods. An evaluation value is given for each optimal solution to assist users in selecting the final optimization solution.

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

[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 The characteristics of each target to be optimized are ignored. The optimal value of some targets to be optimized is greater than the worst value of 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, the weighted distance is used instead of the Euclidean distance, and the evaluation value of the minimization optimization problem becomes:

[0161]

[0162] S304: Since the units and magnitudes of the targets to be optimized are different, the above evaluation method is very disadvantageous for targets with small magnitudes. 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 magnitudes of the targets are unified through calculations, and the maximum value of the targets to be optimized in the Pareto optimal solution set is determined. 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 and minimum values ​​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] Embodiment 1:

[0171] Take a typical rotary relay as an example (such as Figure 3 The effect of the multi-objective dimension reduction optimization and optimal solution evaluation method of the relay proposed in the present invention is verified. Taking the electromagnetic torque, closing speed, closing time, coil power, reed initial pressure and five-objective optimization problems of the relay as an example, the optimization design is carried out.

[0172] First, the dimension of the optimization problem is reduced by the hierarchical sequence method. According to the importance of the target, the most important pull-in speed and the second most important electromagnetic torque are optimized separately. Then the two target optimization results are set as constraints, and the remaining targets are optimized by multi-objective optimization, and finally the Pareto optimal solution set is obtained.

[0173] Figure 4 The optimal solution set is given. The optimal result of the pull-in speed is 446rad / s, which is 5.51% better than the current level. The optimal result of the electromagnetic force is 1.90N×mm, which is 6.15% better than the current level. For the secondary goals, the optimal result of the pull-in time is 1.18ms, which is 2.5% better than the current level. The optimal result of the coil power is 0.439W, which is 6.00% better than the current level. The optimal result of the initial pressure of the reaction spring is 0.014N, which is 16.67% better than the current level. Since each goal cannot be optimized at the same time, the final optimization result is selected here according to 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 equations (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 objectively analyzing the coil power based on the entropy weight method alone is higher than that of the pull-in time and the initial pressure.

[0175] Combined with subjective experience, here according to the hierarchical analysis method, the pull-in time is defined as target 1, the coil power entropy weight is target 2, and the initial pressure entropy weight is target 3, and the above targets are compared in pairs. 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] According to the relationship matrix, the weights of comprehensive subjective experience and objective analysis calculated by formulas (13) to (15) are: pull-in time 0.12, coil power 0.18, and initial pressure 0.70. According to formulas (7) to (10), the consistency ratio CR of the relationship matrix is ​​0.05, which satisfies CR < 0.1. The above weight setting is reasonable. The matrix reflects both subjective and objective factors and describes the importance relationship between each target.

[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 is 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 relay after optimization by the method of the present invention

[0182]

[0183] After optimization, the main target closing speed and electromagnetic torque increased by 4.45% and 3.41% respectively; there was no problem of optimizing one main target while the other main targets deteriorated, and the secondary targets such as coil power and reed initial pressure increased by 5.80% and 13.33% respectively. The effect is better than directly optimizing the relay 5-target problem, which proves that this patented method is more suitable for multi-target optimization of relays.

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

[0185] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description 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 may also be appropriately combined to form other implementation modes 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 in that: The method comprises the following steps: S1: Determine the relay multi-objective optimization tolerance hierarchical sequence dimensionality reduction method; S2: Set the evaluation weight of the relay optimal solution; 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.

2. A relay multi-objective dimensionality reduction optimization and optimal solution evaluation method according to claim 1, characterized in that: The S1 comprises the following steps: S101: The optimization objectives are sorted in descending order of importance using the hierarchical sequence method as f1(X), f2(X)...f i (X); 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 targets to be optimized as constraints. op <m op , then the optimization function is as follows: In formula (1): F(X) means including m op The objective function of the target to be optimized; f1(X),f2(X)...f i (X) represents the targets to be optimized sorted in descending order of importance; Represents the expected value of each target to be optimized; 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; g j (X) represents the jth equality constraint; h k (X) represents the kth inequality constraint; m e 、m u They are all counting units and have no special meaning; X=[x1,x2...x n ] represents n-dimensional decision variables; D represents the n-dimensional decision space; S103: Optimize the most important target to be optimized, and obtain the optimal solution, which is recorded as f1 * : 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: 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 optimization design is performed through an intelligent algorithm to obtain a Pareto optimal solution set, thereby achieving the purpose of reducing the number of targets to be optimized simultaneously.

3. A relay multi-objective dimensionality reduction optimization and optimal solution evaluation method according to claim 2, characterized in that: The S2 comprises the following steps: S201: Standardize each target to be optimized to eliminate the impact of dimension and magnitude differences: 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; Y ij represents the jth objective value of the i-th optimal solution in the Pareto optimal solution; S302: Calculate the empirical distribution of the target value of each optimal solution S203: Calculate the information entropy E of each target to be optimized j : 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: 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 the users. Therefore, the objective importance obtained by the entropy weight method is introduced into the hierarchical analysis method. The weights are obtained by the hierarchical analysis method, 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 subjective and objective data.

4. A relay multi-objective dimensionality reduction optimization and optimal solution evaluation method according to claim 3, characterized in that: The S206 comprises 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: construct a pairwise comparison relationship matrix A through the mutual relationship between the targets to be optimized in the criterion layer, and obtain the relative weights between all the targets to be optimized: In formula (8): a ij Represents the value of the i-th row and j-th column of the relationship matrix A; S20603: Normalize by column to get a normalized matrix S20604: Calculate weight In formula (11): W i Represents the conversion value; S20605: Since the relationship matrix obtained by comparing any two targets to be optimized may not necessarily satisfy consistency: a ij ·a jk =a ik (12) Therefore, the consistency ratio CR is used to verify whether the relationship matrix meets the consistency and determine whether the weight setting is reasonable: In formulas (13)-(16): λ max and CI are conversion values ​​and have no special meaning; RI is the coefficient value; S30606: Consistency determination: If the consistency ratio CR < 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.

5. A relay multi-objective dimensionality reduction optimization and optimal solution evaluation method according to claim 4, characterized in that: The S3 comprises the following steps: S301: Define the minimization optimization problem evaluation value: In formula (17): τ j 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 The characteristics of each target to be optimized are ignored. The optimal value of some targets to be optimized is greater than the worst value of other targets to be optimized. Therefore, the minimum case of each target to be optimized is introduced. 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, the weighted distance is used instead of the Euclidean distance, and the evaluation value of the minimization optimization problem becomes: S304: Determine the maximum situation of each target to be optimized in the Pareto optimal solution set And satisfy formula (19): 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 and minimum values ​​are swapped; S306: The evaluation value of the minimization optimization problem becomes:

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