An Iterated Local Search method for the constrained two-dimensional non-guillotine cutting problem is presented. This problem consists in cutting pieces from a large stock rectangle to maximize the total value of pieces cut. In this problem, we take into account restrictions on the number of pieces of each size required to be cut. It can be classified as 2D-SLOPP (two dimensional single large o...

Starting from a two-dimensional rectangular Cutting-Stock pattern with gaps, this paper is focuses on the problem of determination if the pattern is with guillotine restrictions or not and proposes an algorithm for solving it. First we present two new graph representations of the cutting pattern, weighted graph of downward adjacency and weighted graph of rightward adjacency. Using these represe...

We consider a two-dimensional rectangular Cutting-Stock problem in case of a cutting pattern with gaps. First we present two new graph representations of the cutting pattern, weighted graph of downward adjacency and weighted graph of rightward adjacency. Using this kind of representation we propose a method to verify guillotine restrictions of the pattern which can be applied for cutting-stock ...

We introduce an evolutionary stochastic-local-search (SLS) algorithm for addressing a generalized version of the so-called 1/V/D/R cutting-stock problem. Cutting-stock problems are encountered often in industrial environments and the ability to address them efficiently usually results in large economic benefits. Traditionally linear-programmingbased techniques have been utilized to address such...

In this paper, we compare the computational results of cutting pattern of Category II in One Dimensional Cutting Stock Problem in view of first order sustainable trim introduced by Powar et al, with the cutting pattern developed by Gradisar. The comparison has been carried over on the data taken by Gradisar by using the upper limit of the stock length as mentioned in the constraint and observed...

Original scientific papers This paper mainly addresses a two-dimensional defective stocks guillotine cutting stock problem where stock of different sizes is available. Herein a new heuristic algorithm which is based on tree is proposed to discuss this problem. In particular, such an algorithm consists of two parts: the first part is an initial solution of the cutting stock problem where there a...