Concrete pump truck optimal selection method based on criterion removal and double normalization

Abstract

The invention provides a concrete pump truck optimal selection method based on criterion removal and double normalization, and relates to the technical field of constructional engineering, and the method comprises the steps: determining a plurality of basic concrete pump truck value evaluation standards and a plurality of concrete pump truck alternative schemes; determining the weight of each value evaluation standard by adopting a criterion removal effect method; performing normalization processing on the data of each alternative scheme by adopting a linear normalization method to obtain an extended linear normalization matrix; performing normalization processing on the data of each alternative scheme by adopting a vector normalization method to obtain an extended vector normalization matrix; determining a comprehensive utility value of each alternative scheme based on the extended linear normalization matrix, the extended vector normalization matrix and the weight of each value evaluation standard; and according to the comprehensive utility value of each alternative scheme, selecting the concrete pump truck required by the constructional engineering. According to the scheme, the accuracy and credibility of optimizing the concrete pump truck can be improved.

Description

Technical Field

[0001] The 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, and the selection of construction equipment has become particularly important. Especially in the selection of key equipment such as concrete pump trucks, wrong decisions may lead to inefficient construction, increased costs and project delays. Therefore, how to make scientific and reasonable choices among many options has become a major challenge facing the current construction industry. In order to deal with this problem, researchers have been exploring more effective multi-criteria decision-making methods to improve the accuracy and reliability of equipment selection.

[0003] In the process of selecting construction equipment, decision makers usually need to consider multiple conflicting criteria, such as the price, performance, environmental protection and service life of the equipment. The complexity and diversity of these criteria make it difficult for traditional single-criteria decision-making methods to meet actual needs. For example, there are many types of concrete pump trucks available on the market, and each type of equipment performs differently under different criteria, which further increases the complexity of decision-making. In the face of these problems, how to effectively integrate multiple evaluation criteria to make the best choice has become a problem that needs to be solved urgently.

[0004] Existing multi-criteria decision-making methods, such as TOPSIS, VIKOR, and MARCOS, can handle complex decision-making problems to a certain extent, but they usually rely on a single standardization technology, which often leads to deviations and distorted results when facing different types of data, and it is difficult to fully reflect the relative importance of each criterion. Moreover, the above multi-criteria decision-making methods involve more subjective judgments, which leads to larger subjective judgment deviations, greatly 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 a number of basic concrete pump truck value evaluation standards and a number of 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 standard;

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

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

[0010] Using a vector normalization method to normalize the data of each of the alternative solutions 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 weight 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 each value evaluation standard;

[0015] Determining a first overall performance of each alternative plan using a logarithmic measurement method according to the normalized decision matrix;

[0016] Each time a value evaluation criterion is removed from the normalized decision matrix, a second overall performance after removing one value evaluation criterion from each alternative plan is determined by a logarithmic measurement method;

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

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

[0019] Preferably, the linear normalization processing of 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 linear normalized value, x ijIt is used to represent the performance parameter value of the jth value evaluation criterion corresponding to the ith 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.

[0023] and / or,

[0024] Determining the first overall performance of each alternative solution by using a logarithmic measurement method according to 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] The step of 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 comprises:

[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 ith alternative when the jth 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] The calculating of 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 It is used to represent the impact value of eliminating the j-th value evaluation criterion, S i ' j It is used to characterize the second overall performance of the ith alternative when the jth value evaluation criterion is removed, S i A first overall performance for characterizing the i-th alternative;

[0038] and / or,

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

[0040] The weight of each value evaluation criterion is calculated using the following formula:

[0041]

[0042] Among them, w j The weight value used to represent the jth value evaluation criterion, E j It is used to represent the impact value of eliminating the j-th value evaluation criterion, 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 of the alternative solutions 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 jth value evaluation criterion corresponding to the ith 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 jth 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 type, and Cost is used to represent the type of value evaluation criterion as cost type.

[0047] The linear normalized matrix is ​​expanded by introducing the ideal solution and anti-ideal solution through the following calculation formula to 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 adopting of a vector normalization method to normalize the data of each of the alternative solutions comprises:

[0051] The initial matrix M = [α ij ] m×n Perform vector normalization to obtain a 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 the 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 weight of the value evaluation criteria and the extended linear normalized matrix;

[0059] Determining a weighted extended vector normalization matrix according to the weight of the value evaluation standard and the extended vector normalization matrix;

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

[0061] Determining the utility of each alternative for the complete compensation model, the non-compensation model and the incomplete compensation model, respectively, according to the subordinate values ​​of each alternative with respect to the complete 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 alternatives corresponding to each model, the comprehensive utility value of the alternatives is determined.

