Research On Rectangular Packing Problem Based On The Grey Wolf Optimization Algorithm With Its Application In Plate Furniture Cutting

The cutting of panel furniture can be defined as using mechanical equipment to cut the artificial board in certain size into many rectangular pieces used to build the furniture.The number of used panel should be minimal for the purpose of reducing the cost when cutting a batch of rectangular parts.So the optimization research on the cutting problem of the panel furniture is to optimize the layout of a batch of rectangular parts with the objective of maximizing the utilization of rectangular board.The researched problem is classified as the rectangular cutting stock problem which belongs to cutting and packing problem field.This paper conducts the research with the aim of increasing the utilization of rectangular board.At first,the paper concisely introduces the origin of the subject,the background and significance of the research.The purpose,necessity and field of the research are briefly stated,as well as the current domestic and foreign research progress.The research tendency of rectangular cutting stock problem is simply analyzed,and the mathematical model of the problem is constructed.After that,this work discusses the characteristics of the problem from the perspective of practical production and computational mathematics,summarizes the solution framework of the problem and introduces many algorithms with the content of both the basic principle and the solving process.Secondly,the basic principle and application area of the grey wolf optimization(GWO)is introduced.There are many key points and difficulties of applying GWO to solve the rectangular packing problem.More specifically,it includes the following contents: coding mode,the design of encoding algorithm,the definition of distance between wolves,discretization of scouting,encircling and hunting intelligent behavior,assuring the effective of coding during the intelligent behavior.After researching,the decimal grey wolf optimization(DGWO)based on lowest horizontal line is proposed to solve rectangular packing problem.Computational results on widely used benchmark instances show that the DGWO is effective and efficient,surpassing most of the previously reported meta-heuristics in the utilization of material.Thirdly,the improved decimal grey wolf optimization(IDGWO)is presented,which is improved from two aspects of locating and sequencing algorithm.The lowest horizontal line locating algorithm is enhanced in the principle of fitness,and the algorithm flow is also slightly changed in order to solve both two-dimensional rectangular strip packing problem(2DRSP)and two-dimensional rectangular packing problem(2DRP),as well as the flow of the grey wolf.Computational results on widely used benchmark instances show that the performance of the IDGWO is largely better than DGWO.It means that the utilization of material will be raised by using IDGWO compared with DGWO.Hence,the IDGWO can effectively and preferably solve the cutting problem of the panel furniture.At last,after analyzing the technological process of nesting,a software system for automatic layout is developed,which be combined with actual demands of cutting optimization for the panel furniture.The layout task in reality shows that the software system is effective and practical.