Courtyard-combined type dwelling courtyard spatial form design method based on multi-objective optimization

Abstract

The invention discloses a multi-objective optimization-based courtyard-combined type residential courtyard spatial form design method. The method comprises the following specific steps of S1, setting an optimization objective, an optimization variable and an optimization variable range constraint; s2, according to the optimization target, the optimization variable and the optimization variable range constraint in the step S1, performing programming on a Grasshopper platform to calculate an optimization target index value, and through multi-target optimization programming, obtaining a multi-target optimization-based courtyard-combined residential courtyard spatial form design solution set; s3, performing weighting on the optimization target based on an index correlation index weighting method CRITIC; and S4, carrying out scheme comprehensive empowerment sorting based on CRITIC + TOPSIS, and recommending an optimal solution according to the maximum value of the comprehensive score index. The scientific and reasonable method is provided for environment-friendly and low-carbon design and transformation of courtyard-combined residential courtyard space, reference is provided for comprehensive scheme selection through comprehensive scheme sorting, and therefore the optimal design scheme is obtained.

Description

Technical Field

[0001] The invention belongs to the technical field of green and low-carbon design and transformation of courtyard-type dwellings, and relates to a courtyard-type dwelling patio space form design method based on multi-objective optimization. Background Art

[0003] Traditional dwellings contain rich regional culture and passive energy-saving technologies. Among them, the traditional courtyard dwellings in the north and south have strong regional characteristics. The traditional courtyard dwellings in the north are mainly courtyards, while the courtyard dwellings with patios are widely distributed in the south. Relevant research points out that patios not only have the function of cultural inheritance, but also play an important role in regulating the physical environment of traditional dwellings.

[0004] The patio space is the main lighting channel for traditional courtyard-style residential buildings. The increase in the amount of daylight can meet the indoor lighting needs, but it is also easy to cause too many extreme glare areas. At the same time, the building heat generated by daylighting will cause changes in the indoor thermal environment, thereby affecting the building energy consumption. Therefore, there is a complex coupling relationship between improving the lighting environment, avoiding glare and reducing building energy consumption. Optimizing only one of the goals will easily lead to poor effects on other design goals in residential design, which is not enough to achieve a more comprehensive improvement of the physical environment. The spatial morphological elements of the patio in traditional residential buildings include the length, width, height, sunshade, window area, and window visible light transmittance.

[0005] With the development of computer simulation experimental technology, the research and practice of multi-objective optimization of building form with the help of parametric platforms and artificial intelligence algorithms to improve indoor light environment and reduce building energy consumption have been developed to a certain extent. Although there are many studies and practices that use building form as an optimization parameter to perform multi-objective optimization of building physical environment and building energy consumption, there are still obvious deficiencies in the multi-objective optimization research based on light environment and energy saving. First, there are obvious differences in the importance of optimization objectives in multi-objective optimization calculations, but current studies are based on the average weight recommendation of optimization objectives as the optimal solution. Not only is there a lack of in-depth research on the importance of different optimization objectives, but there is also no full use of the results of optimization objective weighting in multi-objective optimization decision-making. Secondly, the Pareto front solution based on the multi-objective genetic algorithm is usually a non-inferior solution set, containing multiple solutions, which requires further decision-making. The current research lacks a comprehensive and scientific method for comprehensively ranking multiple solutions in the solution set, and fails to provide a comprehensive reference for decision makers to select the optimal solution. Summary of the invention

[0006] To solve the above technical problems, the present invention provides a courtyard space morphology design method for courtyard-style residential buildings based on multi-objective optimization, which provides a scientific and reasonable method for the green and low-carbon design and transformation of courtyard space in courtyard-style residential buildings, thereby obtaining the optimal design solution.

