Dissertation > Mathematical sciences and chemical > Mathematics > Operations Research > Planning Theory ( mathematical programming) > Linear programming

The Research and Application of One-dimensional Multi-material Cutting Stock Problem

Author WangXinDong
Tutor WangZuChao
School Chinese Geology University (Beijing)
Course Applied Mathematics
Keywords One-dimensional cutting issues Linear Programming Genetic Algorithms
CLC O221.1
Type Master's thesis
Year 2007
Downloads 348
Quotes 3
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In recent years , with the rapid development of the national economy , one-dimensional cutting issues in construction, electricity, water conservancy and other fields has been more and more widely used. Looking for an optimal cutting programs , not only can save raw materials , lower production costs , but also to bring direct economic benefits for the enterprise , and promote the healthy development of the national economy . Therefore , to carry out one-dimensional cutting stock problem research has important theoretical significance and engineering application value. Firstly, in-depth analysis of the one -dimensional cutting stock problem , we propose a truncation scheme automatically generated by a computer algorithm to establish a mathematical model of such problems . Then, two methods were used for one-dimensional cutting optimization problem solving , and conducted comparative analysis of specific examples . A linear programming . Linear programming simplex method for solving the problem of one-dimensional cutting traditional methods . This article first application of this method for one-dimensional cutting optimization problem solving , and analyzes the defects of this method , such as: the results of failure is an integer ; or because of the scale of the problem caused by too large algorithm failed , there morbid solution even no solution situation. Two genetic algorithms. This article from the perspective of the application of genetic algorithm to do a careful analysis and research, and then applied to one-dimensional cutting problem solving , we propose a solution method based on genetic algorithm . In the solution process , genetic algorithm is given encoding method , fitness function is defined , genetic operators and key parameters. The practical application shows that this method is feasible solution , and achieved better optimization results.

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