Concrete pump truck preferred method based on criteria removal and double normalization

Abstract

The application provides a kind of concrete pump truck preferred method based on criteria removal and double normalization, it is related to building engineering technical field, the method comprises: determining several basic concrete pump truck value evaluation criteria and several concrete pump truck alternative schemes;Using the method of criteria removal effect to determine the weight of each value evaluation criterion;Using linear normalization method to normalize the data of each alternative scheme, to obtain extended linear normalization matrix;Using vector normalization method to normalize the data of each alternative scheme, to obtain extended vector normalization matrix;Based on extended linear normalization matrix, extended vector normalization matrix and the weight of each value evaluation criterion, determine the comprehensive utility value of each alternative scheme;According to the comprehensive utility value of each alternative scheme, select the concrete pump truck needed by building engineering.This scheme can improve the accuracy and reliability of the optimization of concrete pump truck.

Description

Technical Field

[0001] The present invention relates to the technical field of construction engineering, and in particular to a concrete pump truck optimization method based on criterion removal and double normalization. Background Art

[0002] With the acceleration of globalization and urbanization, the scale and complexity of construction projects are increasing, making the selection of construction equipment even more crucial. This is especially true when selecting critical equipment like concrete pump trucks. Misjudgment can lead to inefficient construction, increased costs, and project delays. Therefore, making informed choices among numerous options has become a major challenge facing the current construction industry. To address this challenge, researchers have been exploring more effective multi-criteria decision-making methods to improve the accuracy and reliability of equipment selection.

[0003] When selecting construction equipment, decision-makers often need to consider multiple, conflicting criteria, such as price, performance, environmental friendliness, and service life. The complexity and diversity of these factors make traditional single-criteria decision-making methods difficult to meet real-world needs. For example, the vast array of concrete pump trucks available on the market, each with its own unique performance under different criteria, further complicating decision-making. Faced with these challenges, effectively integrating multiple evaluation criteria to optimize the selection has become a pressing issue.

[0004] Existing multi-criteria decision-making methods, such as TOPSIS, VIKOR, and MARCOS, while capable of handling complex decision-making problems to a certain extent, typically rely on a single standardization technique. This single standardization technique often leads to bias and distorted results when used with diverse data types, making it difficult to fully reflect the relative importance of each criterion. Furthermore, these multi-criteria decision-making methods often involve a high degree of human subjective judgment, which in turn leads to significant bias, significantly reducing the accuracy and credibility of the decision results. Summary of the Invention

[0005] In view of this, in order to address the above shortcomings, it is necessary to propose a concrete pump truck optimization method based on criterion removal and double normalization to improve the accuracy and credibility of concrete pump truck optimization.

[0006] The present invention provides a concrete pump truck optimization method based on criterion removal and double normalization, the optimization method comprising:

[0007] Determine several basic concrete pump truck value evaluation criteria and several alternative concrete pump truck options; wherein the alternative options include the types of alternative concrete pump trucks and the performance parameters of each type of concrete pump truck in terms of each value evaluation criterion;

[0008] The weight of each value evaluation criterion is determined by using the criterion removal effect method;

[0009] Normalizing the data of each of the alternative solutions using a linear normalization method to obtain an extended linear normalization matrix;

[0010] Normalizing the data of each of the alternative solutions using a vector normalization method to obtain an extended vector normalization matrix;

[0011] Determining the comprehensive utility value of each alternative plan based on the extended linear normalized matrix, the extended vector normalized matrix, and the weights of each value evaluation criterion;

[0012] According to the comprehensive utility value of each alternative plan, the concrete pump truck required for the construction project is selected.

[0013] Preferably, the method of using the criterion removal effect to determine the weight of each value evaluation criterion includes:

[0014] Performing linear normalization processing on the initial decision matrix to obtain a normalized decision matrix; wherein the initial decision matrix is ​​a matrix composed of performance parameters of the concrete pump truck corresponding to each alternative solution in terms of each value evaluation standard;

[0015] Determining a first overall performance of each alternative plan using a logarithmic metric based on the normalized decision matrix;

[0016] Removing one value evaluation criterion from the normalized decision matrix one at a time, and determining the second overall performance of each alternative plan after removing one value evaluation criterion in turn by using a logarithmic measurement method;

[0017] Calculating the deviation between the second overall performance and the first overall performance corresponding to each value evaluation standard to obtain the impact value corresponding to each value evaluation standard after excluding the value evaluation standard;

[0018] The weight value of each value evaluation criterion is determined based on the impact value corresponding to each value evaluation criterion.

[0019] Preferably, the performing linear normalization processing on the initial decision matrix includes:

[0020] The initial decision matrix is ​​linearly normalized using the following formula:

[0021]

[0022] in, is the element x in the initial decision matrix ij The value after linear normalization, x ijIt is used to represent the performance parameter value of the j-th value evaluation criterion corresponding to the i-th alternative in the initial decision matrix. Benefit is used to represent the type of value evaluation criterion as benefit, and Cost is used to represent the type of value evaluation criterion as cost.

