CN116701830B - Pareto front edge solution optimization method based on fuzzy rule and stability reasoning control - Google Patents

Abstract

The present application is a Pareto front solution optimization method based on fuzzy rules and stability reasoning control. The above method includes: obtaining the function value of the first objective function and the function value of the second objective function respectively, and then determining the steady-state solution according to the function value of the first objective function and the function value of the second objective function, and finally determining the objective function according to the feasible solution set and steady-state solution of the first objective function and the second objective function obtained in advance. The present application can realize the automatic selection of the Pareto optimal solution, and the selected Pareto optimal solution is accurate, which can be widely used in the multi-objective optimization problem of generating the Pareto front solution set, and improve the intelligence of reasoning decision-making and computational efficiency.

Description

Pareto front solution optimization method based on fuzzy rules and stability inference control

Technical Field

The present application relates to the technical field of multi-objective optimization, and in particular to a Pareto frontier solution optimization method based on fuzzy rules and stability reasoning control.

Background Art

In actual multi-objective optimization problems, solving multi-objective optimization problems usually does not result in a global optimal solution, but rather multiple Pareto front solutions. The selection of a better Pareto front solution from the Pareto front solution set is usually done manually. However, the above manual selection can easily lead to inaccurate selection of the better Pareto front solution.

Summary of the invention

Based on this, it is necessary to provide a Pareto front solution optimization method based on fuzzy rules and stability reasoning control that can select a more accurate objective function in response to the above technical problems.

In a first aspect, the present application provides a Pareto front solution optimization method. The method comprises:

Obtaining a function value of the first objective function and a function value of the second objective function respectively;

Determining a steady-state solution according to a function value of the first objective function and a function value of the second objective function;

The target Pareto optimal solution is selected from the feasible solution set of the first objective function and the second objective function according to the steady-state solution.

In one embodiment, determining the steady-state solution according to the function value of the first objective function and the function value of the second objective function includes:

The function value of the first objective function and the function value of the second objective function are input into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system.

In one embodiment, the above method inputs the function value of the first objective function and the function value of the second objective function into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system, including:

The function value of the first objective function and the function value of the second objective function are input into the fuzzy inference system, and the fuzzy inference system determines the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base, and outputs a steady-state solution according to the centroid real value and the membership area; wherein the centroid real value is the centroid real value of the membership function of the decision variable, and the membership area is the membership area corresponding to the membership function of the decision variable.

In one embodiment, the membership function includes a first membership function corresponding to the first objective function, a second membership function corresponding to the second objective function, and a third membership function corresponding to the decision variable; determining the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base includes:

According to the first membership function and the second membership function, respectively obtaining the membership corresponding to the first objective function and the membership corresponding to the second objective function;

Determine the matching degree according to the membership degree corresponding to the first objective function and the membership degree corresponding to the second objective function;

According to the matching degree, the third membership function and the fuzzy rule base, the centroid real value and the membership area are determined.

In one embodiment, the process of establishing the fuzzy inference system includes:

Determining the rate of change of the truth value of the ideal inference conditional statement based on the ideal inference conditional statement;

A fuzzy reasoning system is established according to the changing rate of the antecedent sentence of the ideal reasoning conditional sentence and the changing rate of the truth value of the ideal reasoning conditional sentence.

In one embodiment, the method further comprises:

The standby objective function is determined from the first objective function and the second objective function according to the objective Pareto optimal solution.

In one embodiment, the method further comprises:

Obtain multiple Pareto optimal solutions to multi-dimensional objective optimization problems;

Multiple Pareto optimal solutions are normalized to obtain a feasible solution set.

In a second aspect, the present application also provides a Pareto front solution optimization device. The above device comprises:

A function value determination module, used to obtain the function value of the first objective function and the function value of the second objective function respectively;

A steady-state solution determination module, used to determine a steady-state solution according to a function value of the first objective function and a function value of the second objective function;

The optimal solution selection module is used to select the target Pareto optimal solution from the feasible solution set of the first objective function and the second objective function according to the steady-state solution.

In a third aspect, the present application further provides a computer device. The computer device includes a memory and a processor, the memory stores a computer program, and the processor implements the steps described in the first aspect when executing the computer program.

In a fourth aspect, the present application further provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps described in the first aspect are implemented.

In a fifth aspect, the present application further provides a computer program product, which includes a computer program. The computer program product stores a computer program, and when the computer program is executed by a processor, the steps described in the first aspect are implemented.

The above-mentioned Pareto front solution optimization method based on fuzzy rules and stability reasoning control obtains the function value of the first objective function and the function value of the second objective function respectively, and then determines the steady-state solution according to the function value of the first objective function and the function value of the second objective function, and finally determines the objective function according to the feasible solution set and steady-state solution of the first objective function and the second objective function obtained in advance. The present application can realize the automatic selection of the optimal solution, and the selected objective function is relatively accurate. It can be widely used in multi-objective optimization problems in generating Pareto front solution sets, and improve the intelligence of reasoning decisions and computational efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic flow chart of a Pareto front solution optimization method according to an embodiment;

FIG2 is a diagram of a membership function of related variables of a first objective function in one embodiment;

FIG3 is a diagram of a membership function of related variables of a second objective function in one embodiment;

FIG4 is a diagram of membership functions of decision variables corresponding to various fuzzy sets in one embodiment;

FIG5 is a schematic diagram of a process for determining a centroid real value and a membership area in one embodiment;

FIG6 is a diagram of centroid real value and degree of membership area in one embodiment;

FIG7 is a schematic diagram of a flow chart of establishing a fuzzy reasoning system in another embodiment;

FIG8 is a schematic diagram of a flow chart of obtaining a feasible solution set in another embodiment;

FIG9 is a distribution diagram of a solution set for minimizing a two-dimensional objective function in one embodiment;

FIG10 is a schematic flow chart of a Pareto front solution optimization method according to another embodiment;

FIG11 is a structural block diagram of a Pareto front solution optimization device in one embodiment;

FIG. 12 is a diagram showing the internal structure of a computer device in one embodiment.

