| The compact layout of the product is an effective way to reduce the manufacturing cost and improve the utilization rate of the material.Aiming at the multi-specification and large-scale two-dimensional rectangular cutting problem,such as difficulty solving and hugely calculation and so on.How to quickly obtain a reasonable and scientific layout and improve the utilization of materials,which has been the pursuit of scholars and enterprises.In the process of layout,mathematical methods are often used for planning,however,efficient mathematical methods have a critical effect on the quality and speed of layout results,therefore,it is necessary to explore a new method of high accuracy and low computational complexity to deal with the problem of the cutting of multi-specification and large-scale rectangular pieces.Calculation time and material utilization are taken into account in the paper,and it aims to find an efficient mathematical method to obtain information data(such as the number of materials)in the process of layout,which provide a effective guidance for highly efficient and reasonable layout method.On the basis of fully studying the layout process and layout target of the two-dimensional rectangular material cutting,the advantages and disadvantages of the dynamic programming method,the backpack problem algorithm and linear programming method based on the column are analyzed.The mathematical method based on column generation,for the importance of generation of two-dimensional rectangular pieces-cutting stock layout scheme,is analyzed.Moreover,the traditional linear programming method,for column generation of matrix,is studied and analyzed,and its optimization process has many problems such as the number of iterations.Therefore,a linear programming method based on matrix change column generation,in this paper,is proposed,which can improve the calculation speed and reduce the number of iterations,enriching the theory and method of two-dimensional rectangular pieces-cutting stock layout.The linear programming model of the two-dimensional rectangular material cutting problem is analyzed and the matrix generation method is proposed.The iterative model of linear programming is established.The data of the layout information is obtained according to the results of the model calculation,and the corresponding layout strategy and the specific layout steps are initially studied.This paper focuses on the process of solving the linear programming model of the material layout problem with the consideration of the layout constraint.By participating in the change of the layout matrix in the form of an unknown vector,and the variation rule of the unknown vector(column generation)in the process of the change of the layout matrix is deduced.In order to simplify the cumbersome process of matrix change calculation,it is proposed to use matrix to record the linear relationship between elements in unknown vector,and then the simplex function in MATLAB is used to optimize,which can avoid the cumbersome inverse matrix solution,and the number of iterations is reduced,and the computation time is reduced.The algorithmic program is written by the MATLAB language,and the calculation process of matrix change algorithm,for column generation,is realized,and random examples and related literature cases are calculated and compared.In contrast to the case in[31],the results show that the number of iterations of the algorithm is 4,but the number of iterations of the method is 10.According to the optimized results,a better layout strategy can be used to guide the layout of the rectangle,which verifies the feasibility and effectiveness of the algorithm. |
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