A Genetic Algorithm Based Method For Optimization Of One-Dimensional Cutting-Stock Without Replicated Sizes

One-dimensional cutting stock problem widely occurs in many construction and industry areas. Looking for an optimum cutting method can not only save raw materials and decrease product cost and stock ,but also is an efficient method to improve the utilization of materials and to increase the benefit of enterprises, so it can give a guidance and bring to immediate economic benefits for enterprises and accelerate development of national economy. So it's very useful to practice and theory in solving One-Dimensional Cutting-Stock problem, at the same time, this subject is also significant for design automation.Because One-Dimensional Cutting-Stock problem has NP complete properties and it's a classical NP-hard problem of operations research ,we solve this problem with great difficulty, in order to meet a great deal of limited conditions, and find corresponding relations among quantity,the length of raw materials and quantity length of part blank, the collected way of solving this problem is very huge. At present, most of the research for One-Dimensional Cutting-Stock is limited to rough pattern of figural and replicated size in length; it's rare that the research for analyzing model of one-dimensional cutting-stock problem without replicated sizes.As a technology of optimizing at random searching in use ,Genetic Algorithm can solve the sort of complicated problem effectively .Through comprehensive and systematically analysis to the cutting-stock problem, this article presented GA-based mathematical model of one-dimensional cutting-stock without replicated sizes for the cutting-stock problem after analyzing from the angle of application: designs the coding style for solving this sort of problem; to ensure the effective operating and get the optimization method, this article use one-point crossover during the calculation procedures. According to the fitness function data of solving the problem, this article use roulette wheel method to generate the next population and with Elitist Model to make new algorithm more effective. Crossover and mutation are developed to construct genetic algorithm of one-dimensional cutting stock problem.The result demonstrates that Genetic Algorithm based method for optimization of One-Dimensional Cutting-Stock without Replicated Sizes algorithm is valid and efficient.