[0023] and / or,

[0024] Determining the first overall performance of each alternative solution using a logarithmic measurement method based on the normalized decision matrix includes:

[0025] The first overall performance of each alternative is determined using the following calculation formula:

[0026]

[0027] Among them, S i is used to characterize the first overall performance of the i-th alternative, m is used to characterize the number of types of value evaluation criteria, is the element x in the initial decision matrix ij The value after linear normalization;

[0028] and / or,

[0029] Removing one value evaluation criterion from the normalized decision matrix each time and determining the second overall performance of each alternative solution after removing one value evaluation criterion in turn by using a logarithmic measurement method includes:

[0030] For each value evaluation criterion, the second overall performance of each alternative solution when the value evaluation criterion is removed is calculated using the following formula:

[0031]

[0032] Among them, S i ' j It is used to represent the second overall performance of the i-th alternative when the j-th value evaluation criterion is removed, and m is used to represent the number of types of value evaluation criteria. is the element x in the initial decision matrix ik The value after linear normalization, and the k-th value evaluation criterion is not the j-th value evaluation criterion currently removed;

[0033] and / or,

[0034] Calculating the deviation between the second overall performance and the first overall performance corresponding to each value evaluation standard includes:

[0035] The deviation between the second overall performance and the first overall performance is calculated using the following formula:

[0036]

[0037] Among them, E j Used to represent the impact value of eliminating the j-th value evaluation criterion, S i ' j Used to characterize the second overall performance of the i-th alternative when the j-th value evaluation criterion is removed, S i used to characterize the first overall performance of the i-th alternative;

[0038] and / or,

[0039] Determining the weight of each value evaluation criterion according to the impact value corresponding to each value evaluation criterion includes:

[0040] Use the following formula to calculate the weight of each value evaluation standard:

[0041]

[0042] Among them, w j The weight value used to represent the j-th value evaluation criterion, E j Used to represent the impact value of eliminating the j-th value evaluation standard, E k Used to represent the impact value of eliminating the k-th value evaluation criterion.

[0043] Preferably, the method of normalizing the data of each alternative solution using a linear normalization method includes:

[0044] The initial matrix M = [α ij ] m×n Perform linear normalization processing to obtain a linear normalized matrix; where m represents the number of alternatives, n represents the number of value evaluation criteria, and α ij The performance parameter representing the j-th value evaluation criterion corresponding to the i-th alternative:

[0045]

[0046] Among them, α i ' j is the linear normalization matrix, α ij It is used to represent the performance parameter value of the j-th value evaluation criterion corresponding to the i-th alternative in the initial matrix. Benefit is used to represent the type of value evaluation criterion as benefit, and Cost is used to represent the type of value evaluation criterion as cost.

[0047] The ideal solution and anti-ideal solution are introduced by the following calculation formula to expand the linear normalized matrix and obtain the extended linear normalized matrix:

[0048]

[0049] in, and are the extended linear normalized matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

[0050] Preferably, the normalization process for the data of each of the alternative solutions is performed using a vector normalization method, including:

[0051] The initial matrix M = [α ij ] m×n Perform vector normalization to obtain the vector normalization matrix:

[0052]

[0053] Among them, α i ' j ′ is the vector normalization matrix;

[0054] The vector normalization matrix is ​​expanded by introducing the ideal solution and anti-ideal solution through the following calculation formula to obtain the expanded vector normalization matrix:

[0055]

[0056] in, and are the extended vector normalization matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

[0057] Preferably, the determining of the comprehensive utility value of each alternative solution based on the extended linear normalized matrix, the extended vector normalized matrix and the weight of each value evaluation criterion includes:

[0058] Determining a weighted extended linear normalized matrix according to the weights of the value evaluation criteria and the extended linear normalized matrix;

[0059] Determining a weighted extended vector normalization matrix based on the weights of the value evaluation criteria and the extended vector normalization matrix;

[0060] Determining, according to the weighted extended linear normalization matrix and the weighted extended vector normalization matrix, the subordinate values ​​of each alternative scheme with respect to a complete compensation model, a non-compensation model, and an incomplete compensation model;

[0061] Determining the utility of each alternative for the full compensation model, the non-compensation model, and the incomplete compensation model, respectively, according to the membership values ​​of each alternative with respect to the full compensation model, the non-compensation model, and the incomplete compensation model;

[0062] Determining the utility value of each alternative solution corresponding to each model according to the utility degree of each alternative solution corresponding to each model;

[0063] According to the utility values ​​of the alternative plans corresponding to each model, the comprehensive utility value of the alternative plans is determined.

[0064] Preferably, determining the weighted extended linear normalized matrix according to the weight of the value evaluation standard and the extended linear normalized matrix includes:

[0065] The weighted extended linear normalization matrix is ​​determined using the following formula:

[0066]

[0067] in, is the weighted linear normalization matrix, and are the weighted extended linear normalized matrices corresponding to the ideal solution and anti-ideal solution, w j is the weight of the jth value evaluation criterion, α i ' j is the linear normalized matrix, and are the extended linear normalized matrices obtained by introducing the ideal solution and anti-ideal solution respectively;

[0068] and / or,

[0069] The step of determining the weighted extended vector normalization matrix according to the weight of the value evaluation standard and the extended vector normalization matrix includes:

[0070] The weighted expansion vector normalization matrix is ​​determined using the following calculation formula:

[0071]

[0072] in, is the weight vector normalization matrix, and are the weighted expansion vector normalization matrices corresponding to the ideal solution and anti-ideal solution, w j is the weight of the jth value evaluation criterion, α i ' j ′ is the vector normalization matrix, and are the extended vector normalization matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

[0073] Preferably, the determining of the subordinate values ​​of each alternative scheme with respect to the complete compensation model, the non-compensation model and the incomplete compensation model respectively according to the weighted extended linear normalization matrix and the weighted extended vector normalization matrix includes:

[0074] The following formula is used to calculate the membership value of the i-th alternative based on the full compensation model:

[0075] The following calculation formula is used to calculate the membership value of the i-th alternative solution corresponding to the ideal solution and the anti-ideal solution of the fully compensated model respectively: and

[0076]

[0077]

[0078] The membership value of the i-th alternative based on the non-compensation model is calculated using the following formula:

[0079] The following calculation formula is used to calculate the membership value of the i-th alternative solution corresponding to the ideal solution and the anti-ideal solution of the non-compensated model respectively: and

[0080]

[0081] The following formula is used to calculate the membership value of the i-th alternative based on the incomplete compensation model:

[0082] Use the following calculation formula to calculate the membership value of the i-th alternative solution of the incomplete compensation model corresponding to the ideal solution and the anti-ideal solution respectively: and

[0083]

[0084]

[0085] Here, π is used to represent the quadrature.