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

[0065] The weighted extended linear normalization matrix is ​​determined using the following calculation 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, respectively, w j is the weight of the jth value evaluation criterion, α i ' j is the linear normalization matrix, and are the extended linear normalized matrices obtained by introducing the ideal solution and the 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, respectively, 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 comprises:

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

[0075] The following calculation formula is used to calculate the subordinate 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 following calculation formula is used to calculate the subordinate value of the i-th alternative based on the non-compensation model:

[0079] The following calculation formula is used to calculate the subordinate 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 calculation formula is used to calculate the subordinate value of the i-th alternative solution based on the incomplete compensation model:

[0082] The following calculation formula is used to calculate the subordinate values ​​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 step of determining 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 comprises:

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

[0089]

[0090]

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

[0092] The utility of each alternative solution 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 solution 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] 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:

[0102] The utility value of the ith 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 ith 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 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 characterize the comprehensive utility value of the ith alternative, and p, q and (1-pq) respectively characterize the weights of the complete compensation model, non-compensation model and incomplete compensation model.

[0118] It can be seen from the above technical scheme that in the concrete pump truck optimization method based on criterion removal and double normalization provided by the present invention, firstly, several basic concrete pump truck value evaluation standards and several alternative schemes of concrete pump trucks are determined, and then the weight of each value evaluation standard is determined by using the method of criterion removal effect; further, the data of the alternative schemes are 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 scheme in combination with the weight of the value evaluation standard, and then according to the comprehensive utility value of each alternative scheme, the optimal scheme of the required concrete pump truck can be selected in the construction process. It can be seen that this scheme determines the weight value of each value evaluation standard more objectively based on the criterion removal effect, 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, overcomes the shortcomings of the deviation caused by single normalization, strong subjectivity of weight allocation, and lack of multi-dimensional evaluation, so that the optimal choice can be made in the selection scheme of concrete pump trucks, greatly improving the accuracy and credibility of optimizing 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 briefly introduces 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 creative work.

[0121] The main drawback of the traditional MARCOS method is that it uses a single normalization (linear normalization) technique. 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, and then 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 values ​​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, and the optimization method may include the following steps:

[0122] Step 10: Determine several basic concrete pump truck value evaluation standards and several alternative plans for concrete pump trucks; wherein the alternative plans 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 standard;

[0123] Step 20: Determine the weight of each value evaluation criterion by 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: normalizing 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 normalized matrix, the extended vector normalized 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 standard 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 adopts 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, so that the best choice can be made in the selection scheme of concrete pump trucks, which greatly improves the accuracy and credibility of the optimization of concrete pump trucks.

[0129] For step 10, several basic concrete pump truck value evaluation criteria and several alternative concrete pump truck solutions are determined;

[0130] In this step, the value evaluation standard of the vehicle-mounted concrete mixing pump is considered. When determining the standard, it is necessary to verify whether the value of the standard should be maximized or minimized. Standards that expect their values ​​to be as high as possible should belong to the category of benefit standards, while standards that expect their values ​​to be as low as possible should belong to the category of cost standards. For example, the standards of one embodiment determined 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 the models are the same, but they differ in age and price. By giving the performance parameters of each alternative corresponding to the value evaluation standard, we can get 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-making objectives, the weights of each value evaluation criterion are determined based on the criterion removal effect, which 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 each value evaluation standard;

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

[0141]

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

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

[0144] Table 3

[0145]

[0146]

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

[0148] In this step, the following calculation formula is considered 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 result based on the above example is as follows: S 1 =0.408, S 2 =0.411, S 3 =0.386, S 4 =0.221, S 5 =0.177, S 6 =0.202, S 7 =0.145, S 8 =0.0.198,S 9 =0.253, S 10 =0.222, S 11 =0.226, S 12 =0.187, S13 =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 each 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;

[0154] In this step, consider the stage of calculating each alternative by removing each value evaluation criterion and using a logarithmic measurement method. 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 ith alternative when the jth 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 S 1 ' 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 influence value corresponding to each value evaluation standard after eliminating 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 It is used to represent the impact value of eliminating the j-th value evaluation criterion, S i ' j It is used to characterize the second overall performance of the ith alternative when the jth 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 get E 1 =8.161.

[0163] Step S25: Determine the weight value of each value evaluation criterion according to the influence 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 standard. Specifically, the weight value of each value evaluation standard can be calculated as follows:

[0165]

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

[0167] For example, the w calculated in the above example is 1 =0.100, and the weight values ​​of other value evaluation criteria can be obtained similarly.

