Floor tile cutting optimization method in decoration project
By obtaining floor tile parameter information and optimizing the cutting plan using integer planning model, the balance problem of traditional floor tile cutting solutions between material utilization and construction efficiency is solved, and the efficiency and economicality of floor tile cutting is achieved.
Patent Information
- Application Number
- CN202510395109.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-31
- Publication Date
- 2025-08-01
AI Technical Summary
Traditional floor tile cutting solutions are difficult to balance material utilization and construction efficiency, especially when dealing with unequal floor tile, the complexity of the cutting solutions increases, and it is difficult to quickly generate and adjust the cutting solutions during construction to adapt to on-site changes.
By obtaining the parameter information of floor tiles, all matching combinations are calculated, and the cutting scheme is optimized using the integer planning model to determine the cutting scheme with the smallest total number of bricks. Combined with the priority optimization model, reduce cross-block cutting and output the optimal cutting scheme.
It has achieved minimizing the number of floor tiles used and cross-platform cutting, improved construction efficiency and material utilization, and provided an efficient and economical cutting solution.
Smart Images
Figure CN120408945A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of decoration information technology, and particularly to a method for optimizing floor tile cutting in decoration projects. Background Art
[0002] In large-scale construction, floor tile laying is a complex and crucial process. Traditional floor tile cutting schemes often struggle to balance material utilization rate and construction efficiency. On the one hand, to minimize waste, it is necessary to accurately calculate the cutting method for each floor tile to maximize the use of each piece of material. However, this approach may lead to a large number of cross-tile cuts, increasing construction difficulty and time costs. On the other hand, if too much emphasis is placed on reducing cross-tile cuts, it may result in increased material waste and affect the economy of the project. In addition, when faced with floor tiles of different sizes and shapes, how to achieve an optimal cutting scheme while ensuring aesthetics becomes a thorny problem. This situation is particularly prominent when dealing with non-equilateral floor tiles because their special shapes increase the complexity of the cutting scheme. More importantly, during the actual construction process, how to quickly generate and adjust the cutting scheme to adapt to possible changes on-site is also an urgent problem to be solved. These factors combined form a multi-dimensional technical problem, challenging the limitations of traditional floor tile laying methods and highlighting the importance and urgency of optimizing floor tile cutting schemes in large-scale and complex environments. Summary of the Invention
[0003] The main purpose of the present invention is to provide a method for optimizing floor tile cutting in decoration projects, which solves the problem that traditional floor tile cutting schemes often struggle to balance material utilization rate and construction efficiency.
[0004] To solve the above technical problems, the technical solution adopted by the present invention is: A method for optimizing floor tile cutting in decoration projects, including obtaining parameter information of floor tiles of the same model during the construction period, where the parameter information at least includes the width, non-equilateral length, quantity, and the plot to which the floor tiles belong; Calculating all the matching combinations of the floor tiles according to the parameter information; Optimizing the matching combinations through a pre-established integer programming model to obtain a cutting scheme with the least total number of used floor tiles; According to the cutting scheme and the plot to which the floor tiles belong, determining the optimization result with the least cross-tile cuts through a pre-established priority optimization model, and outputting the optimization result as the optimal cutting scheme.
[0005] In a preferred solution, the obtaining of the parameter information of floor tiles of the same model during the construction period includes: for the incomplete floor tiles at the paving edge position during the construction period, determining that the width of the incomplete floor tiles is a unified value; For the incomplete floor tiles, obtain the unequal side lengths, quantities, and the plots to which each floor tile belongs. Generate an array of parameter information based on the width, unequal side lengths, quantities, and the plots to which they belong.
[0006] In a preferred embodiment, the width of the floor tile is denoted as a , the unequal widths, corresponding quantities, and the plots to which they belong are represented by arrays b , array c and array d respectively. Array b , array c and array d are represented as: b = , c = , d = where b i , c i and d i represent the unequal side widths, quantities of floor tiles, and plot numbers of the i th equal-width floor tiles respectively.
[0007] In a preferred embodiment, calculating all the matching combinations of floor tiles based on the parameter information includes: For the unequal side lengths in the parameter information, calculate the ratio of the width to each unequal side length and round down to obtain an initial array; Generate an initial matrix containing all possible cutting times based on the initial array; Gradually increase the cutting times in the initial matrix, calculate the combined length of each column, and delete the columns that exceed the width to obtain the final matching combination matrix.
