The Optimal Layout Of Circular Parts

The Circular blank layout problems exist widely in all kinds of manufacturing, such as machinery manufacturing, clothing manufacturing, furniture manufacturing, wood processing industry, leather products manufacturing and so on. However, because the Circular blank layout problems has been proved to be quite difficult completely NP-hard problem, at home and abroad, the research method of the scholars is very few, partly, the circular parts are processed for rectangular components (seeking for the minimum envelope moment), and then use the research methods for rectangle parts layout problem to deal with the optimize layout of circular parts. Basically, there are dynamic programming algorithm, branch bound algorithm, neural network algorithm, genetic algorithm, tabu search algorithm, particle swarm algorithm and so on, but the effect of the optimization is not obvious. But in recent years, some scholars use the bar band method to divide the circular parts into bar band of X and Y directions, and then use dynamic programming algorithm to obtain optimal solution. In some degree ,although it has obtained good effect, it still can't meet the requirements of production. So the further researches of the circular blank layout problem have theoretical and practical significance. The Circular blank layout problem include constrained layout and unconstrained layout. Unconstrained layout does not require times of appearance of all sorts of circular piece, only makes the utilization rate (value) of raw materials largest. This kind of layout problem relatively simple, it mostly uses linear programming algorithm to solve; However constrained layout demand to meet the requirement of all sorts of circular piece, and make the utilization rate of raw materials largest, this problem in actual production is used widely, but the research is very difficult.This paper studies the constrained layout of the circular pieces, and cutting rounds on the raw material of rectangular. In the course of the study, the main research is the single round of layout and the nesting layout. In the research of the single layout, firstly, there are given respectively highest utilization rate model and the model of least consumption of raw materials ,then it introduces two kinds of typical layout way—the layout model A and the layout mode B, and the layout mode B is divided into two kinds of situations: the most number of parts in the odd and the even lines is same and the most number of parts in the odd lines is one more than the most number of parts in the even lines, and are given, In the final ,by analysis the layout process and the solving of the example, it sums up to that the two layout ways have optimization effects under the different situations. In the study of the nesting layout of circular parts, the firstly, inspiration by the single row layout patterns, it seeks out two kinds of layout way of the nesting layout–the NEST layout and the BLOCK layout, and gives the specific layout process. But by analysis the two layout process ,it is sure that, although NEST layout mode is greatly raised the utilization rate of the raw materials, in the layout process, it is according to the order of the diameter of the round parts from the large to the small, by the NEST layout of characteristics, when the difference of two kinds of round the diameter of the piece is great, it will create a lot of waste and the chaos of the raw material of the layout. And in BLOCK layout mode ,it is not appear mentioned problems of the above, but when the diameter of the round piece changes, it also can create a lot of waste materials, therefore, this paper puts forward to the radius search method, it is effective optimized combination of the two kinds of layout mode, it meets the requirement of all sorts of circular piece. In addition, it makes the requirement of the raw materials least, so as to increases the utilization ratio of the raw materials. Finally through the examples and the matlab7.1 operational results, it proves that the radius search method is effective and feasible.