[0007] The technical solution adopted by the present invention is:

[0008] A method for designing the spatial form of courtyard-style residential patios based on multi-objective optimization is provided, and the specific steps are as follows:

[0009] S1, setting optimization objectives, optimization variables and optimization variable range constraints;

[0010] S2, according to the optimization goal, optimization variable setting and optimization variable range constraint in step S1, the optimization target index value is calculated by programming on the Grasshopper platform, and a courtyard-style residential patio space form design solution set based on multi-objective optimization is obtained through multi-objective optimization programming;

[0011] S3, the indicator weighting method CRITIC (Criteria Importance Through Intercriteria Correlation, CRITIC) based on indicator correlation is used to weight the optimization target;

[0012] S4, based on CRITIC + TOPSIS, the schemes are comprehensively weighted and ranked, and the optimal solution is recommended according to the maximum value of the comprehensive score index. TOPSIS refers to the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS).

[0013] Furthermore, the optimization objectives in step S1 include the lighting index O1 and the glare index O2 of the light environment optimization objective and the energy saving index O3 of the energy saving optimization objective, and the optimization variables are C1, C2, ..., C q , q is the number of optimization variables.

[0014] Furthermore, the optimization target in step S1 is calculated by parameterized programming, and the specific steps are as follows:

[0015] S21, parametric architectural geometry modeling and physical modeling are implemented by programming on the Grasshopper platform;

[0016] S22, using Ladybug plug-in on Grasshopper platform to obtain local meteorological parameters;

[0017] S23, calculate the daylighting index O1 using the HB-Daylight plug-in on the Grasshopper platform;

[0018] S24, glare index O2 is calculated using HB-Annual Glare plug-in on Grasshopper platform;

[0019] S25, calculate the energy saving index O3 using the HB-ModelToOSM plug-in on the Grasshopper platform;

[0020] S26, Wallacei plug-in was used for multi-objective optimization programming on the Grasshopper platform to obtain a set of solutions for the spatial form design of courtyard-style residential courtyards based on multi-objective optimization.

[0021] Furthermore, in step S3, the optimization target is weighted based on the CRITIC weighting method. The specific steps are as follows:

[0022] S31, construct standardized decision matrix A ij As shown in formula (1),

[0023]

[0024] In formula (1): a ij Refers to the jth optimization target index value of the ith solution; i = 1, 2, ..., m; j = 1, 2, ..., n; m refers to the total number of solutions; n refers to the number of optimization targets, and in this method, n is equal to 3;

[0025] S32, using formula (2) to perform min-max data normalization processing on the forward optimization target index in formula (1);

[0026]

[0027] In formula (2): x ij Refers to the standardized value of the jth optimization target indicator of the i-th solution;

[0028] S33, using formula (3) to perform min-max data normalization on the negative indicators in formula (1);

[0029]

[0030] S34, using formula (4) to calculate the standardized arithmetic mean of the optimization target index Formula (5) is used to calculate the optimization target index variability S j ;

[0031]

[0032] S35, using formula (6) to construct the correlation coefficient matrix R of the optimization target index jj ;

[0033]

[0034] Where r 11 =r 22 =r 33 =1, r 12 =r 21 , r 13 =r 31 , r 23 =r 32 ;

[0035] S36, using formula (7), formula (8), formula (9) to calculate r 12 、r 13 、r 23 ; And use formula (10), formula (11), and formula (12) to calculate the optimization target index conflicts B1, B2, and B3 respectively;

[0036]

[0037]

[0038] S37, using formula (13) to calculate the information carrying capacity C of the optimization target indicator j ;

[0039] C j =S j ×B j (13)

[0040] S38: Calculate the weight W of the optimization target using formula (14) j ;

[0041]

[0042] Furthermore, in step S4, the schemes are comprehensively weighted and ranked based on CRITIC+TOPSIS. The specific steps are as follows:

[0043] S41, use formula (15) to calculate the standardized decision matrix Z assigned with target weights ij :

[0044]

[0045] S42, using formula (16) to define the ideal solution Z + ;

[0046]

[0047] S43, using formula (17) to define the negative ideal solution Z - ;

[0048]

[0049] S44, using formula (18) to calculate the distance between solution i and the ideal solution

[0050]

[0051] S45, use formula (19) to calculate the distance between solution i and the negative ideal solution

[0052]

[0053] S46, using formula (20) to calculate the comprehensive score index Y of scheme i i , the higher the comprehensive score index value, the better the solution is and the higher the ranking is;

[0054]

[0055] The beneficial effects of the present invention are as follows: a scientific and reasonable method is provided for the green and low-carbon transformation of the patio space of courtyard-style residential buildings, and the comprehensive scheme sorting provides a reference for comprehensive scheme selection, thereby obtaining the optimal design scheme. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a schematic diagram of the process framework of the present invention.