[0008] In a preferred embodiment, the steps for calculating the matching combinations include: S1. Calculate a / b i and round down to obtain the array N 1 N 2… N i …]; S2. Establish the matrix Z = [0 1 … N 1]; S3. Starting from i = 2, increment by 1 in each loop i until i = len( b), the following calculations are performed in each loop: Starting from k = 0, in each loop k increment by 1 until k = N i , the following calculations are performed in each loop: Construct a matrix Z k , Z k is Z add a row with all elements being k ; Calculate Z k the combined length of each column, and delete the columns with a length greater than a ; All Z k ( k = 0, 1… N i ) are horizontally merged into a new matrix Z ; S4. Finally, obtain the combined matching matrix Z .
[0009] In the preferred solution, optimizing the matching combination through the pre-established integer programming model includes: For the matching combination, determine the usage times of each matching combination as decision variables; Establish an objective function based on the decision variables, and the objective function is the sum of the total number of whole floor tiles corresponding to the matching combination; According to the quantity in the parameter information, set the constraint condition that the number of floor tiles corresponding to each non-equilateral length is not less than the required quantity; Solve the objective function through the integer programming model to obtain the cutting plan with the least total number of used bricks.
[0010] In the preferred solution, optimizing the matching combination through the pre-established integer programming model to obtain the cutting plan with the least total number of used bricks includes: For the matching combination, determine the usage times of each matching combination as decision variables , ; Establish an objective function based on the decision variables, and the objective function is the sum of the total number of whole floor tiles corresponding to the matching combination, that is ; According to the quantity in the parameter information, set the constraint condition that the number of floor tiles corresponding to each non-equilateral length is not less than the required quantity. According to the quantity in the parameter information, set the constraint condition that the number of floor tiles corresponding to each non-equilateral length is not less than the required quantity, that is ; Solve the objective function through an integer programming model to obtain a cutting plan with the least total number of bricks used, and calculate the total number of bricks used according to the solution result. .
[0011] In the preferred solution, optimizing the combination by using the pre-established integer programming model includes: For the combination, determine the usage times of each combination; According to the usage times and the quantities in the parameter information, calculate the total number of floor tiles corresponding to each unequal side length; If the total number of floor tiles meets the required quantity, output the total number of bricks used through the integer programming model; Set constraint conditions according to the total number of bricks used for subsequent cross-plot optimization.
[0012] In the preferred solution, determine the optimization result with the least cross-plot cutting through the pre-established priority optimization model according to the cutting plan and the plot to which it belongs; For the combination in the cutting plan, convert the combination matrix into a 0-1 matrix. The conversion method is that the zero elements remain unchanged, and the non-zero elements are replaced by 1. Then each element in this 0-1 matrix is multiplied by the in respectively to obtain a matrix containing plot information ; Calculate the number of plots involved in each combination according to the matrix to obtain an array of plot numbers , , indicating the number of plots involved in the th column combination in ; Establish an objective function according to the array of plot numbers. The objective function is the sum of the number of plots involved in the combination, that is ; Solve the objective function through the priority optimization model. The constraint conditions are that the number of floor tiles corresponding to each unequal side length is not less than the required quantity and the total number of bricks used is not higher than , and the programming model is: s.t. ; Solve the integer programming model to obtain the optimal solution x , that is, obtain the optimal cutting plan for floor tiles with equal width and unequal length.
[0013] In the preferred solution, outputting the optimization result as the optimal cutting plan includes: For the optimization result, obtain the usage times of each combination and the corresponding plot information; Determine the cutting method for each whole floor tile according to the number of uses and plot information; Generate a final floor tile cutting plan through the cutting method, where the cutting plan includes the unequal side lengths of each floor tile and the allocation results of the plots to which they belong.
