Part-oriented cutting layout mathematical modeling and solving by genetic algorithm for rectangular wood based panel parts

Abstract

Objective: In order to find gap of non-availability in most domestic literatures,which sawing velocity was dropped down due to the frequent change of saw line,this research investigated a heuristic rule for rectangular parts cutting layout of wood-based panel,built mathematical model and studied solving method. Method: Based on the situation that in a suit of material list, coupled dimension existed among two or more kinds of parts, therefore, a grouping and dimension reducing heuristic rule was put forward. All rectangle parts were sorting by coupled dimension in descending order, each group consisting no more than four kinds parts. Taking the minimum remaining area as evaluation index, a part-oriented mathematical model was set up. In this model, the quantity demanded for base panel was estimated by setting redundancy factor, and four aspects including quantity, length, width and area of placed parts on base panel should be all wlthin the limitation value. Moreover, layout width ratio was set and single unit saw line width was added on length and width of both rectangular parts and base panel so as to offset fictitious saw line loss located at undermost and rightmost side of base panel. Genetic algorithm (GA) was adopted to find global optimal solution for layout and punishment function was used to deal with constrains. By integer coding of chromosome, establishing of initial population, punishment factors with certain adaptability and fitness function based on exterior point punishment function and genetic manipulation, vector on behalf of layout solution was calculated through the layout algorithm which was built in cooperation with GA toolbox of MATLAB. Instances were applied to test feasibility of the model and algorithm. Result: Layout solution of all rectangular parts was described by four parameters, consisting of code,row and direction (vertical and transverse). Layout matrix has 4 rows, and the column was the total quantity of all parts. Each column represented layout solution of each part. The instances showed that multiple parts could be grouped based on coupled dimension-based heuristic rule, optimal controlled vector standing for layout solution for each group was divided into four sections with varied height, and these four sections meant the four parameters. It was also demonstrated that GA tended to convergence within limited iterations and gave relatively good capability of global optimization. In addition, visualization of layout solution displayed meet the demand of “guillotine cutting” and the regular saw line was good for increasing sawing efficiency. Conclusion: The coupled dimension-based heuristic rule and part-oriented mathematical model were suitable for cutting layout of wood-based panel and therefore a new method was presented for cutting layout of panel-type furniture. However, in order to enhance cutting productivity, the elements such as feeding times of cutting saw, optimized selection of punishment factor should also be taken into account comprehensively. © 2016, Editorial Department of Scientia Silvae Sinicae. All right reserved.