[0086] Preferably,

[0087] The determining of the utility of each alternative scheme for the complete compensation model, the non-compensation model and the incomplete compensation model according to the subordinate values ​​of each alternative scheme with respect to the complete compensation model, the non-compensation model and the incomplete compensation model respectively includes:

[0088] The utility of each alternative plan corresponding to the complete compensation model is calculated using the following formula:

[0089]

[0090]

[0091] in, and are the utilities of the alternatives corresponding to the perfect compensation model for the ideal solution and the anti-ideal solution respectively;

[0092] The utility of each alternative plan corresponding to the non-compensation model is calculated using the following formula:

[0093]

[0094]

[0095] in, and are the utilities of the alternatives of the non-compensation model corresponding to the ideal solution and the anti-ideal solution respectively;

[0096] The utility of each alternative plan corresponding to the incomplete compensation model is calculated using the following formula:

[0097]

[0098]

[0099] in, and are the utilities of the alternatives of the incomplete compensation model corresponding to the ideal solution and the anti-ideal solution respectively;

[0100] and / or,

[0101] The determining of the utility value of each alternative solution corresponding to each model according to the utility degree of each alternative solution corresponding to each model includes:

[0102] The utility value of the i-th alternative of the perfect compensation model corresponding to the ideal solution and the anti-ideal solution is calculated using the following formula:

[0103]

[0104]

[0105] in, and are the utility values ​​of the ith alternative of the perfect compensation model corresponding to the ideal solution and the anti-ideal solution, respectively;

[0106] The utility value of the i-th alternative of the non-compensation model corresponding to the ideal solution and the anti-ideal solution is calculated using the following formula:

[0107]

[0108]

[0109] in, and are the utility values ​​of the i-th alternative of the non-compensation model corresponding to the ideal solution and the anti-ideal solution, respectively;

[0110] The utility value of the i-th alternative of the incomplete compensation model corresponding to the ideal solution and the anti-ideal solution is calculated using the following formula:

[0111]

[0112]

[0113] in, and are the utility values ​​of the i-th alternative plan of the incomplete compensation model corresponding to the ideal solution and anti-ideal solution, respectively.

[0114] Preferably, determining the comprehensive utility value of each alternative solution according to the utility value of each alternative solution corresponding to each model includes:

[0115] The comprehensive utility value of each alternative plan is calculated using the following formula:

[0116]

[0117] Among them, λ i It is used to represent the comprehensive utility value of the ith alternative, and p, q and (1-pq) represent the weights of the complete compensation model, non-compensation model and incomplete compensation model respectively.

[0118] From the above technical solution, it can be seen that in the concrete pump truck optimization method based on criterion removal and double normalization provided by the present invention, several basic concrete pump truck value evaluation criteria and several alternative concrete pump truck solutions are first determined, and then the weight of each value evaluation criterion is determined by using the criterion removal effect method; the data of the alternative solutions are further normalized by using linear normalization and vector normalization respectively, and the obtained extended linear normalization matrix and extended vector normalization matrix are used to determine the comprehensive utility value of each alternative solution in combination with the weight of the value evaluation criterion, and then the optimal solution of the required concrete pump truck can be selected in the construction process according to the comprehensive utility value of each alternative solution. It can be seen that this solution more objectively determines the weight value of each value evaluation criterion based on the criterion removal effect, avoids the bias caused by subjective judgment, and makes the optimization solution more fair and reliable; moreover, this solution uses a double normalization method to process the data, overcoming the shortcomings of single normalization, strong subjectivity in weight allocation, and lack of multi-dimensional evaluation, so that the optimal choice can be made in the selection of concrete pump truck solutions, greatly improving the accuracy and credibility of the optimization of concrete pump trucks. BRIEF DESCRIPTION OF THE DRAWINGS

[0119] Figure 1 A flowchart of a method for optimizing a concrete pump truck based on criterion removal and double normalization is provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0120] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following is a brief introduction to the drawings required for use in the embodiments. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0121] The main drawback of the traditional MARCOS method is that it uses a single normalization (linear normalization) technique. In order to address this drawback, this scheme proposes a dual normalization method. In the dual normalization method, two types of normalization methods are used, namely linear normalization and vector normalization. The method can be further composed of three aggregation models, namely the complete compensation model (CCM), the uncompensated model (UCM) and the incomplete compensation model (ICM). For the CCM-based model, the good performance of an alternative under certain criteria can completely make up for the poor performance of the alternative under other criteria. Subsequently, the best alternative derived obtains the maximum comprehensive value in terms of all criteria. In addition, the UCM model shows the worst performance of an alternative in terms of all criteria. The potential problem that the good performance of a particular alternative can make up for the performance defects of some alternatives prompted the construction of the ICM model. By merging the final results of the above three aggregation models, it is possible to obtain the result value of each alternative. Therefore, this scheme considers optimizing concrete pump trucks by combining dual normalization and removal criteria. As Figure 1 As shown, the present invention provides a concrete pump truck optimization method based on criterion removal and double normalization, which may include the following steps:

[0122] Step 10: Determine several basic concrete pump truck value evaluation criteria and several alternative concrete pump truck options; the alternative options include the types of alternative concrete pump trucks and the performance parameters of each type of concrete pump truck in terms of each value evaluation criterion;

[0123] Step 20: Determine the weight of each value evaluation criterion using the criterion removal effect method;

[0124] Step 30: normalize the data of each alternative solution using a linear normalization method to obtain an extended linear normalization matrix;

[0125] Step 40: normalize the data of each alternative solution using a vector normalization method to obtain an extended vector normalization matrix;

[0126] Step 50: Determine the comprehensive utility value of each alternative plan based on the extended linear normalization matrix, the extended vector normalization matrix, and the weights of each value evaluation criterion;

[0127] Step 60: Select the concrete pump truck required for the construction project based on the comprehensive utility values ​​of the alternative solutions.