[0014] The present invention provides a method for optimizing floor tile cutting in decoration and fit-out projects. For the laying problem of floor tiles of the same model during the construction period, the present invention first obtains the parameter information of the floor tiles, including width, unequal side lengths, quantity, and the plot to which they belong. Then, by calculating all possible combinations and optimizing these combinations using an integer programming model, a cutting plan with the least total number of tiles used is obtained. Finally, through further optimization using a priority optimization model, a plan with the least cross-plot cutting is determined. The core of the present invention lies in multi-step optimization, which not only minimizes the use quantity of floor tiles but also reduces the cross-plot cutting situation, thereby improving construction efficiency and material utilization rate. This method can effectively solve the complex cutting problems in large-scale floor tile laying and provides an efficient and economical solution for building construction. BRIEF DESCRIPTION OF THE DRAWINGS
[0015] The present invention will be further described below with reference to the drawings and embodiments: Figure 1 is the flowchart of the combination calculation of the present invention; Figure 2 is the flowchart of the method for optimizing floor tile cutting in the decoration and fit-out project of the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS Embodiment 1 As Figure 1-2 shown, a method for optimizing floor tile cutting in a decoration and fit-out project includes obtaining the parameter information of floor tiles of the same model during the construction period, where the parameter information at least includes the width, unequal side lengths, quantity, and the plot to which the floor tiles belong; when obtaining the floor tile width parameter, it is necessary to confirm the standard size through a measuring tool or a production specification table.
[0016] Calculate all combinations of the floor tiles according to the parameter information; Optimize the combinations through a pre-established integer programming model to obtain a cutting plan with the least total number of tiles used; such an optimized plan can not only meet the construction requirements but also minimize the construction cost and improve the construction efficiency to the greatest extent. For example, in a specific case, through the optimization model, the total number of tiles used is reduced from the original 120 pieces to 100 pieces, and the number of cross-plot cutting times is reduced from 15 times to 5 times. This optimization effect significantly improves the economy and feasibility of the construction and provides a scientific basis and practical solution for the cutting of floor tiles with equal width and unequal lengths.
[0017] According to the cutting plan and the plot, determine the optimization result with the least cross-plot cutting through a pre-established priority optimization model, and output the optimization result as the optimal cutting plan. After priority optimization, in the sorting process, it is only necessary to transport by plot classification, and there is no need to secondarily disassemble and mix the bricks. This effect is particularly significant in large-scale projects. For example, when the construction of a subway station involves dozens of plots, a 10% reduction in cross-plot cutting can reduce the sorting cost by hundreds of hours.
[0018] In the preferred solution, obtaining the parameter information of floor tiles of the same model during the construction period includes: for the incomplete floor tiles at the paving edge position during the construction period, determining that the width of the incomplete floor tiles is a unified value; For the incomplete floor tiles, obtain the unequal side lengths, quantities, and the plots to which they belong for each floor tile; Generate an array of parameter information based on the width, unequal side lengths, quantities, and the plots to which they belong.
[0019] In the preferred solution, the width of the floor tile is denoted as a , the unequal widths, the corresponding quantities, and the plots to which they belong are represented by the arrays b , the array c and the array d respectively. The arrays b , the array c and the array d are expressed as: b = , c = , d = Among them, b i , c i and d i respectively represent the unequal side widths, the quantities of floor tiles, and the plot numbers to which the i th type of equal-width floor tiles belong.
[0020] In the decoration and renovation project of a villa group, by obtaining and organizing this parameter information, the floor tile cutting plan can be effectively optimized, material waste can be reduced, and construction efficiency can be improved. At the same time, this systematic data management method also provides reference for other similar projects.
[0021] In the preferred solution, calculating all the matching combinations of floor tiles according to the parameter information includes: For the unequal side lengths in the parameter information, calculate the ratio of the width to each unequal side length and round down to obtain an initial array; Generate an initial matrix containing all possible cutting times based on the initial array; Successively increase the number of cuts from the initial matrix, calculate the combined length of each column, and delete the columns that exceed the width to obtain the final matching combination matrix.
[0022] In the preferred solution, the steps for calculating the matching combination include: S1. Calculate a / b i and round down to obtain the array N 1 N 2… N i …]; S2. Establish the matrix Z = [0 1 … N 1]; S3. Starting from i = 2, increment by 1 in each loop i until i = len( b ). In each loop, perform the following calculations: Starting from k = 0, increment by 1 in each loop k until k = N i . In each loop, perform the following calculations: Establish the matrix Z k , Z k is Z add a row, and all elements of this row are k ; Calculate Z k the combined length of each column, and delete the columns with a length greater than a ; All Z k ( k = 0, 1… N i ) are horizontally merged into the new matrix Z ; S4. Finally, obtain the combined matching matrix Z .
[0023] The significance of this step is to ensure that all combinations in the final matching combination matrix meet the limit of the floor tile width, thereby providing an effective data basis for subsequent optimization.