[0057] Figure 2 This is a schematic diagram of a building according to an embodiment of the present invention.

[0058] Figure 3 This is a partial program schematic diagram of the present invention using the HB-Daylight plug-in to calculate the effective illumination index for daylighting.

[0059] Figure 4 This is a partial program diagram for calculating glare indicators using the HB-Annual Glare plug-in.

[0060] Figure 5 This is a partial program schematic diagram of the present invention using the HB-ModelToOSM plug-in to calculate energy consumption indicators. DETAILED DESCRIPTION

[0061] The present invention is further described below in conjunction with specific embodiments, but the present invention is not limited to these specific embodiments. Those skilled in the art should recognize that the present invention covers all possible alternatives, improvements and equivalents within the scope of the claims.

[0062] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "clockwise", "counterclockwise" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, the meaning of "multiple" is two or more, unless otherwise clearly defined.

[0063] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0064] In the present invention, unless otherwise clearly specified and limited, a first feature being "above" or "below" a second feature may include that the first and second features are in direct contact, or may include that the first and second features are not in direct contact but are in contact through another feature between them. Moreover, a first feature being "above", "above" and "above" a second feature includes that the first feature is directly above and obliquely above the second feature, or simply indicates that the first feature is higher in level than the second feature. A first feature being "below", "below" and "below" a second feature includes that the first feature is directly below and obliquely below the second feature, or simply indicates that the first feature is lower in level than the second feature.

[0065] Reference Figure 1 This embodiment provides a courtyard-style residential patio space form design method based on multi-objective optimization, and the specific steps are as follows:

[0066] S1, setting optimization objectives, optimization variables and optimization variable range constraints;

[0067] This embodiment uses a residential building plot in a community in an urban-rural integration area of ​​a certain province and a certain city as a case demonstration. The case building is designed with the most basic "mouth" shape in the courtyard-style courtyard house. The building faces northwest and southeast. The building shape is a regular square with a length of 12 meters and a width of 10.5 meters. The designed building area is 173 square meters in total. The patio space is located in the center of the case building, and windows are opened on all four sides of the patio. The method of the present invention is used to perform a multi-objective optimization design of the patio space form of the case building based on lighting, glare and energy saving. The case building is shown in the figure below. Figure 2 shown.

[0068] According to the 2021 version of the provincial residential building design standard, the heat transfer coefficient of the building wall is set to 0.9W / (m 2 ·℃), the roof heat transfer coefficient is set to 0.25W / (m 2 ·℃), the glass heat transfer coefficient is set to 1.8W / (m 2 ·℃), and the solar heat gain coefficient was set to 0.375.

[0069] Setting the lighting environment optimization target lighting index O udi is the effective illumination UDI 300-2000 , the unit is percentage (%); set the glare index O of the light environment optimization target dgp is the extreme sunlight glare probability DGP, in percentage (%); set the energy saving optimization target O energy is the annual energy consumption intensity of the building, in units of (kwh / (m 2 a).

[0070] The following seven optimization variables were set: C1 patio length, C2 patio width, C3 patio height, C4 patio internal overhang ratio, C5 window visible light transmittance, C6 patio internal east-west window-to-wall ratio, C7 patio internal north-south window-to-wall ratio; among them, C4 patio internal overhang ratio refers to the ratio of the overhang length in the patio space to the total length of the patio in the same direction.