[0128] In this embodiment, the weight value of each value evaluation criterion is determined more objectively based on the criterion removal effect, which avoids the deviation caused by subjective judgment and makes the optimization scheme more fair and reliable. Moreover, this scheme uses a double normalization method to process the data, which overcomes the shortcomings of bias caused by single normalization, strong subjectivity in weight allocation, and lack of multi-dimensional evaluation, thereby making it possible to make the best choice in the selection scheme of concrete pump trucks, greatly improving the accuracy and credibility of the optimization of concrete pump trucks.

[0129] For step 10, determine several basic concrete pump truck value evaluation criteria and several alternative concrete pump truck options;

[0130] In this step, we consider selecting a value evaluation standard for a truck-mounted concrete mixer pump. When determining a standard, we need to verify whether the value of the standard should be maximized or minimized. Standards that are expected to have the highest possible value should be classified as benefit-oriented, while standards that are expected to have the lowest possible value should be classified as cost-oriented. For example, the standards for one embodiment can be shown in Table 1:

[0131] Table 1

[0132]

[0133]

[0134] The alternatives may include the following 16 concrete pump truck models: MagnumMK 24.4Z-80 / 115RH(A1); Magnum MK 28L-5-80 / 115RH(A2); Magnum MK25 H80 RH(A3); Iveco MK 28(A4); Iveco MK24.4Badanie(A5); Mercedes-Benz Actros MB4144B(A6); Renault Kerax 420(A7); Mercedes-Benz Actros 3241(A8); Mercedes-Benz Actros 3241(A9); Mercedes-Benz 3244(A10); Mercedes-Benz3241(A11); Mercedes-Benz Actros 3241(A12); MANTGA 37.410 (A13); MAN 41460 (A14); MAN TGA (A15); Iveco 500 (A16); some of these models are identical, but they differ in age and price. By giving each alternative the performance parameters corresponding to the value evaluation criteria, we can obtain the data table shown in Table 2:

[0135] Table 2

[0136]

[0137] For step 20, the weight of each value evaluation criterion is determined by using the criterion removal effect method;

[0138] Once the value evaluation criteria and the types of pump trucks in the alternatives are defined, the initial decision matrix is ​​determined as shown in Table 2. In order to determine the priority of the alternatives and select the alternative that best meets the established decision objectives, the weights of each value evaluation criterion are determined based on the criterion removal effect. This can be achieved through the following steps:

[0139] Step S21: performing linear normalization processing on the initial decision matrix to obtain a normalized decision matrix; wherein the initial decision matrix is ​​a matrix composed of performance parameters of the concrete pump truck corresponding to each alternative solution in terms of each value evaluation standard;

[0140] In this step, consider using the following formula to perform linear normalization on the initial decision matrix:

[0141]

[0142] in, is the element x in the initial decision matrix ij The value after linear normalization, xij It is used to represent the performance parameter value of the j-th value evaluation criterion corresponding to the i-th alternative in the initial decision matrix. Benefit is used to represent the type of value evaluation criterion as benefit type, and Cost is used to represent the type of value evaluation criterion as cost type.

[0143] For example, after normalizing the initial decision matrix corresponding to Table 2 based on the above calculation formula, the normalized results shown in Table 3 can be obtained:

[0144] Table 3

[0145]

[0146]

[0147] Step S22: Determine the first overall performance of each alternative solution using a logarithmic measurement method based on the normalized decision matrix;

[0148] In this step, the following calculation formula is used to determine the first overall performance of each alternative solution:

[0149]

[0150] Among them, S i is used to characterize the first overall performance of the i-th alternative, m is used to characterize the number of types of value evaluation criteria, is the element x in the initial decision matrix ij The value after linear normalization;

[0151] In this embodiment, a logarithmic metric with the same standard priority weight is used to determine the overall performance of each alternative, which is based on a nonlinear function. Based on the normalized values ​​obtained in the previous stage, it ensures a lower Value can produce a larger efficiency value S i .

[0152] For example, the first overall performance calculation results based on the above example are as follows: S1 = 0.408, S2 = 0.411, S3 = 0.386, S4 = 0.221, S5 = 0.177, S6 = 0.202, S7 = 0.145, S8 = 0.0.198, S9 = 0.253, S 10 =0.222, S 11 =0.226, S 12 =0.187, S 13 =0.196, S 14 =0.214, S 15 =0.244, S 16 =0.192.

[0153] Step S23: removing one value evaluation criterion from the normalized decision matrix one at a time, and determining the second overall performance of each alternative solution after removing one value evaluation criterion in turn using a logarithmic measurement method;

[0154] In this step, consider the stage of calculating each alternative by removing each value evaluation criterion and using a logarithmic metric. In this stage, the performance of each alternative is evaluated by removing one criterion at a time. Specifically, for each value evaluation criterion, the second overall performance of each alternative when the value evaluation criterion is removed can be calculated using the following calculation formula:

[0155]

[0156] Among them, S i ' j It is used to represent the second overall performance of the i-th alternative when the j-th value evaluation criterion is removed, and m is used to represent the number of types of value evaluation criteria. is the element x in the initial decision matrix ik The value after linear normalization, and the k-th value evaluation criterion is not the j-th value evaluation criterion currently removed;

[0157] For example, based on the above example, the obtained S1′1=1.225.

