Research For The Problem Of Rectangular Layer Packing Based On Hybrid Genetic Algorithm

The problem of rectangular layer packing is to place different rectangle objectsinto a big sheet material. The major objective is to make the ratio of material highlyunder the conditions of no overlap and not beyond the boundary. The problem existswidely in the industries of glass, timber and steel plate. It influences the economiceffectiveness of industries. The problem of rectangle layout is a typical NP complete.The solution of valid polynomial calculate way cannot find out by now.The rectangular layer packing problem in this paper is different from thetraditional rectangle layout. The big object needs to splice by various different sheetmaterial with no overlap. The object must be completely covered. This is also a NPcomplete problem. Solving the problem effectively has extensive influence toproduction.Considering the constraints of rectangular layer packing, the improved geneticalgorithm is used as the global search algorithm. The layering lowest horizontal linealgorithm is designed to pack the rectangle materials to realize to calculation of fitnessfunction. The algorithm is written in Java and the data from practical projects ofindustry is used in the experiments. The results of experiments approved the validityand rationality of algorithm.There is no reasonable algorithm to solve rectangular layer packing problem. Sothe results in this paper cannot be compared with other algorithms. But thepreliminary solution to the problem has some significance for the research in thefuture.