In this work a solution using evolutionary algorithms with penalty function for the non-guillotine cutting problem is presented. In this particular problem, the rectangular pieces have to be cut from an unique large object, being the goal to maximize the total value of cut pieces. Some chromosomes can hold pieces to be cut, but some pieces cannot be arranged into the object, generating infeasib...

The manufacture of parts made of metal sheet often includes two successive processes: the cutting process at which a guillotine shear cuts the sheet into strips, and the punching process at which a stamping press punches out the blanks from the strips. This paper presents an algorithm for generating optimal two-staged cutting patterns of strips for the cutting process. At the first stage the sh...

In this paper, six different approaches using genetic algorithms (GA) and/or simulated annealing (SA) with improved bottom left (I-BL) algorithm [1] were applied for solution of two dimensional non-guillotine cutting problems. As examples, test problems including 29 individual rectangular pieces were used [2]. Performances of hybrid approaches on solutions of cutting problems were compared. Due...

Gilmore and Gomory's algorithm is one of the better actually known exact algorithms for solving unconstrained guillotine two-dimensional cutting problems. Herz's algorithm is more effective, but only for the unweighted case. We propose a new exact algorithm adequate for both weighted and unweighted cases, which is more powerful than both algorithms. The algorithm uses dynamic programming proced...

Abstract We advance the state of art in Mixed-Integer Linear Programming formulations for Guillotine 2D Cutting Problems by (i) adapting a previously-known reduction to our preprocessing phase (plate-size normalization) and (ii) enhancing previous formulation (PP-G2KP from Furini et alli) cutting down its size symmetries. Our focus is Knapsack Problem with orthogonal unrestricted cuts, constrai...

We describe an exact model for the two-dimensional Cutting Stock Problem with two stages and the guillotine constraint. It is a linear programming arc-flow model, formulated as a minimum flow problem, which is an extension of a model proposed by Valério de Carvalho for the one dimensional case. In this paper, we explore how this model behaves when it is solved with a commercial software, explic...

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...

In this paper the solution of two-stage guillotine cutting stock problems is considered. Especially such problems are under investigation where the sizes of the order demands diier in a large range. We propose a new approach dealing with such situations and compare it with the classical Gilmore/Gomory approach. We report results of extensive numerical experiments which show the advantages of th...

A strong hyperbox-respecting coloring of an n-dimensional hyperbox partition is a coloring of the corners of its hyperboxes with 2n colors such that any hyperbox has all the colors appearing on its corners. A guillotine-partition is obtained by starting with a single axis-parallel hyperbox and recursively cutting a hyperbox of the partition into two hyperboxes by a hyperplane orthogonal to one ...