[0168] For step 30, a linear normalization method is used to normalize the data of each alternative solution to obtain an extended linear normalization matrix;

[0169] In this step, when the linear normalization method is used for normalization processing, 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 jth value evaluation criterion corresponding to the ith 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 jth 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 type, and Cost is used to represent the type of value evaluation criterion as cost type.

[0173] It should be noted that the α ijWith the above x ij They are consistent, and both represent 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 linear normalized matrix is ​​expanded by introducing the ideal solution and anti-ideal solution through the following calculation formula to 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 a 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 the 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 normalized matrix, the extended vector normalized matrix and the weights of each value evaluation criterion, the comprehensive utility value of each alternative solution is determined;

[0192] This step can be implemented 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 standard:

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

[0194] In this step, the weighted extended linear normalization matrix is ​​determined by the following calculation 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, respectively, w j is the weight of the jth value evaluation criterion, α i ' j is the linear normalization matrix, and are the extended linear normalized matrices obtained by introducing the ideal solution and the 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 by the following calculation 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, respectively, 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 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;

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

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

[0204] The following calculation formula is used to calculate the subordinate 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 non-compensation model UCM:

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

[0209] The following calculation formula is used to calculate the subordinate 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] The following calculation formula is used to calculate the subordinate values ​​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 according to the subordinate 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 corresponding to the full compensation model:

[0226]

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

[0228] (2) For the non-compensation model UCM:

[0229] Consider using the following formula to calculate the utility of each alternative solution for 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 solution for 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 ith alternative of the perfect compensation 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 non-compensation 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 ith 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 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 according to 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 of the full compensation model, the non-compensation model and the incomplete compensation model respectively. These weights can be selected according to the decision maker's preference based on the comprehensive performance of the alternatives or their poor performance. If the decision maker can pay attention to the comprehensive performance of the alternatives, then he tends to choose the full compensation model. If the decision maker is unwilling to take risks, then a larger weight can be given to the non-compensation model.

[0261] For example, the overall utility value of each alternative solution obtained based on the above example is: (taking p = q = 0.3): 1 =0.7055,λ 2 =0.6909,λ 3 =0.6784,λ 4 =0.6345,λ 5 =0.6261,λ 6 =0.6408,λ 7 =0.6021,λ 8 =0.6237,λ 9 =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 according to the comprehensive utility values ​​of the alternative solutions.

[0263] In this step, consider sorting the alternatives according to the comprehensive utility value, and then select the use of the corresponding concrete pump truck according to the sorting result. For example, in the above example, the sorting results from large to small 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 to ensure the objectivity of the weight distribution and reduce human interference. Then, the extended linear normalization matrix and the extended vector normalization matrix are constructed respectively using double normalization technology to improve the comprehensiveness of data processing. Furthermore, this method performs a multi-dimensional comprehensive evaluation through three models of complete compensation, non-compensation and incomplete compensation, and finally obtains the best 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 on which a computer program is stored. 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 executable code is stored in the memory, 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 described in detail here.

[0268] The modules or units in the device of the embodiment of the present invention can be combined, divided and deleted according to actual needs. The above disclosure is only the preferred embodiment of the present invention, and of course it cannot be used to limit the scope of the rights of the present invention. Those skilled in the art can understand that all or part of the processes of the above embodiment are implemented, and the equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A method for optimizing concrete pump trucks based on criterion removal and double normalization, characterized in that: The preferred method comprises: Determine a number of basic concrete pump truck value evaluation standards and a number of 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 standard; The weight of each of the value evaluation criteria is determined by using the method of removing the effect of the criteria; Normalizing the data of each of the alternative solutions using a linear normalization method to obtain an extended linear normalization matrix; Using a vector normalization method to normalize the data of each of the alternative solutions 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 weight of each value evaluation criterion; According to the comprehensive utility value of each alternative plan, the concrete pump truck required for the construction project is selected.

2. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 1, characterized in that: The method of using criteria to remove the 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 each value evaluation standard; Determining a first overall performance of each alternative plan using a logarithmic measurement method according to the normalized decision matrix; Each time a value evaluation criterion is removed from the normalized decision matrix, a second overall performance after removing one value evaluation criterion from each alternative plan is determined by a logarithmic measurement method; Calculate the deviation between the second overall performance and the first overall performance corresponding to each value evaluation standard, and obtain the impact value corresponding to each value evaluation standard after eliminating the value evaluation standard; The weight value of each value evaluation criterion is determined according to the impact value corresponding to each value evaluation criterion.

3. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 2, characterized in that: The linear normalization process 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 linear normalized value, x ij It is used to represent the performance parameter value of the jth value evaluation criterion corresponding to the ith 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. and / or, Determining the first overall performance of each alternative solution by logarithmic measurement according to 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, The step of 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 comprises: 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 ith alternative when the jth 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, The calculating of 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 It is used to represent the impact value of eliminating the j-th value evaluation criterion, S i ' j It is used to characterize the second overall performance of the ith alternative when the jth value evaluation criterion is removed, S i A first overall performance for characterizing the i-th alternative; and / or, Determining the weight value of each value evaluation standard according to the impact value corresponding to each value evaluation standard includes: The weight of each value evaluation criterion is calculated using the following formula: Among them, w j The weight value used to represent the jth value evaluation criterion, E j It is used to represent the impact value of eliminating the j-th value evaluation criterion, E k Used to represent the impact value of eliminating the k-th value evaluation criterion.

4. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 1, characterized in that: The method of normalizing the data of each of the alternative solutions by using a linear normalization method includes: 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 jth value evaluation criterion corresponding to the ith alternative: Among them, α i ' j is the linear normalization matrix, α ij It is used to represent the performance parameter value of the jth 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 type, and Cost is used to represent the type of value evaluation criterion as cost type. The linear normalized matrix is ​​expanded by introducing the ideal solution and anti-ideal solution through the following calculation formula to obtain the extended linear normalized matrix: Among them, α′ j (+) and α′ j (-) are the extended linear normalized matrices obtained by introducing the ideal solution and anti-ideal solution, respectively.

5. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 4, characterized in that: The method of using a vector normalization method to normalize the data of each of the alternative solutions includes: The initial matrix M = [α ij ] m×n Perform vector normalization to obtain a vector normalization matrix: Among them, α i ' j ′ is the vector normalization matrix; The vector normalization matrix is ​​expanded by introducing the ideal solution and the 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 the comprehensive utility value of each alternative plan based on the extended linear normalized matrix, the extended vector normalized matrix and the weight of each value evaluation standard includes: Determining a weighted extended linear normalized matrix according to the weight of the value evaluation criteria and the extended linear normalized matrix; Determining a weighted extended vector normalization matrix according to the weight of the value evaluation standard and the extended vector normalization matrix; Determining the subordinate values ​​of each alternative scheme with respect to a complete compensation model, a non-compensation model and an incomplete compensation model respectively according to the weighted extended linear normalization matrix and the weighted extended vector normalization matrix; Determining the utility of each alternative for the complete compensation model, the non-compensation model and the incomplete compensation model, respectively, according to the subordinate values ​​of each alternative with respect to the complete 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 alternatives corresponding to each model, the comprehensive utility value of the alternatives is determined.

7. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 6, characterized in that: Determining the 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 calculation 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, respectively, w j is the weight of the jth value evaluation criterion, α′ ij is the linear normalization matrix, α′ j (+) and α′ j (-) are the extended linear normalized matrices obtained by introducing the ideal solution and the 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, respectively, w j is the weight of the jth value evaluation criterion, α i ' j ′ 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.

8. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 7, 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 respectively according to the weighted extended linear normalization matrix and the weighted extended vector normalization matrix comprises: The following calculation formula is used to calculate the dependency value S of the i-th alternative solution based on the full compensation model: i (1) : The following calculation formula is used to calculate the subordinate 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 calculation formula is used to calculate the subordinate value of the i-th alternative based on the non-compensation model: The following calculation formula is used to calculate the subordinate 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 calculation formula is used to calculate the subordinate value of the i-th alternative solution based on the incomplete compensation model: The following calculation formula is used to calculate the subordinate values ​​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.

9. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 8, characterized in that: The step of determining 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 comprises: The utility of each alternative solution corresponding to the complete compensation model is calculated using the following formula: in, and are the utilities of the alternatives for the perfect compensation model corresponding to the ideal solution and the anti-ideal solution respectively; The utility of each alternative solution 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 solution 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 ith 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 ith 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 of the incomplete compensation model corresponding to the ideal solution and anti-ideal solution, respectively.

10. The method for selecting a concrete pump truck based on criterion removal and double normalization according to claim 9, 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 characterize the comprehensive utility value of the ith alternative, and p, q and (1-pq) respectively characterize the weights of the complete compensation model, non-compensation model and incomplete compensation model.

Images