[0024] In the preferred solution, optimizing the matching combination through the pre-established integer programming model includes: For each combination, determine the number of times each combination is used as a decision variable; Establish an objective function based on the decision variable, where the objective function is the sum of the total number of whole floor tiles corresponding to the combinations; According to the quantities in the parameter information, set the constraint condition that the number of floor tiles corresponding to each unequal side length is not less than the required quantity; Solve the objective function through the integer programming model to obtain the cutting plan with the least total number of tiles used.
[0025] The application of the integer programming model makes the optimization process more systematic and scientific, can effectively reduce resource waste, and improve construction efficiency. Through the above steps, the integer programming model can transform the complex cutting problem into a quantifiable optimization problem and find the optimal solution through mathematical methods. This method can not only reduce the total number of tiles used but also ensure that the construction requirements are met, thus playing an important role in actual projects.
[0026] In the preferred solution, optimize the combinations through a pre-established integer programming model to obtain the cutting plan with the least total number of tiles used, including: For the combinations, determine the number of times each combination is used as a decision variable , ; Establish an objective function based on the decision variable, where the objective function is the sum of the total number of whole floor tiles corresponding to the combinations, that is ; According to the quantities in the parameter information, set the constraint condition that the number of floor tiles corresponding to each unequal side length is not less than the required quantity. According to the quantities in the parameter information, set the constraint condition that the number of floor tiles corresponding to each unequal side length is not less than the required quantity, that is ; Solve the objective function through the integer programming model to obtain the cutting plan with the least total number of tiles used, and calculate the total number of tiles used according to the solution result .
[0027] In the preferred solution, the optimization of the combinations through the pre-established integer programming model includes: For the combinations, determine the number of times each combination is used; According to the number of times used and the quantities in the parameter information, calculate the total number of floor tiles corresponding to each unequal side length; If the total number of floor tiles meets the required quantity, output the total number of tiles used through the integer programming model; Set the constraint condition according to the total number of tiles used for subsequent cross-plot optimization.
[0028] In the preferred solution, according to the cutting plan and the plot to which it belongs, the optimization result with the least cross-plot cutting is determined through a pre-established priority optimization model; For the combination in the cutting plan, the combination matrix is transformed into a 0-1 matrix. The transformation method is that the zero elements remain unchanged, and the non-zero elements are replaced by 1. Then each element in this 0-1 matrix is multiplied by the in respectively to obtain a matrix containing plot information; According to the matrix calculate the number of plots involved in each combination to obtain an array of plot numbers , , indicating that in the column combination involves the number of plots; Establish an objective function based on the array of plot numbers. The objective function is the sum of the number of plots involved in the combination, that is ; Solve the objective function through the priority optimization model. The constraint condition is that the number of floor tiles corresponding to each unequal side length is not less than the required quantity and the total number of tiles used is not higher than , and the programming model is: s.t. ; Solve the integer programming model to obtain the optimal solution x , that is, obtain the optimal cutting plan for the floor tiles with equal width and unequal length.
[0029] In the preferred solution, the output of the optimization result as the optimal cutting plan includes: For the optimization result, obtain the usage times of each combination and the corresponding plot information; According to the usage times and plot information, determine the cutting method of each whole floor tile; Generate the final floor tile cutting plan through the cutting method. The cutting plan includes the unequal side lengths of each floor tile and the allocation result of the plot to which it belongs.
[0030] At the technical effect level, this process binds mathematical optimization with physical cutting to achieve two key goals: one is to ensure that the theoretical optimal solution is not damaged by construction deviations, such as maintaining the accuracy of the plan by marking the cutting allowance; the other is to avoid material mismatch through the plot label system. For example, when the colors required for plots Y and Q are different, the label can prevent mixing. This seamless conversion from digital to physical is the core guarantee for the implementation of multi-objective optimization.
[0031] Example 2 Further illustrate in combination with Example 1. As Figure 1-2 shown, scenario parameterization In the decoration project of a villa complex, a batch of incomplete square floor tiles of a certain model are required during a certain construction period. The width of this model of floor tile is 800mm, and the widths of the other pair of sides, corresponding quantities, and affiliated plots are shown in the following table:
[0032] From the above information, it can be seen that a = 800, b = , c = , d = .
[0033] 2) Calculation of floor tile matching combinations Calculation of S1 a / b i And take the integer part downwards to obtain the array [51 21 21].
[0034] Establishment of matrix S2 Z = [0 1 … 5].