[0071] According to the case building site conditions and general qualitative knowledge, the optimization variable range constraints are set for the optimization variables as shown in Table 1:

[0072] Table 1 Case building optimization variable range

[0073]

[0074] S2, according to the optimization goal, optimization variable setting and optimization variable range constraint in step S1, the optimization target index value is calculated by programming on the Grasshopper platform, and a courtyard-style residential patio space form design solution set based on multi-objective optimization is obtained through multi-objective optimization programming;

[0075] The specific steps are as follows:

[0076] S21, parametric architectural geometry modeling and physical modeling are implemented by programming on the Grasshopper platform;

[0077] S22, using Ladybug plug-in on Grasshopper platform to obtain local meteorological parameters;

[0078] S23, using the HB-Daylight plug-in on the Grasshopper platform to calculate the lighting index O1; this embodiment uses HB-Daylight on the Grasshopper platform to calculate the effective illumination UDI 300-2000 Simulate and constrain the indicator to be within the effective illumination range for at least 30% of the time and 60% of the space. Figure 3 .

[0079] S24, using the HB-Annual Glare plug-in on the Grasshopper platform to calculate the glare index O2; this embodiment uses HB-Annual Glare on the Grasshopper platform to simulate the probability of sunlight glare. Part of the programming content is shown in Figure 4 .

[0080] S25, calculate the energy saving index O3 using the HB-ModelToOSM plug-in on the Grasshopper platform; use HB-ModelToOSM on the Grasshopper platform to simulate energy consumption. Some of the programming content can be found in Figure 5 .

[0081] S26, using the Wallacei plug-in to perform multi-objective optimization programming on the Grasshopper platform, obtain a set of solutions for the courtyard space form design of courtyard-style residential buildings based on multi-objective optimization. In this embodiment, the population number is set to 10, the number of iterations is set to 20, and other parameters are kept at the original default values. The program is run to obtain a set of solutions for the courtyard space form design of courtyard-style residential buildings based on multi-objective optimization of lighting, glare and energy saving. The solution set of this embodiment contains 50 solutions as shown in Table 2, solution ID Gen.A|Ind.B, where A refers to the A+1th iteration number, and B refers to the B+1th population number.

[0082] Table 2 Solution set for courtyard-style residential patio space form design based on multi-objective optimization of lighting, glare and energy saving

[0083]

[0084]

[0085] S3, the indicator weighting method CRITIC (Criteria Importance Through Intercriteria Correlation, CRITIC) based on indicator correlation is used to weight the optimization target;

[0086] The specific steps are as follows:

[0087] S31, construct standardized decision matrix A ij As shown in formula (1),

[0088]

[0089] In formula (1): a ij Refers to the jth optimization target index value of the ith solution; i = 1, 2, ..., m; j = 1, 2, ..., n; m refers to the total number of solutions, m is equal to 50 in this case; n refers to the number of optimization targets, n is equal to 3 in this method;

[0090] S32, using formula (2) to perform min-max data normalization processing on the forward optimization target index (the larger the index value, the better) in formula (1);

[0091]

[0092] In formula (2): x ij Refers to the standardized value of the jth optimization target indicator of the i-th solution;

[0093] S33, using formula (3) to perform min-max data standardization processing on the negative index (the smaller the index value, the better) in formula (1);

[0094]

[0095] S34, using formula (4) to calculate the standardized arithmetic mean of the optimization target index Formula (5) is used to calculate the optimization target index variability S j ;

[0096]

[0097] S35, using formula (6) to construct the correlation coefficient matrix R of the optimization index jj ;

[0098]

[0099] Where r 11 =r 22 =r 33 =1, r 12 =r 21 , r 13=r 31 , r 23 =r 32 ;

[0100] S36, using formula (7), formula (8), formula (9) to calculate r 12 、r 13 、r 23 ; And use formula (10), formula (11), and formula (12) to calculate the optimization index conflict B1, B2, and B3 respectively;

[0101]

[0102] S37, use formula (13) to calculate the information carrying capacity C of the evaluation index j ;

[0103] C j =S j ×B j (13)

[0104] S38: Calculate the objective weight W of the target using formula (14) j ;

[0105]

[0106] This embodiment executes steps S31 to S33 to perform standardization processing of the optimization target value.

[0107] Execute step S34 to calculate the index variability S of the optimization target respectively. udi , S dgp and S energy , S udi =0.293, S dgp =0.302, S energy =0.304.

