In this paper, the authors present a hybrid genetic approach for the two-dimensional rectangular guillotine oriented cutting-stock problem. In this method, the genetic algorithm is used to select a set of cutting patterns while the linear programming model permits one to create the lengths to produce with each cutting pattern to fulfil the customer orders with minimal production cost. The effec...

In this paper we present a heuristic method to generate constrained two-dimensional guillotine cutting patterns. This problem appears in different industrial processes of cutting rectangular plates to produce ordered items, such as in the glass, furniture and circuit board business. The method combines a state space relaxation of a dynamic programming formulation of the problem, an and/or-graph...

The paper deals with the purpose of one hybrid approach for solving the constrained two-dimensional cutting (2DC) problem. The authors study this hybrid approach that combines the genetic algorithm and the Tabu search method. For this problem, they assume a packing of a whole number of rectangular pieces to cut, and that all cuts are of guillotine type in one sheet of a fixed width and an infin...

Victor Parada a,∗, Rodrigo Palma a, Daniel Sales b and Arlindo Gómes c a Departamento de Ingeniería Informática, Universidad de Santiago de Chile, Av. Ecuador 3659, Santiago, Chile E-mail: [email protected] b Departamento de Ingeniería Eléctrica, Universidad de Santiago de Chile, Av. Ecuador 3659, Santiago, Chile c Departamento de Informática, Universidad Federal de Espı́rito Santo, Campus ...

In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...

The oriented non-guillotine two-dimensional strip packing problem is investigated. Several 1D relaxations are considered and compared. Moreover, an ILP formulation of the 1D contiguous relaxation is given. The appropriate combination of some of the relaxations enables us the formulate a new ILP model of the strip packing problem.

This study presents an application to optimise the use of an Lcut guillotine machine. The application has two distinct parts to it; first, a number of rectangular shapes are placed on as few metal sheets as possible by using Genetic Algorithms. Secondly, the sequence for cutting these pieces has to be generated. The guillotine’s numeric control then uses this sequence to make the cuts.

Given a convex polyhedron P of n vertices inside a sphere Q, we give an O(n)-time algorithm that cuts P out of Q by using guillotine cuts and has cutting cost O(log n) times the optimal.

The practical problem we are trying to model is: we have to cover a room with a material(carpet or linolleum). This material is in a roll of fixed width. We want to cover the room with a minimum number of pieces and to waste a minimum amount of material. We present in this paper a synthesis of our works. We can easily see that the two criteria, the minimum loss of material and the minimumnumber...

In this paper we present a new parallelization of an efficient best-first branch-and-bound algorithm to solve the constrained two-dimensional single stock guillotine cutting stock problem (CSP) to optimality. The underlying sequential branch-and-bound algorithm is based on an exact version of Wang's heuristic suggested by Viswanathan and Bagchi. In our algorithm we improve the upper bound and i...