DETAILED DESCRIPTION

In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

In actual multi-objective selection problems, multidimensional objective functions represent trade-offs in many aspects. For example, in the multi-objective selection problem of minimizing the two-dimensional objective function [J ₁ , J ₂ ], the objective function J ₁ represents the system performance evaluation, and J ₂ represents the system cost evaluation. The two are mutually restrained because high performance and low cost are often difficult to achieve at the same time. At present, the objective function for the final practical application is usually selected manually. However, the above manual selection can easily lead to inaccurate selected objective functions.

As shown in FIG1 , a Pareto front solution optimization method is provided. The embodiment of the present application takes the method applied to a terminal as an example for illustration. It is understandable that the method can also be applied to a server, and can also be applied to a system including a terminal and a server, and is implemented through the interaction between the terminal and the server. In this embodiment, the method includes the following steps:

Step 201, respectively obtain the function value of the first objective function and the function value of the second objective function.

The first objective function and the second objective function refer to multidimensional functions acquired by the terminal, and the first objective function and the second objective function include but are not limited to multidimensional or one-dimensional functions.

When selecting the objective function, the user starts a selection program or inputs a selection instruction. The terminal obtains the first objective function and the second objective function respectively according to the selection program or the selected instruction, and processes the first objective function and the second objective function to obtain corresponding function values.

Exemplarily, the terminal acquires the first objective function J ₁ and the second objective function J ₂ , and obtains a function value j ₁ =2.5 of the first objective function and a function value j ₂ =8 of the second objective function.

Step 202: Determine a steady-state solution according to the function value of the first objective function and the function value of the second objective function.

Among them, the steady-state solution refers to the one that meets the Lyapunov stability. The steady-state solution can control the fuzzy reasoning system to be in a state of non-increasing truth value and reaching the steady-state point. Specifically, the fuzzy reasoning system refers to a system based on fuzzy set theory and fuzzy reasoning that has the ability to process fuzzy information.

The terminal processes the acquired function values of the first objective function and the second objective function to obtain a steady-state solution that can make the truth value of the fuzzy inference system non-increasing and reach a steady-state point.

Exemplarily, if the function value j1 of the first objective function input to the fuzzy inference system is 2.5, and the function value j2 of the second objective function is 8, then the steady-state solution output by the fuzzy inference system is.

Step 203: Select a target Pareto optimal solution from the feasible solution sets of the first objective function and the second objective function according to the steady-state solution.

The target Pareto optimal solution is obtained from the optimal solution on the Pareto frontier, and the target Pareto optimal solution can be determined by the positional relationship between the steady-state solution and the feasible solution. The positional relationship may include but is not limited to angles and coordinates.

According to the steady-state solution output by the fuzzy inference system, the closest feasible solution is determined through the positional relationship between the steady-state solution and the feasible solution, and this feasible solution is the target Pareto optimal solution.

For example, if the steady-state solution is φ _opt = 4.71°, according to the azimuths corresponding to the obtained feasible solutions, the feasible solution corresponding to the closest azimuth is X2, then the target Pareto optimal solution is

In the above embodiment, the function value of the first objective function and the function value of the second objective function are obtained respectively, and then the steady-state solution is determined according to the function value of the first objective function and the function value of the second objective function, and finally the target Pareto optimal solution is determined according to the feasible solution set and the steady-state solution of the first objective function and the second objective function obtained in advance. The embodiment of the present application can realize the automatic selection of the optimal solution, and the selected target Pareto optimal solution is relatively accurate.

In one embodiment, the step of determining a steady-state solution based on the function value of the first objective function and the function value of the second objective function may include: inputting the function value of the first objective function and the function value of the second objective function into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system.

Among them, the fuzzy reasoning system refers to a system that has the ability to process fuzzy information based on fuzzy set theory and fuzzy reasoning techniques. It uses fuzzy theory as the main computing tool to achieve complex nonlinear mapping and its input and output are both precise numerical values.

The steady-state solution includes but is not limited to angles and coordinates, and the membership function of the steady-state solution is a bijective function, that is, the steady-state solution corresponds to a unique membership function value within the definition domain.

The terminal inputs the acquired function value of the first objective function and the function value of the second objective function into the fuzzy inference system, and the fuzzy inference system performs fuzzy inference on the function value of the first objective function and the function value of the second objective function to obtain a precise numerical steady-state solution.

Exemplarily, if the obtained function value of the first objective function is j ₁ =2.5 and the function value of the second objective function is j ₂ =8, the function values of the first objective function and the second objective function are input into the fuzzy inference system to obtain a steady-state solution φ _ppt =45°.

In the above embodiment, the function value of the first objective function and the function value of the second objective function are input into the fuzzy inference system, and the fuzzy inference system performs fuzzy inference on the above function values to obtain a steady-state solution with an accurate numerical value. The embodiment of the present application obtains an accurate steady-state solution through fuzzy inference, which can improve the computational efficiency in solving multi-objective optimization problems.

In one embodiment, the above-mentioned step of inputting the function value of the first objective function and the function value of the second objective function into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system may include: inputting the function value of the first objective function and the function value of the second objective function into the fuzzy inference system, and the fuzzy inference system determines the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base, and outputs the steady-state solution according to the centroid real value and the membership area; wherein the centroid real value is the centroid real value of the membership function of the decision variable, and the membership area is the membership area corresponding to the membership function of the decision variable.