[0035] S3 i = 2, and perform the following calculations: A1 k = 0, and perform the following calculations: Establishment of matrix B1 Z 0, Z 0 is Z Add a row with all elements being 0, that is Z 0 = .
[0036] Calculation of B2 Z The combined length of each column of 0, and the combined length of each column is not greater than a , without any processing.
[0037] A2 k = 1, and perform the following calculations: Establishment of matrix B1 Z 1, Z 1 is Z Add a row with all elements being 1, that is Z 1 = .
[0038] Calculation of B2 Z The combined length of each column of 1, and delete the columns with combined length greater than a to obtain Z 1 = .
[0039] All of A3Z 0, Z 1 is horizontally merged into a new matrix Z , Z =
[0040] S4 i Take 3 to 6 and perform loop calculations to finally obtain the full combination matrix Z , Z = , The matrix has 28 columns, that is, it contains 28 combinations.
[0041] 3) Optimization with the least number of bricks Decision variable x is Z the number of times each column combination in x = , where x i is Z the number of times the column combination in the i th column. The objective function is the sum of the elements in x is the smallest, and the constraint condition is that the number of floor tiles of each corresponding width cannot be less than its corresponding x demand quantity in c . The integer programming model is as follows: min
[0042] s.t.
[0043] Solve the integer programming model to obtain the optimal solution x 1 = [0 0 0 0 0 0 20 0 1 … 9 3], according to x 1 calculate the total number of bricks used Q m = = 48.
[0044] 4) Optimization with priority for the same plot Convert Z into a 0-1 matrix. The conversion method is that the zero elements remain unchanged, and the non-zero elements are replaced by 1. Then each element in this 0-1 matrix is multiplied by the d in d i respectively to obtain the matrix Y , Y = . For each column in the matrix Y , calculate the number of different elements among the non-zero elements in this column to obtain the row matrix h , h = ,h i Can be measured Z In the i The number of plots involved in the column combination. Mathematical modeling is carried out, and the decision variable remains x = , where x i Is Z In the i The number of times the column matching combination is used, and the optimization goal is x The sum of the number of plots involved in each corresponding combination is minimized, and the constraint condition is x The number of floor tiles of each corresponding width cannot be less than its corresponding c In the required quantity, and the total number of bricks used does not exceed Q m ( Q m = 48), the integer programming model is established as follows: min
[0045] s.t. ； Solve the integer programming model to obtain the optimal solution x , x = [0 0 0 0 0 0 20 0 1 … 5 7], that is, the optimal cutting plan for floor tiles with equal width and unequal length is obtained.
[0046] The above embodiments are only the preferred technical solutions of the present invention and should not be regarded as limitations on the present invention. The protection scope of the present invention should be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, the equivalent replacement improvements within this scope are also within the protection scope of the present invention.
Claims
1. An optimized method for floor tile cutting in decoration and fit-out works, characterized in that: The method includes obtaining parameter information of the same type of floor tiles during the construction period, wherein the parameter information includes at least the width, unequal side length, quantity and land plot of the floor tiles; Calculate all matching combinations of floor tiles according to the parameter information; Optimizing the matching combination through a pre-established integer programming model to obtain a cutting plan with the least number of bricks; According to the cutting scheme and the land parcels to which it belongs, an optimization result with the least cross-plot cutting is determined through a pre-established priority optimization model, and the optimization result is output as the optimal cutting scheme.
2. The optimized floor tile cutting method in a decoration and fit-out project according to claim 1, wherein: The obtaining of parameter information of the same type of floor tiles during the construction period includes: determining that the width of incomplete floor tiles at the edge of the tiles during the construction period is a uniform value; For the incomplete floor tiles, obtain the unequal side length, quantity and land plot of each floor tile; Generate a parameter information array according to the width, unequal side length, quantity and the land parcel to which it belongs.
3. The method for optimizing floor tile cutting in a decoration and renovation project according to claim 2, characterized in that: The width of the floor tile is recorded as a , different widths, corresponding quantities and plots are represented by arrays b , array c and arrays d Indicates that the array b , array c and arrays d Expressed as: b = , c = , d = in, b i 、 c i and d i Respectively represent i The unequal width of the equal-width floor tiles, the number of floor tiles and the plot number to which they belong.