[0108] Execute steps S35 to S36: Calculate the index conflict B of the optimization target according to the correlation coefficient of the optimization index udi , B dgp and B energy , B udi =2.945, B dgp =3.024, B energy =2.643.

[0109] Execute step S37: Calculate the information carrying capacity C of the optimization target respectively udi , C dgp and C energy , C udi =0.862, C dgp =0.913, C energy =0.803.

[0110] Execute step 38: Calculate the target weight W of the optimization target according to the information carrying capacity udi , W dgp and W energy , W udi =33.446%, W dgp =35.422%, W energy =31.133%.

[0111] S4, based on CRITIC+TOPSIS, comprehensively weighted ranking of solutions is performed, and the optimal solution is recommended according to the maximum value of the comprehensive score index.

[0112] The specific steps are as follows:

[0113] S41, use formula (15) to calculate the standardized decision matrix Z assigned with target weights ij :

[0114]

[0115] S42, using formula (16) to define the ideal solution Z + ;

[0116]

[0117] S43, using formula (17) to define the negative ideal solution Z - ;

[0118]

[0119] S44, using formula (18) to calculate the distance between the solution and the ideal solution

[0120]

[0121] S45, using formula (19) to calculate the distance between the solution and the negative ideal solution

[0122]

[0123] S46, use formula (20) to calculate the comprehensive score index Y i , the higher the comprehensive score index value, the better the solution is and the higher the ranking is;

[0124]

[0125] According to Y i The values ​​​​arrange the order of advantages and disadvantages of the solutions from large to small, Y iThe one with the largest value is the optimal solution, and the comprehensive solution ranking provides a reference for comprehensive solution selection.

[0126] In this embodiment, according to steps S41 to S46, the distance between each solution and the ideal solution is evaluated after the data is normalized by a weighted normalization matrix. Negative ideal solution distance The comprehensive score index Y of each solution is calculated by comparing its relative closeness to the ideal solution. i The higher the comprehensive score index value, the better the solution is and the higher the ranking is. The ranking of the solutions is shown in Table 3.

[0127] Table 3 CRITIC+TOPSIS ranking of traditional courtyard-style residential patio space form design case solutions based on lighting, glare and energy saving

[0128]

[0129]

[0130] According to Table 3, the comprehensive score index value of Scheme Gen.0|Ind.3 is the largest and is ranked first, which is the best scheme. The comprehensive score index and ranking of the remaining schemes provide a reference for the design of this building scheme.

[0131] This embodiment conducts the following experimental results comparison and analysis. Using the TOPSIS method, the single lighting target O udi (Effective Illuminance UDI 300-2000 ) of the scheme priority weighting value, based on the single target of glare O dgp (extreme sunlight glare probability) scheme priority weighting value, based on the single goal of energy saving O energy The scheme priority weighting values ​​of (building annual energy consumption intensity) are respectively expressed in Table 4, Table 5 and Table 6. According to Table 4, scheme Gen.19|Ind.1 is the optimal scheme. According to Table 5, scheme Gen.9|Ind.2 is the optimal scheme. According to Table 6, scheme Gen.19|Ind.0 is the best scheme. The optimal solution obtained by running wallacei is Gen.12|Ind.5. Based on the scheme priority weighting value of the present invention, Gen.0|Ind.3 is the optimal scheme. It can be seen that the method of the present invention significantly improves the scientificity, comprehensiveness and flexibility of the scheme priority sorting, and fully considers the optimization target weight and the solution obtained by wallacei, providing a more comprehensive reference for the courtyard space form design of courtyard-style residential buildings based on multi-objective optimization of lighting, glare and energy saving.