Among them, the fuzzy reasoning system needs to perform fuzzy reasoning based on the pre-established fuzzy rule base. The fuzzy rule base is a clue that has spare power in its design based on the experience and knowledge of experts, including multiple fuzzy rules. Fuzzy rules are used to define and describe the empirical relationship between the trade-offs of various dimensional objectives and the selection of Pareto optimal solutions, that is, to define the relationship between the Pareto optimal frontier solution set of the multi-dimensional objective function and the decision. For example, in a multi-objective optimization problem considering the two objective functions of performance and cost, if the budget is sufficient and the performance requirements are high, it is more inclined to choose the Pareto optimal solution with a better performance evaluation function; if the budget is limited and the performance requirements are not very high, it is more inclined to choose the Pareto optimal solution with a better cost evaluation function.

The fuzzy rule base R consists of n _R if-then rules as shown in formula (1):

Each if-then rule _ri , i = 1, 2, ..., _nR defines the empirical relationship between the M-dimensional goal and the Pareto optimal solution selection decision. Its structure generally includes M propositions related to the goal ( _p1 , _p2 , ..., _pM ) and 1 proposition related to the Pareto optimal solution selection decision (q), as shown in formula (2):

Ifp ₁ andp ₂ and…andp _M ,thenq........................(2)

Among them, p ₁ ,p ₂ ... _pm describe the requirements or constraints related to the objective function _Ji , and can be customized according to the actual task and specific target dimension. For example, if in a design problem, _Ji measures the system performance, _Pi can be defined as "high/low system performance requirements" or "low/high system tolerance for errors and delays", etc.; if _Ji measures the system cost, _Pi can be defined as "more/less system budget", etc. In general, _Pi has the form of " _{ji isFi} ", where _Ji is a variable related to the target dimension, such as "system performance requirements", "system tolerance for errors and delays", "system budget", etc., and _Fi is a fuzzy set describing _Ji , such as "very high (more)", "higher (more)", "neither high nor low (neither more nor less)", "lower (less)", "very low (less)", etc. In general, sets such as positive large (PB), positive medium (PM), positive small (PS), zero (ZO), negative small (NS), negative medium (NM), and negative large (NB) can be used to uniformly represent concepts such as high and low, how much, and size.

In addition, the proposition q describes the decision of selecting the Pareto optimal solution, such as "the cost-performance ratio of the selected Pareto optimal solution is high/low". It should be noted that when defining the proposition q, it is necessary to have the ability to uniquely distinguish each solution on the frontier. Taking the above definition as an example, it is necessary to ensure that the cost-performance ratio of each point on the frontier is different (in fact, all points on the Pareto frontier considering the two-dimensional objective function of performance and cost have different cost-performance ratios). Only in this way can we ensure that after we determine the value of the ideal cost-performance ratio through reasoning, this ideal cost-performance ratio can uniquely determine a point on the frontier as the optimal solution finally selected. Generally, q also has the form of "φisG", φ is a variable related to the decision of selecting the Pareto optimal solution, such as "cost-performance ratio", etc., and G is a fuzzy set describing the decision-related variable φ, such as "high", "low", "large", "small", etc., which is generally also uniformly represented by sets such as positive large (PB), positive medium (PM), positive small (PS), zero (ZO), negative small (NS), negative medium (NM), and negative large (NB).

Therefore, as shown in formula (3), each rule is also written as:

Ifj ₁ isF ₁ andj ₂ isF ₂ and…andj _M isF _M ,thenφisG......(3)

When F _i and G are described by 7 sets, namely, positive large (PB), positive middle (PM), positive small (PS), zero (ZO), negative small (NS), negative middle (NM), and negative large (NB), a total of n _R = 7 ^M rules can be formulated. The following is an example of a rule, as shown in formula (4):

Ifj ₁ isPBandj ₂ isNMand…andj _M isZO,thenφisPS.....(4)

Wherein, the membership function refers to the membership of an element to a fuzzy set. The embodiment of the present application establishes a membership function according to the pre-established fuzzy set and the actual values of the target variable and the decision variable. As shown in Figures 2 to 4, the membership function of the embodiment of the present application includes a first target function J ₁ used to measure performance, a second target function J ₂ used to measure cost, and a membership function corresponding to the decision variable. As shown in Figure 2, the horizontal axis of the J ₁ target function represents the relevant variable j ₁ , which is used to represent the "system performance requirement level", and the value range is [0, 10]. The closer the value is to 10, the higher the system performance requirement level is, that is, the smaller the corresponding requirement target function J ₁ is, and the vertical axis represents the membership of the relevant variable to each fuzzy subset. As shown in Figure 3, the horizontal axis of the J ₂ target function represents the relevant variable j ₂ , which is used to represent the "system remaining budget", and the value is [0, 10], the unit is thousands of yuan, the larger the value is, the more the system remaining budget is, and the vertical axis represents the membership of the relevant variable to each fuzzy subset. As shown in Figure 4, the horizontal axis of the decision variable membership function represents the azimuth of each Pareto front point relative to the origin after normalization, with a value range of [0, 90] and a unit of degree (°). The vertical axis represents the membership of the relevant variable to each fuzzy subset.

Among them, the centroid real value of the membership function of the decision variable refers to the centroid value of the figure enclosed by the membership function of the decision variable and the horizontal axis, and the membership area refers to the membership area "cut down" from the membership function of the decision variable.

The terminal inputs the acquired function value of the first objective function, the function value of the second objective function, the membership function corresponding to the first objective function, the membership function of the second objective function, and the membership function of the decision variable into the fuzzy inference system. The fuzzy inference system determines the centroid real value and the membership area based on the above-mentioned membership functions and a pre-established fuzzy rule base, and obtains and outputs a steady-state solution based on the centroid real value and the membership area.