[0158] Step S24: Calculate the deviation between the second overall performance and the first overall performance corresponding to each value evaluation standard to obtain the impact value corresponding to each value evaluation standard after excluding the value evaluation standard;

[0159] This step considers calculating the absolute value deviation comprehensive affected by the values ​​obtained in step S23 and step S24, that is, the elimination effect of the j-th value evaluation criterion. Specifically, it can be obtained by the following calculation formula:

[0160]

[0161] Among them, E j Used to represent the impact value of eliminating the j-th value evaluation criterion, S i ' j Used to characterize the second overall performance of the i-th alternative when the j-th value evaluation criterion is removed, S i Used to characterize the first overall performance of the i-th alternative.

[0162] For example, based on the above example, we obtain E1=8.161.

[0163] Step S25: Determine the weight value of each value evaluation criterion according to the impact value corresponding to each value evaluation criterion.

[0164] This step considers the elimination effect E obtained in step S24. j To determine the final target weight of each value evaluation criterion. Specifically, the weight value of each value evaluation criterion can be calculated as follows:

[0165]

[0166] Among them, w j The weight value used to represent the j-th value evaluation criterion, E j Used to represent the impact value of eliminating the j-th value evaluation standard, E k Used to represent the impact value of eliminating the k-th value evaluation criterion.

[0167] For example, the w1 calculated in the above example is 0.100, and the weight values ​​of other value evaluation criteria can be obtained similarly.

[0168] In step 30, the data of each alternative solution is normalized using a linear normalization method to obtain an extended linear normalization matrix;

[0169] In this step, when the linear normalization method is used for normalization, it can be specifically implemented in the following manner:

[0170] The initial matrix M = [α ij ] m×n Perform linear normalization processing to obtain a linear normalized matrix; where m represents the number of alternatives, n represents the number of value evaluation criteria, and α ij The performance parameter representing the j-th value evaluation criterion corresponding to the i-th alternative:

[0171]

[0172] Among them, α i ' j is the linear normalization matrix, α ij It is used to represent the performance parameter value of the j-th value evaluation criterion corresponding to the i-th alternative in the initial matrix. Benefit is used to represent the type of value evaluation criterion as benefit, and Cost is used to represent the type of value evaluation criterion as cost.

[0173] It should be noted that the α here ij With the above x ij They are consistent, both representing the performance parameter value of the j-th value evaluation criterion of the i-th alternative in the value evaluation criterion matrix corresponding to the alternative.

[0174] For example, the obtained results can be seen in Table 3.

[0175] The ideal solution and anti-ideal solution are introduced by the following calculation formula to expand the linear normalized matrix and obtain the extended linear normalized matrix:

[0176]

[0177]

[0178] in, and are the extended linear normalized matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

[0179] In this embodiment, the ideal solution and the anti-ideal solution correspond to the optimal solution and the worst solution, respectively.

[0180] Similarly, for step 40, the data of each alternative solution is normalized using a vector normalization method to obtain an extended vector normalization matrix;

[0181] In this step, when the vector normalization method is used for normalization processing, it can be specifically implemented in the following way:

[0182] The initial matrix M = [α ij ] m×n Perform vector normalization to obtain the vector normalization matrix:

[0183]

[0184] Among them, α i ' j ′ is the vector normalization matrix;

[0185] For example, the obtained results can be seen in Table 4 below.

[0186] Table 4

[0187]

[0188] The vector normalization matrix is ​​expanded by introducing the ideal solution and anti-ideal solution through the following calculation formula to obtain the expanded vector normalization matrix:

[0189]

[0190] in, and are the extended vector normalization matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

[0191] For step 50, based on the extended linear normalization matrix, the extended vector normalization matrix and the weights of each value evaluation criterion, the comprehensive utility value of each alternative solution is determined;

[0192] This step can be achieved by the following steps when determining the comprehensive utility value of each alternative plan based on the extended linear normalization matrix, the extended vector normalization matrix, and the weights of each value evaluation criterion:

[0193] Step S51: determining a weighted extended linear normalization matrix according to the weight of the value evaluation standard and the extended linear normalization matrix;

[0194] In this step, the weighted extended linear normalization matrix is ​​determined using the following formula:

[0195]

[0196] in, is the weighted linear normalization matrix, and are the weighted extended linear normalized matrices corresponding to the ideal solution and anti-ideal solution, w j is the weight of the jth value evaluation criterion, α i ' j is the linear normalized matrix, and are the extended linear normalized matrices obtained by introducing the ideal solution and anti-ideal solution respectively;

[0197] Step S52: determining a weighted extended vector normalization matrix according to the weight of the value evaluation standard and the extended vector normalization matrix;

[0198] In this step, the weighted expansion vector normalization matrix is ​​determined using the following formula:

[0199]

[0200] in, is the weight vector normalization matrix, and are the weighted expansion vector normalization matrices corresponding to the ideal solution and anti-ideal solution, w j is the weight of the jth value evaluation criterion, α i ' j ′ is the vector normalization matrix, and are the extended vector normalization matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

[0201] Step S53: determining the subordinate values ​​of each alternative solution with respect to the complete compensation model, the non-compensation model, and the incomplete compensation model according to the weighted extended linear normalization matrix and the weighted extended vector normalization matrix;

[0202] (1) For the fully compensated model CCM:

[0203] Consider using the following formula to calculate the membership value of the ith alternative based on the full compensation model:

[0204] The following calculation formula is used to calculate the membership value of the i-th alternative solution corresponding to the ideal solution and the anti-ideal solution of the fully compensated model respectively: and

[0205]

[0206]

[0207] (2) For the uncompensated model UCM:

[0208] Consider using the following formula to calculate the membership value of the i-th alternative based on the non-compensation model:

[0209] The following calculation formula is used to calculate the membership value of the i-th alternative solution corresponding to the ideal solution and the anti-ideal solution of the non-compensated model respectively: and

[0210]

[0211]

[0212] (3) For the incomplete compensation model ICM:

[0213] Consider using the following formula to calculate the subordinate value of the i-th alternative based on the incomplete compensation model:

[0214]

[0215]

[0216] Use the following calculation formula to calculate the membership value of the i-th alternative solution of the incomplete compensation model corresponding to the ideal solution and the anti-ideal solution respectively: and

[0217]

[0218]

[0219] Here, π is used to represent the quadrature.