[0132] Table 4 Based on the single lighting objective O udi (Effective Illuminance UDI 300-2000 ) solution set TOPSIS ranking

[0133]

[0134]

[0135]

[0136] Table 5 Based on glare single target O dgp TOPSIS ranking of the solution set (extreme sunlight glare probability)

[0137]

[0138]

[0139] Table 6 Based on the single goal of energy saving energy TOPSIS ranking of the solution set (building annual energy consumption intensity)

[0140]

[0141]

Claims

1. A courtyard-style residential patio space form design method based on multi-objective optimization, the specific steps are as follows: S1, setting optimization objectives, optimization variables and optimization variable range constraints; S2, according to the optimization goal, optimization variable setting and optimization variable range constraint in step S1, the optimization target index value is calculated by programming on the Grasshopper platform, and a courtyard-style residential patio space form design solution set based on multi-objective optimization is obtained through multi-objective optimization programming; S3, the indicator weighting method CRITIC based on indicator correlation is used to weight the optimization target; S4, based on CRITIC+TOPSIS, comprehensively weighted ranking of solutions is performed, and the optimal solution is recommended according to the maximum value of the comprehensive score index.

2. The method for designing the spatial form of courtyard-style residential patios based on multi-objective optimization according to claim 1 is characterized by: The optimization objectives in step S1 include the lighting index O1 and the glare index O2 of the light environment optimization objective and the energy saving index O3 of the energy saving optimization objective. The optimization variables are C1, C2, ..., C q , q is the number of optimization variables.

3. The method for designing the spatial form of courtyard-style residential patios based on multi-objective optimization according to claim 2 is characterized by: The optimization target in step S1 is calculated by parametric programming, and the specific steps are as follows: S21, parametric architectural geometry modeling and physical modeling are implemented by programming on the Grasshopper platform; S22, using Ladybug plug-in on Grasshopper platform to obtain local meteorological parameters; S23, calculate the daylighting index O1 using the HB-Daylight plug-in on the Grasshopper platform; S24, glare index O2 is calculated using HB-Annual Glare plug-in on Grasshopper platform; S25, calculate the energy saving index O3 using the HB-ModelToOSM plug-in on the Grasshopper platform; S26, Wallacei plug-in was used for multi-objective optimization programming on the Grasshopper platform to obtain a set of solutions for the spatial form design of courtyard-style residential courtyards based on multi-objective optimization.

4. The method for designing the spatial form of courtyard-style residential patios based on multi-objective optimization according to claim 3 is characterized by: In step S3, the optimization target is weighted based on the CRITIC weighting method. The specific steps are as follows: S31, construct standardized decision matrix A ij As shown in formula (1), In formula (1): a ij Refers to the jth optimization target index value of the ith solution; i = 1, 2, ..., m; j = 1, 2, ..., n; m refers to the total number of solutions; n refers to the number of optimization targets, and in this method, n is equal to 3; S32, using formula (2) to perform min-max data normalization processing on the forward optimization target index in formula (1); In formula (2): x ij Refers to the standardized value of the jth optimization target indicator of the i-th solution; S33, using formula (3) to perform min-max data normalization on the negative indicators in formula (1); S34, using formula (4) to calculate the standardized arithmetic mean of the optimization target index Formula (5) is used to calculate the optimization target index variability S j ; S35, using formula (6) to construct the correlation coefficient matrix R of the optimization target index jj ; Where r 11 =r 22 =r 33 =1, r 12 =r 21 , r 13 =r 31 , r 23 =r 32 ; S36, using formula (7), formula (8), formula (9) to calculate r 12 、r 13 、r 23 ; And use formula (10), formula (11), and formula (12) to calculate the optimization target index conflicts B1, B2, and B3 respectively; S37, using formula (13) to calculate the information carrying capacity C of the optimization target indicator j ; C j =S j ×B j (13) S38: Calculate the weight W of the optimization target using formula (14) j ; 5. The method for designing the spatial form of courtyard-style residential patios based on multi-objective optimization according to claim 4 is characterized by: In step S4, the schemes are comprehensively weighted and ranked based on CRITIC+TOPSIS. The specific steps are as follows: S41, use formula (15) to calculate the standardized decision matrix Z assigned with target weights ij : S42, using formula (16) to define the ideal solution Z + ; S43, using formula (17) to define the negative ideal solution Z - ; S44, using formula (18) to calculate the distance between solution i and the ideal solution S45, use formula (19) to calculate the distance between solution i and the negative ideal solution S46, using formula (20) to calculate the comprehensive score index Y of scheme i i , the higher the comprehensive score index value, the better the solution is and the higher the ranking is;

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