In the above embodiment, the function value of the first objective function, the function value of the second objective function, the membership function corresponding to the first objective function, the membership function of the second objective function, and the membership function of the decision variable are input into the fuzzy inference system, and the fuzzy inference system determines the centroid real value and the membership area according to the above membership functions and the pre-established fuzzy rule base, and outputs a steady-state solution according to the centroid real value and the membership area. The embodiment of the present application obtains an accurate steady-state solution by calculating the centroid real value and the membership area, thereby improving the calculation efficiency and calculation accuracy.

In one embodiment, the membership function includes a first membership function corresponding to the first objective function, a second membership function corresponding to the second objective function, and a third membership function corresponding to the decision variable; as shown in FIG5 , the step of determining the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base may include:

Step 301: Obtain, according to the first membership function and the second membership function, the membership corresponding to the first objective function and the membership corresponding to the second objective function respectively.

Among them, membership degree refers to the degree to which an element belongs to a fuzzy set.

The terminal obtains the first objective function and the second objective function, obtains the first membership function corresponding to the first objective function and the second membership function corresponding to the second objective function according to the fuzzy set, and obtains the membership of the first objective function and the second objective function to the corresponding fuzzy sets according to the fuzzy sets corresponding to the first membership function and the second membership function in the current fuzzy rule in the fuzzy rule base.

Exemplarily, the first objective function J1 and the second objective function J2 are obtained. According to the fuzzy set PB corresponding to the first objective function J1, the fuzzy set NB corresponding to the second objective function J2, the first membership function _A1 (x) and the second membership function _A2 (x), the membership of the first objective function J1 to the fuzzy set PB is 0.3, and the membership of the second objective function J2 to the fuzzy set NB is 0.7.

Step 302: Determine the matching degree according to the membership degree corresponding to the first objective function and the membership degree corresponding to the second objective function.

The matching degree refers to the matching degree of the objective function to the rules in the fuzzy rule base.

After finding the membership belonging to the corresponding fuzzy set according to the first membership function and the second membership function, the membership with the smallest value is selected from the membership of the first membership function and the membership of the second membership function; the matching degree with the current fuzzy rule in the fuzzy rule base is determined according to the membership with the smallest value.

For example, if the current fuzzy rule is r _i :If j ₁ is PB and _{j 2} is NM, then φ is PS., then the membership of the function value of j ₁ to the fuzzy set PB is μ _PB (j ₁ ) = 0.7, and the membership of the function value of j ₂ to the fuzzy set NM is μ _NM (j ₂ ) = 0.3. The minimum membership is μ _NM (j ₂ ) = 0.3. Then the matching degree of [j ₁ , j ₂ ] to the current fuzzy rule r _i is as shown in formula (5):

w _i =min{μ _PB (j ₁ ),μ _NM (j ₂ )}=0.3............................. .....(5)

Step 303, determining the centroid real value and the membership area according to the matching degree, the third membership function and the fuzzy rule base.

The third membership function refers to the membership function corresponding to the decision variable.

According to the matching degree of the fuzzy rules calculated above, the third membership function corresponding to the decision variable and the pre-established fuzzy rule base, as shown in FIG6 , the membership area is “cut down” from the third membership function according to the matching degree, and the centroid real value is the centroid value of the figure (triangle) formed by the third membership function and the horizontal axis.

In the above embodiment, the centroid real value and the membership area are calculated according to the matching degree of the fuzzy rules, the third membership function corresponding to the decision variables and the pre-established fuzzy rule base. The embodiment of the present application solves the centroid real value and the membership area according to the matching degree of the fuzzy rules, the third membership function corresponding to the decision variables and the pre-established fuzzy rule base. By calculating the centroid real value and the membership area, a stable solution can be accurately obtained, thereby accurately selecting the objective function based on the stable solution.

In one embodiment, as shown in FIG7 , the process of establishing the fuzzy inference system includes:

Step 401, determining the rate of change of the truth value of the ideal reasoning conditional statement according to the ideal reasoning conditional statement.

Among them, the ideal reasoning conditional statement refers to the "if-then ideal reasoning conditional statement", as shown in formula (6), the "if-then ideal reasoning conditional statement" means:

If the decision-related variable φisH, then the decision result is good..............................(6)

Among them, the truth value of the if-then ideal reasoning conditional statement is represented by the fuzzy implication I(x,f(x)).

x is the truth value of the if antecedent statement (i.e., "decision-related variable φisH"), which is equal to the membership of φ to the fuzzy set H, i.e., x= _μH (φ). Here, the fuzzy set H and the membership function _μH (·) of φ to the fuzzy set H need to be specifically defined. The membership function _μH (·) is required to be a bijective function, i.e., each φ∈[ _φmin , _φmax ] corresponds to a unique and different _μH (φ) value. The fuzzy set H can generally be defined as "large/small", "close to the upper/lower bound of φ", etc.

f(x) is the truth value of the then statement (i.e., "the decision result is better"), and is a function about x pre-set by the fuzzy reasoning system. It is necessary to ensure that the steady-state point of the subsequently designed dynamic fuzzy reasoning system corresponds to a better decision result.

The truth value of the if-then ideal reasoning conditional statement I(x,f(x)) takes the Reichenbach type fuzzy implication, and the truth value symbol is simplified to z, as shown in formula (7), which has the following form:

z＝I(x,f(x))＝1-x+xf(x)........................ ........(7)

As shown in formula (8), the rate of change of the truth value of the if-then ideal reasoning conditional statement is:

The Pareto optimal solution is selected by reasoning in combination with the fuzzy rule base, and the rate of change of the truth value of the ideal reasoning conditional statement is determined according to the ideal reasoning conditional statement.

For example, if the ideal ideal reasoning conditional statement is as shown in formula (9):

If the decision-related variable φisH, then the decision result is good..............................(9)

As shown in formula (10), the rate of change of the truth value of the ideal reasoning conditional statement is:

Step 402, establishing a fuzzy reasoning system according to the change rate of the antecedent statement of the ideal reasoning conditional statement and the change rate of the truth value of the ideal reasoning conditional statement.