[0220] For example, the membership values ​​of each model are shown in Table 5.

[0221] Table 5

[0222]

[0223] Step S54: determining the utility of each alternative solution for the complete compensation model, the non-compensation model, and the incomplete compensation model, respectively, based on the membership values ​​of each alternative solution with respect to the complete compensation model, the non-compensation model, and the incomplete compensation model;

[0224] (1) For the fully compensated model CCM:

[0225] Consider using the following formula to calculate the utility of each alternative plan corresponding to the complete compensation model:

[0226]

[0227] in, and are the utilities of the alternatives corresponding to the perfect compensation model for the ideal solution and the anti-ideal solution respectively;

[0228] (2) For the uncompensated model UCM:

[0229] Consider using the following formula to calculate the utility of each alternative plan corresponding to the non-compensation model:

[0230]

[0231] in, and are the utilities of the alternatives of the non-compensation model corresponding to the ideal solution and the anti-ideal solution respectively;

[0232] (3) For the incomplete compensation model ICM:

[0233] Consider using the following formula to calculate the utility of each alternative plan corresponding to the incomplete compensation model:

[0234]

[0235] in, and are the utilities of the alternatives of the incomplete compensation model corresponding to the ideal solution and the anti-ideal solution respectively;

[0236] For example, the effectiveness of each model is shown in Table 6.

[0237] Table 6

[0238]

[0239]

[0240] Step S55: determining the utility value of each alternative solution corresponding to each model according to the utility degree of each alternative solution corresponding to each model;

[0241] (1) For the fully compensated model CCM:

[0242] Consider using the following formula to calculate the utility value of the i-th alternative of the fully compensated model corresponding to the ideal solution and the anti-ideal solution:

[0243]

[0244] in, and are the utility values ​​of the ith alternative of the perfect compensation model corresponding to the ideal solution and the anti-ideal solution, respectively;

[0245] (2) For the uncompensated model UCM:

[0246] Consider using the following formula to calculate the utility value of the i-th alternative of the non-compensation model corresponding to the ideal solution and the anti-ideal solution:

[0247]

[0248] Among them, λ i (2)(+) and λ i (2)(-) are the utility values ​​of the i-th alternative of the non-compensation model corresponding to the ideal solution and the anti-ideal solution, respectively;

[0249] (3) For the incomplete compensation model ICM:

[0250] Consider using the following formula to calculate the utility value of the i-th alternative of the incomplete compensation model corresponding to the ideal solution and the anti-ideal solution:

[0251]

[0252] in, and are the utility values ​​of the i-th alternative plan of the incomplete compensation model corresponding to the ideal solution and anti-ideal solution, respectively.

[0253] For example, the utility values ​​corresponding to each model are shown in Table 7.

[0254] Table 7

[0255]

[0256] Step S56: Determine the comprehensive utility value of each alternative solution based on the utility value of each alternative solution corresponding to each model.

[0257] In this step, consider using the following formula to calculate the comprehensive utility value of each alternative plan:

[0258]

[0259] Among them, λ i Used to characterize the comprehensive utility value of the i-th alternative.

[0260] In this step, p, q, and (1-pq) represent the weights for the fully compensating, non-compensating, and incompletely compensating models, respectively. These weights can be selected based on the decision maker's preference for the alternatives' overall performance or their underperformance. If the decision maker prioritizes the overall performance of the alternatives, they will tend to choose the fully compensating model. If the decision maker is risk-averse, they can assign a higher weight to the non-compensating model.

[0261] For example, the overall utility values ​​of the alternatives obtained based on the above example are: (assuming p = q = 0.3): λ1 = 0.7055, λ2 = 0.6909, λ3 = 0.6784, λ4 = 0.6345, λ5 = 0.6261, λ6 = 0.6408, λ7 = 0.6021, λ8 = 0.6237, λ9 = 0.6449, λ 10 =0.6421,λ 11 =0.6221,λ 12 =0.6192,λ 13 =0.6287,λ 14 =0.6394,λ 15 =0.6518,λ 16 =0.6375.

[0262] In step 60 , the concrete pump truck required for the construction project is selected based on the comprehensive utility values ​​of the alternative solutions.

[0263] In this step, consider sorting the alternatives according to their comprehensive utility values, and then select the corresponding concrete pump truck based on the sorting results. For example, in the above example, the sorting results from largest to smallest are: A1, A2, A3, A15, A9, A10, A6, A14, A16, A4, A13, A5, A8, A11, A12, A7.

[0264] In summary, the concrete pump truck optimization method based on criterion removal and double normalization proposed in this scheme can optimize the selection process of concrete pump trucks for construction equipment. This method combines double normalization and criterion removal methods to overcome the decision-making bias and subjectivity caused by traditional single normalization. The weights of the value evaluation indicators are calculated by the criterion removal method, which ensures the objectivity of the weight distribution and reduces human interference. Then, the extended linear normalization matrix and the extended vector normalization matrix are constructed respectively using double normalization technology, which improves the comprehensiveness of data processing. Furthermore, this method conducts a multi-dimensional comprehensive evaluation through three models of full compensation, non-compensation and incomplete compensation, and finally obtains the optimal selection scheme for concrete pump trucks for construction equipment, which significantly improves accuracy and fairness.