4. The optimized method for floor tile cutting in a decoration and fit-out project according to claim 1, characterized in that: Calculating all combinations of floor tiles according to the parameter information includes: For the unequal side lengths in the parameter information, calculate the ratio of the width to each unequal side length and round it down to obtain an initial array; Generating an initial matrix containing all possible cutting times according to the initial array; The number of cuts is gradually increased from the initial matrix, the length of each column combination is calculated, and the columns exceeding the width are deleted to obtain the final combination matrix.
5. The optimized floor tile cutting method in a decoration project according to claim 4, characterized in that: it is paired with The combined calculation steps include: S1. Calculate a / b i and round down to obtain the array N 1 N 2 … N i …]; S2. Establish a matrix Z = [01 … N 1]; S3. Starting from i = 2, increment by 1 in each loop until i reaches i = len( b ). The following calculations are performed in each loop: Starting from k = 0, increment by 1 in each loop k until k = N i , and perform the following calculations in each loop: Create a matrix Z k , Z k is Z Add a row with all elements being k ; Calculation Z k For each column combination length, delete columns with a length greater than a ; all Z k ( k =0,1… N i ) horizontally merged into a new matrix Z ; S4. Finally, obtain the combined matching matrix Z .
6. The optimized floor tile cutting method in a decoration and fitting-out project according to claim 1, characterized in that: The optimizing the collocation combination by using a pre-established integer programming model includes: For the collocation combinations, determining the number of times each collocation combination is used as a decision variable; Establishing an objective function based on the decision variables, wherein the objective function is the sum of the total number of whole floor tiles corresponding to the matching combination; According to the quantity in the parameter information, a constraint condition is set such that the number of floor tiles corresponding to each unequal length is not less than the required number; The objective function is solved by the integer programming model to obtain a cutting solution that uses the least number of bricks.
7. The optimized floor tile cutting method in a decoration project according to claim 6, characterized in that: The pre-established integer programming model is used to optimize the matching combinations and obtain the cutting plan with the least number of bricks, including: For each combination, determine the number of times each combination is used as a decision variable , ; establish an objective function based on the decision variables, where the objective function is the sum of the total number of whole floor tiles corresponding to the combinations, i.e., ; Set the constraint condition according to the quantity in the parameter information that the number of floor tiles corresponding to each unequal side length is not less than the required quantity. Set the constraint condition according to the quantity in the parameter information that the number of floor tiles corresponding to each unequal side length is not less than the required quantity, that is ; Solve the objective function through the integer programming model to obtain the cutting plan with the least total number of bricks used, and calculate the total number of bricks used according to the solution results .
8. The optimized floor tile cutting method in a decoration project according to claim 7, characterized in that: The optimizing the collocation combination by using a pre-established integer programming model includes: For the combination, determining the number of times each combination is used; Calculate the total number of floor tiles corresponding to each unequal length according to the number of times used and the number in the parameter information; If the total number of tiles meets the required number, the total number of tiles used is output through the integer programming model; Constraints are set based on the total number of bricks used for subsequent cross-plot optimization.
9. The method for optimizing floor tile cutting in a decoration and renovation project according to claim 8 is characterized by: According to the cutting scheme and the land parcels to which it belongs, the optimization result with the least cross-plot cutting is determined through the pre-established priority optimization model; For the combination in the cutting plan, the combination matrix is transformed into a 0-1 matrix. The transformation method is that the zero elements remain unchanged, and the non-zero elements are replaced by 1. Then each element in this 0-1 matrix is multiplied by the in the respectively to obtain a matrix containing plot information ; According to the matrix , calculate the number of plots involved in each combination to obtain a plot number array , , represents the number of plots involved in the th column combination; Establish an objective function based on the array of plot numbers. The objective function is the sum of the plot numbers involved in the matching combination, that is ; Solve the objective function through the priority optimization model. The constraint conditions are that the number of floor tiles corresponding to each scalene length is not less than the required quantity and the total number of tiles used is not higher than , and the programming model is: st ； Solve the integer programming model and get the optimal solution x , that is, the optimal cutting solution for tiles of equal width and unequal length is obtained.
10. The optimized floor tile cutting method in a decoration project according to claim 9 is characterized in that: Outputting the optimization result as the optimal cutting solution includes: Based on the optimization results, obtain the number of times each combination is used and the corresponding plot information; Determining a cutting method for each whole floor tile according to the number of uses and the plot information; Generate the final floor tile cutting plan through the described cutting method. The cutting plan includes the unequal side lengths of each floor tile and the allocation result of the affiliated plot.