The fuzzy inference system is controlled by a fuzzy inference controller. During the inference process, we need to continuously adjust (control) the decision-related variable φ, and the variable x = μ _H (φ) directly corresponds to φ. Therefore, we let the fuzzy inference controller u be the rate of change of x, as shown in formula (11):

Substitute the fuzzy inference controller u into the truth value change rate of the if-then ideal reasoning conditional statement to construct a dynamic fuzzy inference system based on fuzzy truth value evolution, as shown in formula (12):

For the fuzzy inference system, for the true value z=1-x+xf(x), the predefined f(x) has the following form, as shown in formula (13):

The corresponding true value and its derivative are as shown in formula (14) and formula (15):

Among them, h _FR is a variable related to the fuzzy rule base constructed based on empirical knowledge in Section 3.2. The expression of h _FR is shown in formula (16):

Where i represents the sequence of rules, _Ci is the centroid real value of the membership function of the decision variable φ in the rule _ri , _Si is the membership area “cut down” from the membership function of the decision variable φ by the matching degree _wi of the current target dimension related variables [j ₁ ,j ₂ ,…,j _M ] to the rule _{ri .} The matching degree _wi of the current target dimension related variables [j ₁ ,j ₂ ,…,j _M ] to the rule ri can be obtained using the min function, as shown in formula (17):

Taking two-dimensional multi-objective optimization as an example to explain the above content, let the objective function be [J ₁ ,J ₂ ], the target dimension related variables be [j ₁ ,j ₂ ], and the fuzzy rule r _i , as shown in formula (18):

r _i :Ifj ₁ isPBand _2i sNM,thenφisPS.............(18)

The membership functions μ _PB (j ₁ ), μ _NM (j ₂ ) and μ _PS (φ) are shown in FIG8 . The function value of the first objective function j ₁ corresponds to the membership of the fuzzy set PB μ _PB (j ₁ ) = 0.7, and the function value of the second objective function j ₂ corresponds to the membership of the fuzzy set NM μ _NM (j ₂ ) = 0.3. Then, the matching degree w _i of [j ₁ , j ₂ ] to the rule r _i is, as shown in formula (19):

w _i =min{μ _PB (j ₁ ),μ _NM (j ₂ )}=0.3............................. (19)

As shown in FIG6 , the membership area S _i “cut down” from the membership function of the decision variable φ by the matching degree _wi is shown in the gray shaded portion, and _Ci is the real value of the centroid of the figure (triangle) formed by the μ _PS (φ) function and the horizontal axis.

The above process obtains the change rate of the antecedent statement and the change rate of the truth value of the ideal reasoning conditional statement according to the ideal reasoning conditional statement, thereby establishing a fuzzy reasoning system.

In the above embodiment, the Pareto optimal solution is selected by reasoning in combination with the fuzzy rule base, and the rate of change of the truth value of the ideal reasoning conditional statement and the rate of change of the antecedent statement and the rate of change of the truth value of the ideal reasoning conditional statement are determined according to the ideal reasoning conditional statement, thereby establishing a fuzzy reasoning system. The fuzzy reasoning system established in the embodiment of the present application can accurately output a steady-state solution, thereby improving the accuracy of selecting the objective function.

In one embodiment, the method further includes: determining a standby objective function from the first objective function and the second objective function according to the objective Pareto optimal solution.

The target Pareto optimal solution is obtained based on the feasible solution set on the Pareto front. The target Pareto optimal solution can be determined by the positional relationship between the steady-state solution and the feasible solution. The positional relationship may include but is not limited to angles and coordinates.

After finding the nearest target Pareto optimal solution according to the steady-state solution, the closest feasible solution is determined by the positional relationship between the steady-state solution and the feasible solution. The target Pareto optimal solution is the feasible solution, and the standby objective function is determined according to the target Pareto optimal solution, where the standby objective function can be one or more, depending on the value of the target Pareto optimal solution.

Exemplarily, the first objective function J1 and the second objective function J2 are obtained, and the feasible solution sets of the first objective function J1 and the second objective function J2 are solved as _X1 : ( _J1,1 , _J2,1 ) = (0.85, ₁₂ ), X2: ( _J1,2 , _J2,2 ) = (0.56, 15), _X3 : (J1,3, _J2,3 ) = (0.36, ₃₂₎ , _X4 : ( _J1,4 , _J2,4 ) = (0.18, 56), _X5 : ( _J1,5 , _J2,5 ) = (0.05, 75), and the obtained steady-state solution is _φopt = 45°. The feasible solution X4 obtained from the steady-state solution is most in line with the actual situation, and then the stand-by objective function is determined to be the first objective function J1 according to the feasible solution X4.

In the above embodiment, the standby objective function is determined from the first objective function and the second objective function according to the target Pareto optimal solution. The embodiment of the present application uses a steady-state solution to ensure that the fuzzy inference controller is always at a steady-state point, thereby improving the stability of the system. In addition, the embodiment of the present application selects the objective function according to the target Pareto optimal solution, thereby improving the accuracy of the selected objective function.

In one embodiment, as shown in FIG8 , the embodiment of the present application may further include the following steps:

Step 501, obtaining multiple Pareto optimal solutions to a multi-dimensional objective optimization problem.

Among them, the Pareto optimal solution means: if there is no other solution in the variable space that is better than this solution, then this solution is called the Pareto optimal solution. Solution x is better than solution y if all the objective functions of solution x are better than the objective functions corresponding to solution y.

Multiple objective functions are obtained according to the multidimensional target selection problem to be solved, and multiple Pareto optimal solutions are calculated based on the multiple objective functions.