[0265] In addition, the present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed in a computer, the computer is caused to execute the method of any of the above embodiments.

[0266] The present invention further provides a computing device including a memory and a processor, wherein the memory stores executable code, and when the processor executes the executable code, the method of any of the above embodiments is implemented.

[0267] The device embodiment and method embodiment of the present invention are based on the same inventive concept. For detailed description, please refer to the method embodiment, which will not be repeated here.

[0268] The modules or units in the apparatus of the embodiments of the present invention may be combined, divided, or deleted as needed. The above disclosure is merely a preferred embodiment of the present invention and is not intended to limit the scope of the present invention. Persons skilled in the art will appreciate that any equivalent variations made by implementing all or part of the processes of the above embodiments in accordance with the claims of the present invention are still within the scope of the invention.

Claims

1. A concrete pump truck optimization method based on criterion removal and double normalization, characterized in that: The preferred method comprises: Determine several basic concrete pump truck value evaluation criteria and several alternative concrete pump truck options; wherein the alternative options include the types of alternative concrete pump trucks and the performance parameters of each type of concrete pump truck in terms of each value evaluation criterion; The weight of each value evaluation criterion is determined by using the criterion removal effect method; Normalizing the data of each of the alternative solutions using a linear normalization method to obtain an extended linear normalization matrix; Normalizing the data of each of the alternative solutions using a vector normalization method to obtain an extended vector normalization matrix; Determining the comprehensive utility value of each alternative plan based on the extended linear normalized matrix, the extended vector normalized matrix, and the weights of each value evaluation criterion; Select the concrete pump truck required for the construction project based on the comprehensive utility value of each alternative plan; The step of determining the comprehensive utility value of each alternative solution based on the extended linear normalized matrix, the extended vector normalized matrix, and the weight of each value evaluation criterion includes: Determining a weighted extended linear normalized matrix according to the weights of the value evaluation criteria and the extended linear normalized matrix; Determining a weighted extended vector normalization matrix based on the weights of the value evaluation criteria and the extended vector normalization matrix; Determining, according to the weighted extended linear normalization matrix and the weighted extended vector normalization matrix, the subordinate values ​​of each alternative scheme with respect to a complete compensation model, a non-compensation model, and an incomplete compensation model; Determining the utility of each alternative for the full compensation model, the non-compensation model, and the incomplete compensation model, respectively, according to the membership values ​​of each alternative with respect to the full compensation model, the non-compensation model, and the incomplete compensation model; Determining the utility value of each alternative solution corresponding to each model according to the utility degree of each alternative solution corresponding to each model; According to the utility values ​​of the alternative plans corresponding to each model, the comprehensive utility value of the alternative plans is determined.

2. The concrete pump truck optimization method based on criterion removal and double normalization according to claim 1, characterized in that: The method of using the criterion removal effect to determine the weight of each value evaluation criterion includes: Performing linear normalization processing on the initial decision matrix to obtain a normalized decision matrix; wherein the initial decision matrix is ​​a matrix composed of performance parameters of the concrete pump truck corresponding to each alternative solution in terms of each value evaluation standard; Determining a first overall performance of each alternative plan using a logarithmic metric based on the normalized decision matrix; Removing one value evaluation criterion from the normalized decision matrix one at a time, and determining the second overall performance of each alternative plan after removing one value evaluation criterion in turn by using a logarithmic measurement method; Calculating the deviation between the second overall performance and the first overall performance corresponding to each value evaluation standard to obtain the impact value corresponding to each value evaluation standard after excluding the value evaluation standard; The weight value of each value evaluation criterion is determined based on the impact value corresponding to each value evaluation criterion.

3. The concrete pump truck optimization method based on criterion removal and double normalization according to claim 2, characterized in that: The linear normalization processing of the initial decision matrix includes: The initial decision matrix is ​​linearly normalized using the following formula: in, is the element x in the initial decision matrix ij The value after linear normalization, x ij It is used to represent the performance parameter value of the j-th value evaluation criterion corresponding to the i-th alternative in the initial decision matrix. Benefit is used to represent the type of value evaluation criterion as benefit, and Cost is used to represent the type of value evaluation criterion as cost. and / or, Determining the first overall performance of each alternative solution using a logarithmic measurement method based on the normalized decision matrix includes: The first overall performance of each alternative is determined using the following calculation formula: Among them, S i is used to characterize the first overall performance of the i-th alternative, m is used to characterize the number of types of value evaluation criteria, is the element x in the initial decision matrix ij The value after linear normalization; and / or, Removing one value evaluation criterion from the normalized decision matrix each time and determining the second overall performance of each alternative solution after removing one value evaluation criterion in turn by using a logarithmic measurement method includes: For each value evaluation criterion, the second overall performance of each alternative solution when the value evaluation criterion is removed is calculated using the following formula: Among them, S′ ij It is used to represent the second overall performance of the i-th alternative when the j-th value evaluation criterion is removed, and m is used to represent the number of types of value evaluation criteria. is the element x in the initial decision matrix ik The value after linear normalization, and the k-th value evaluation criterion is not the j-th value evaluation criterion currently removed; and / or, Calculating the deviation between the second overall performance and the first overall performance corresponding to each value evaluation standard includes: The deviation between the second overall performance and the first overall performance is calculated using the following formula: Among them, E j Used to represent the impact value of eliminating the j-th value evaluation criterion, S′ ij Used to characterize the second overall performance of the i-th alternative when the j-th value evaluation criterion is removed, S i used to characterize the first overall performance of the i-th alternative; and / or, Determining the weight of each value evaluation criterion according to the impact value corresponding to each value evaluation criterion includes: Use the following formula to calculate the weight of each value evaluation standard: Among them, w j The weight value used to represent the j-th value evaluation criterion, E j Used to represent the impact value of eliminating the j-th value evaluation standard, E k Used to represent the impact value of eliminating the k-th value evaluation criterion.

