the one-dimensional cutting stock problem, has so many applications in lots of industrial processes and during the past few years has attracted so many researchers’ attention all over the world. in this paper a meta-heuristic method based on aco is presented to solve this problem. in this algorithm, based on designed probabilistic laws, artificial ants do select various cuts and then select the...

nowadays, one-dimensional cutting stock problem (1d-csp) is used in many industrial processes and re-cently has been considered as one of the most important research topic. in this paper, a metaheuristic algo-rithm based on the simulated annealing (sa) method is represented to minimize the trim loss and also to fo-cus the trim loss on the minimum number of large objects. in this method, the 1d-...

The one-dimensional cutting stock problem, has so many applications in lots of industrial processes and during the past few years has attracted so many researchers’ attention all over the world. In this paper a meta-heuristic method based on ACO is presented to solve this problem. In this algorithm, based on designed probabilistic laws, artificial ants do select various cuts and then select the...

The MAXGAP problem of a linear integer optimization problem P consists in determining the maximum diierence (gap) (P) between the optimal value z (E) of an instance E 2 P and the LP bound z c (E) with respect to all E 2 P. In the case of the one-dimensional cutting stock problem (1D CSP) it is known that (1D CSP) 1 + 5 132 but there is also a conjecture that (1D CSP) 2. In this paper we show th...

Many numerical computations show a small difference only between the optimal value of the one-dimensional cutting stock problem and that of its corresponding linear programming relaxation. In this paper we investigate the one-dimensional cutting stock problem with respect to the modified integer round-up property (MIRUP) and present some results on subproblems having the MIRUP.

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...

Many numerical computations show an only small difference between the optimal value of the one-dimensional cutting stock problem and that of its corresponding linear programming relaxation. In this paper we investigate the one-dimensional cutting stock problem with respect to the modified integer round-up property (MIRUP) and present some results on subproblems having the MIRUP.

Many numerical computations show a small diierence only between the optimal value of the one-dimensional cutting stock problem and that of its corresponding linear programming relaxation. In this paper we investigate the one-dimensional cutting stock problem with respect to the modiied integer roundup property (MIRUP) and present some results on subproblems having the MIRUP.

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 ...