Exemplarily, to solve the cost optimization problem, the optimal performance objective function J ₁ and the cost objective function J ₂ are obtained, and the Pareto optimal solutions are: X ₁ : (J _1,1 , J _2,1 ) = (0.85, 12), X ₂ : (J _1,2 , J _2,2 ) = (0.56, 15), X ₃ : (J _1,3 , J _2,3 ) = (0.36, 32), X ₄ : (J _1,4 , J _2,4 ) = (0.18, 56), X ₅ : (J _1,5 , J _2,5 ) = (0.05, 75).

Step 502: normalize multiple Pareto optimal solutions to obtain a feasible solution set.

Among them, the Pareto optimal solution means: if there is no other solution in the variable space that is better than this solution, then this solution is called the Pareto optimal solution. Solution x is better than solution y means that all objective functions of solution x are better than the objective functions corresponding to solution y. Taking Figure 9 as an example, the figure shows the solution set obtained after solving the minimization of the two-dimensional objective function [J ₁ ,J ₂ ]. The five black points (A~E) are all Pareto optimal solutions, which together constitute the Pareto frontier. Since there are solutions B and C that are better than solution F, and there are solutions C and D that are better than solution G, so solutions F and G are not Pareto optimal solutions.

There is usually no global optimal solution with optimal cost and performance for multi-objective selection problems. Instead, a solution set containing multiple feasible solutions is obtained, that is, multiple Pareto optimal solutions. These Pareto optimal solutions together constitute the Pareto frontier.

After solving the multi-objective selection problem and obtaining multiple feasible solutions on the Pareto front, it is necessary to select one of the multiple feasible solutions as the final solution for practical application. This selection process often needs to be considered in combination with the actual situation. How to select the Pareto optimal solution that is more suitable for the actual situation and problem requirements is an important issue.

Normalization can normalize the objective functions of all dimensions of all Pareto optimal solutions to the range of [0, 1], making the distribution of each solution more even, facilitating subsequent calculations, and avoiding problems such as complex calculations due to large differences in the order of magnitude of different objective functions or multiple solutions being too dense in a certain dimension.

If there are N points on the Pareto front P obtained by solving the M-dimensional objective optimization problem (Pareto optimal solution), then P = {x ₁ ,x ₂ ,…,x _N }

Among them, x _i ,i＝1,2,…,N represents an M-dimensional objective function value, denoted as x _i =[J _1,i ,J _2,i ,…,J _M,i ].

Among them, J _j,i ,j＝1,2,…,M represents the j-th dimension objective function of point _xi .

Record the maximum value of all Pareto optimal solutions on the j-th dimension objective function With minimum As shown in formulas (20) and (21):

Then the normalized value of the Pareto optimal solution x _i is shown in formulas (22) and (23):

for

After normalization, all normalized objective function values All are in the range [0, 1].

The multiple Pareto optimal solutions calculated above are normalized to obtain a feasible solution set in the range of [0, 1].

For example, one of the Pareto frontier points is normalized to obtain the following equation (24):

In the above embodiment, multiple Pareto optimal solutions of the multi-dimensional objective optimization problem are obtained and the multiple Pareto optimal solutions are normalized to obtain a feasible solution set. The normalized feasible solution obtained in the embodiment of the present application solves the problem that multiple solutions are too dense in a certain dimension, thereby improving the convenience of calculation.

In one embodiment, as shown in FIG10 , the embodiment of the present application further includes the following steps:

Step 601, respectively obtain the function value of the first objective function and the function value of the second objective function.

Step 602: input the function value of the first objective function and the function value of the second objective function into a pre-established fuzzy inference system.

Step 603: The fuzzy inference system obtains the membership corresponding to the first objective function and the membership corresponding to the second objective function respectively according to the first membership function and the second membership function.

Step 604: the fuzzy inference system determines a matching degree according to a membership degree corresponding to the first objective function and a membership degree corresponding to the second objective function.

Step 605: The fuzzy inference system determines the centroid real value and the membership area according to the matching degree, the third membership function and the fuzzy rule base.

Step 606: The fuzzy inference system outputs a steady-state solution according to the centroid real value and the membership area.

Step 607 : Select the target Pareto optimal solution from the feasible solution set of the first objective function and the second objective function according to the steady-state solution.

Step 608: determine a standby objective function from the first objective function and the second objective function according to the objective Pareto optimal solution.

This embodiment outputs a steady-state solution by inputting the function value of the first objective function and the function value of the second objective function into a pre-established fuzzy reasoning system, and selects the target Pareto optimal solution from the feasible solution set of the first objective function and the second objective function, thereby determining the objective function. This application controls the fuzzy reasoning system to a steady state by designing a fuzzy reasoning controller to reason and select the Pareto optimal solution. The fuzzy reasoning controller has consistent asymptotic stability, and the steady-state solution of the reasoning system corresponds to the Pareto optimal solution finally selected, which improves accuracy. It can realize automatic reasoning and selection of the optimal solution on the Pareto frontier based on empirical knowledge, and can be widely used in multi-objective optimization problems in generating Pareto frontier solution sets, thereby improving the intelligence of reasoning decisions and computational efficiency.

It should be understood that, although the various steps in the flowcharts involved in the above-mentioned embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-mentioned embodiments can include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

Based on the same inventive concept, the embodiment of the present application also provides a Pareto front solution optimization device for implementing the above-mentioned Pareto front solution optimization method. The implementation scheme for solving the problem provided by the device is similar to the implementation scheme recorded in the above-mentioned method, so the specific limitations in one or more Pareto front solution optimization device embodiments provided below can refer to the limitations of the Pareto front solution optimization method above, and will not be repeated here.