4. The method for optimizing concrete pump trucks based on criterion removal and double normalization according to claim 1, characterized in that: The linear normalization method is used to normalize the data of each alternative solution, including: The initial matrix M = [α ij ] m×n Perform linear normalization processing to obtain a linear normalized matrix; where m represents the number of alternatives, n represents the number of value evaluation criteria, and α ij The performance parameter representing the j-th value evaluation criterion corresponding to the i-th alternative: Among them, α′ ij is the linear normalization matrix, α ij It is used to represent the performance parameter value of the j-th value evaluation criterion corresponding to the i-th alternative in the initial matrix. Benefit is used to represent the type of value evaluation criterion as benefit, and Cost is used to represent the type of value evaluation criterion as cost. The ideal solution and anti-ideal solution are introduced by the following calculation formula to expand the linear normalized matrix and obtain the extended linear normalized matrix: in, and are the extended linear normalized matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

5. The concrete pump truck optimization method based on criterion removal and double normalization according to claim 4, characterized in that: The vector normalization method is used to normalize the data of each alternative solution, including: The initial matrix M = [α ij ] m×n Perform vector normalization to obtain the vector normalization matrix: Among them, α″ ij is the vector normalization matrix; The vector normalization matrix is ​​expanded by introducing the ideal solution and anti-ideal solution through the following calculation formula to obtain the expanded vector normalization matrix: Among them, α′ j ' (+) and α′ j ' (-) are the extended vector normalization matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

6. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 1, characterized in that: The step of determining a weighted extended linear normalized matrix according to the weight of the value evaluation standard and the extended linear normalized matrix includes: The weighted extended linear normalization matrix is ​​determined using the following formula: in, is the weighted linear normalization matrix, and are the weighted extended linear normalized matrices corresponding to the ideal solution and anti-ideal solution, w j is the weight of the jth value evaluation criterion, α′ ij is the linear normalized matrix, and are the extended linear normalized matrices obtained by introducing the ideal solution and anti-ideal solution respectively; and / or, The step of determining the weighted extended vector normalization matrix according to the weight of the value evaluation standard and the extended vector normalization matrix includes: The weighted expansion vector normalization matrix is ​​determined using the following calculation formula: in, is the weight vector normalization matrix, and are the weighted expansion vector normalization matrices corresponding to the ideal solution and anti-ideal solution, w j is the weight of the j-th value evaluation criterion, α″ ij is the vector normalization matrix, α′ j ' (+) and α′ j ' (-) are the extended vector normalization matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

7. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 6, characterized in that: The step of determining the subordinate values ​​of each alternative scheme with respect to a complete compensation model, a non-compensation model, and an incomplete compensation model according to the weighted extended linear normalization matrix and the weighted extended vector normalization matrix comprises: The following formula is used to calculate the membership value of the i-th alternative based on the full compensation model: The following calculation formula is used to calculate the membership value of the i-th alternative solution corresponding to the ideal solution and the anti-ideal solution of the fully compensated model respectively: and The following formula is used to calculate the membership value of the i-th alternative based on the non-compensation model: The following calculation formula is used to calculate the membership value of the i-th alternative solution corresponding to the ideal solution and the anti-ideal solution of the non-compensated model respectively: and The following formula is used to calculate the membership value of the i-th alternative based on the incomplete compensation model: Use the following calculation formula to calculate the membership value of the i-th alternative solution of the incomplete compensation model corresponding to the ideal solution and the anti-ideal solution respectively: and Here, π is used to represent the quadrature.

8. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 7, characterized in that: The determining of the utility of each alternative scheme for the complete compensation model, the non-compensation model and the incomplete compensation model according to the subordinate values ​​of each alternative scheme with respect to the complete compensation model, the non-compensation model and the incomplete compensation model respectively includes: The utility of each alternative plan corresponding to the complete compensation model is calculated using the following formula: in, and are the utilities of the alternatives corresponding to the perfect compensation model for the ideal solution and the anti-ideal solution respectively; The utility of each alternative plan corresponding to the non-compensation model is calculated using the following formula: in, and are the utilities of the alternatives of the non-compensation model corresponding to the ideal solution and the anti-ideal solution respectively; The utility of each alternative plan corresponding to the incomplete compensation model is calculated using the following formula: in, and are the utilities of the alternatives of the incomplete compensation model corresponding to the ideal solution and the anti-ideal solution respectively; and / or, Determining the utility value of each alternative solution corresponding to each model according to the utility degree of each alternative solution corresponding to each model includes: The utility value of the i-th alternative of the perfect compensation model corresponding to the ideal solution and the anti-ideal solution is calculated using the following formula: in, and are the utility values ​​of the ith alternative of the perfect compensation model corresponding to the ideal solution and the anti-ideal solution, respectively; The utility value of the i-th alternative of the non-compensation model corresponding to the ideal solution and the anti-ideal solution is calculated using the following formula: in, and are the utility values ​​of the i-th alternative of the non-compensation model corresponding to the ideal solution and the anti-ideal solution, respectively; The utility value of the i-th alternative of the incomplete compensation model corresponding to the ideal solution and the anti-ideal solution is calculated using the following formula: in, and are the utility values ​​of the i-th alternative plan of the incomplete compensation model corresponding to the ideal solution and anti-ideal solution, respectively.

9. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 8, characterized in that: Determining the comprehensive utility value of each alternative plan according to the utility value of each alternative plan corresponding to each model includes: The comprehensive utility value of each alternative plan is calculated using the following formula: Among them, λ i It is used to represent the comprehensive utility value of the ith alternative, and p, q and (1-pq) represent the weights of the complete compensation model, non-compensation model and incomplete compensation model respectively.

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