In one embodiment, as shown in FIG11 , a Pareto front solution optimization device is provided, comprising:

A function value determination module 701 is used to obtain the function value of the first objective function and the function value of the second objective function respectively;

A steady-state solution determination module 702, configured to determine a steady-state solution according to a function value of the first objective function and a function value of the second objective function;

The optimal solution selection module 703 is used to determine the objective function according to the feasible solution set and the steady-state solution of the first objective function and the second objective function obtained in advance.

In one embodiment, the steady-state solution determination module 702 is specifically used to input the function value of the first objective function and the function value of the second objective function into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system.

In one embodiment, the steady-state solution determination module 702 is specifically used to input the function value of the first objective function and the function value of the second objective function into the fuzzy inference system, and the fuzzy inference system determines the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base, and outputs the steady-state solution according to the centroid real value and the membership area; wherein the centroid real value is the centroid real value of the membership function of the decision variable, and the membership area is the membership area corresponding to the membership function of the decision variable.

In one embodiment, the steady-state solution determination module 702 further includes:

A membership determination submodule, used to obtain the membership corresponding to the first objective function and the membership corresponding to the second objective function respectively according to the first membership function and the second membership function;

A matching degree determination submodule, used to determine the matching degree according to the membership degree corresponding to the first objective function and the membership degree corresponding to the second objective function;

The membership area determination submodule is used to determine the centroid real value and the membership area according to the matching degree, the third membership function and the fuzzy rule base.

In one embodiment, the device further comprises:

A change rate determination module, used to determine the change rate of the truth value of the ideal reasoning conditional statement according to the ideal reasoning conditional statement;

The system building module is used to build a fuzzy reasoning system according to the change rate of the antecedent sentence of the ideal reasoning conditional sentence and the change rate of the truth value of the ideal reasoning conditional sentence.

In one embodiment, the optimal solution selection module 703 includes:

The standby objective function determination submodule is used to determine the standby objective function from the first objective function and the second objective function according to the target Pareto optimal solution.

Each module in the above-mentioned Pareto front solution optimization device can be implemented in whole or in part by software, hardware and a combination thereof. Each of the above-mentioned modules can be embedded in or independent of a processor in a computer device in the form of hardware, or can be stored in a memory in a computer device in the form of software, so that the processor can call and execute the operations corresponding to each of the above modules.

In one embodiment, a computer device is provided, which can be a terminal or a server, and its internal structure diagram can be shown in Figure 12. The computer device includes a processor, a memory, an input/output interface (Input/Output, referred to as I/O) and a communication interface. Among them, the processor, the memory and the input/output interface are connected through a system bus, and the communication interface is connected to the system bus through the input/output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store variable data related to the objective function. The input/output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a Pareto front solution optimization method is implemented.

Those skilled in the art will understand that the structure shown in FIG. 12 is merely a block diagram of a partial structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different arrangement of components.

In one embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor executes the computer program, the following steps are implemented:

Obtaining a function value of the first objective function and a function value of the second objective function respectively;

Determining a steady-state solution according to a function value of the first objective function and a function value of the second objective function;

The target Pareto optimal solution is selected from the feasible solution set of the first objective function and the second objective function according to the steady-state solution.

In one embodiment, when the processor executes the computer program, the processor further implements the following steps:

The function value of the first objective function and the function value of the second objective function are input into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system.

In one embodiment, when the processor executes the computer program, the processor further implements the following steps:

The function value of the first objective function and the function value of the second objective function are input into the fuzzy inference system, and the fuzzy inference system determines the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base, and outputs a steady-state solution according to the centroid real value and the membership area; wherein the centroid real value is the centroid real value of the membership function of the decision variable, and the membership area is the membership area corresponding to the membership function of the decision variable.

In one embodiment, when the processor executes the computer program, the processor further implements the following steps:

According to the first membership function and the second membership function, respectively obtaining the membership corresponding to the first objective function and the membership corresponding to the second objective function;

Determine the matching degree according to the membership degree corresponding to the first objective function and the membership degree corresponding to the second objective function;

According to the matching degree, the third membership function and the fuzzy rule base, the centroid real value and the membership area are determined.

In one embodiment, when the processor executes the computer program, the processor further implements the following steps:

Determining the rate of change of the truth value of the ideal inference conditional statement based on the ideal inference conditional statement;

A fuzzy reasoning system is established according to the changing rate of the antecedent sentence of the ideal reasoning conditional sentence and the changing rate of the truth value of the ideal reasoning conditional sentence.

In one embodiment, when the processor executes the computer program, the processor further implements the following steps:

The standby objective function is determined from the first objective function and the second objective function according to the objective Pareto optimal solution.

In one embodiment, when the processor executes the computer program, the processor further implements the following steps:

Obtain multiple Pareto optimal solutions to multi-dimensional objective optimization problems;

Multiple Pareto optimal solutions are normalized to obtain a feasible solution set.

In one embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, the following steps are implemented:

Obtaining a function value of the first objective function and a function value of the second objective function respectively;

Determining a steady-state solution according to a function value of the first objective function and a function value of the second objective function;

The target Pareto optimal solution is selected from the feasible solution set of the first objective function and the second objective function according to the steady-state solution.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

The function value of the first objective function and the function value of the second objective function are input into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

The function value of the first objective function and the function value of the second objective function are input into the fuzzy inference system, and the fuzzy inference system determines the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base, and outputs a steady-state solution according to the centroid real value and the membership area; wherein the centroid real value is the centroid real value of the membership function of the decision variable, and the membership area is the membership area corresponding to the membership function of the decision variable.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

According to the first membership function and the second membership function, respectively obtaining the membership corresponding to the first objective function and the membership corresponding to the second objective function;

Determine the matching degree according to the membership degree corresponding to the first objective function and the membership degree corresponding to the second objective function;

According to the matching degree, the third membership function and the fuzzy rule base, the centroid real value and the membership area are determined.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

Determining the rate of change of the truth value of the ideal inference conditional statement based on the ideal inference conditional statement;

A fuzzy reasoning system is established according to the changing rate of the antecedent sentence of the ideal reasoning conditional sentence and the changing rate of the truth value of the ideal reasoning conditional sentence.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

The standby objective function is determined from the first objective function and the second objective function according to the objective Pareto optimal solution.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

Obtain multiple Pareto optimal solutions to multi-dimensional objective optimization problems;

Multiple Pareto optimal solutions are normalized to obtain a feasible solution set.

In one embodiment, a computer program product is provided, comprising a computer program, which, when executed by a processor, implements the following steps:

Obtaining a function value of the first objective function and a function value of the second objective function respectively;

Determining a steady-state solution according to a function value of the first objective function and a function value of the second objective function;

The target Pareto optimal solution is selected from the feasible solution set of the first objective function and the second objective function according to the steady-state solution.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

The function value of the first objective function and the function value of the second objective function are input into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

The function value of the first objective function and the function value of the second objective function are input into the fuzzy inference system, and the fuzzy inference system determines the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base, and outputs a steady-state solution according to the centroid real value and the membership area; wherein the centroid real value is the centroid real value of the membership function of the decision variable, and the membership area is the membership area corresponding to the membership function of the decision variable.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

According to the first membership function and the second membership function, respectively obtaining the membership corresponding to the first objective function and the membership corresponding to the second objective function;

Determine the matching degree according to the membership degree corresponding to the first objective function and the membership degree corresponding to the second objective function;

According to the matching degree, the third membership function and the fuzzy rule base, the centroid real value and the membership area are determined.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

Determining the rate of change of the truth value of the ideal inference conditional statement based on the ideal inference conditional statement;

A fuzzy reasoning system is established according to the changing rate of the antecedent sentence of the ideal reasoning conditional sentence and the changing rate of the truth value of the ideal reasoning conditional sentence.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

The standby objective function is determined from the first objective function and the second objective function according to the objective Pareto optimal solution.

In one embodiment, when the computer program is executed by a processor, the following steps are also implemented:

Obtain multiple Pareto optimal solutions to multi-dimensional objective optimization problems;

Multiple Pareto optimal solutions are normalized to obtain a feasible solution set.

It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant laws, regulations and standards of relevant countries and regions.

Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims (8)

1. A Pareto front solution optimization method, characterized in that the method comprises: The terminal obtains a function value of a first objective function and a function value of a second objective function respectively; the first objective function includes a performance evaluation function, and the second objective function includes a cost evaluation function; The terminal inputs the function value of the first objective function and the function value of the second objective function into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system; The terminal selects a target Pareto optimal solution from a feasible solution set of the first objective function and the second objective function according to the steady-state solution; The terminal inputs the function value of the first objective function and the function value of the second objective function into a pre-established fuzzy inference system to obtain the steady-state solution output by the fuzzy inference system, including: The function value of the first objective function and the function value of the second objective function are input into the fuzzy inference system, and the fuzzy inference system determines the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base, and outputs the steady-state solution according to the centroid real value and the membership area; wherein the centroid real value is the centroid real value of the membership function of the decision variable, and the membership area is the membership area corresponding to the membership function of the decision variable. 2. The method according to claim 1, characterized in that the membership function includes a first membership function corresponding to the first objective function, a second membership function corresponding to the second objective function, and a third membership function corresponding to the decision variable; and determining the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base comprises: According to the first membership function and the second membership function, respectively obtaining a membership corresponding to the first objective function and a membership corresponding to the second objective function; Determining a matching degree according to a membership degree corresponding to the first objective function and a membership degree corresponding to the second objective function; The centroid real value and the membership area are determined according to the matching degree, the third membership function and the fuzzy rule base. 3. The method according to any one of claims 1-2, characterized in that the process of establishing the fuzzy inference system comprises: Determining a rate of change of a truth value of an ideal reasoning conditional statement according to the ideal reasoning conditional statement; The fuzzy reasoning system is established according to the change rate of the antecedent statement of the ideal reasoning conditional statement and the change rate of the truth value of the ideal reasoning conditional statement. 4. The method according to any one of claims 1 to 2, characterized in that the method further comprises: A standby objective function is determined from the first objective function and the second objective function according to the objective Pareto optimal solution. 5. The method according to claim 4, characterized in that the method further comprises: Obtain multiple Pareto optimal solutions to multi-dimensional objective optimization problems; The multiple Pareto optimal solutions are normalized to obtain the feasible solution set. 6. A Pareto front solution optimization device, characterized in that the device comprises: A function value determination module, used for the terminal to respectively obtain a function value of a first objective function and a function value of a second objective function; the first objective function includes a performance evaluation function, and the second objective function includes a cost evaluation function; A steady-state solution determination module, used for the terminal to input the function value of the first objective function and the function value of the second objective function into a pre-established fuzzy inference system to obtain a steady-state solution output by the fuzzy inference system; An optimal solution selection module, used for the terminal to select a target Pareto optimal solution from a feasible solution set of the first objective function and the second objective function according to the steady-state solution; Among them, the steady-state solution determination module is specifically used to input the function value of the first objective function and the function value of the second objective function into the fuzzy inference system, and the fuzzy inference system determines the centroid real value and the membership area according to the pre-established membership function and fuzzy rule base, and outputs the steady-state solution according to the centroid real value and the membership area; wherein the centroid real value is the centroid real value of the membership function of the decision variable, and the membership area is the membership area corresponding to the membership function of the decision variable. 7. A computer device, comprising a memory and a processor, wherein the memory stores a computer program, wherein the processor implements the steps of the method according to any one of claims 1 to 5 when executing the computer program. 8. A computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.