We present a variable neighborhood search (VNS) for the 3-staged 2-dimensional cutting stock problem employing “ruin-and-recreate”-based very large neighborhood search in which parts of the incumbent solution are destroyed and rebuilt using construction heuristics and dynamic programming. Experimental results show that for instances where the sizes of the elements are not too small compared to ...

In this paper, we develop a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional two-staged cutting stock problem. This is a special cutting problem in which the cut is performed in two phases. In the first phase, the stock rectangle is slit down its width into different vertical strips and in the second phase, each of these strips is processed to obtain the f...

CHIP is a new constraint logic programnu ‘ng language combining the declarative aspect of logic progranuni ng with the efficiency of constraint manipulation techniques. In the present paper, we show an application of CHIP to a two-dimensional cutting stock problem. This problem is highly combinatorial and is generally solved by specific programs written in procedural languages. We present two a...

In this paper, the two-dimensional cutting/packing problem with items that correspond to simple polygons that may contain holes are studied in which we propose algorithms based on No-Fit polygon computation. We present a GRASP based heuristic for the 0/1 version of the Knapsack Problem, and another heuristic for the unconstrained version of the Knapsack Problem. This last heuristic is divided i...

The nesting problem is an irregular two-dimensional cutting problem where the shapes of the pieces to cut and the master surfaces are irregular in shape and different in size. In particular, we consider nesting problems where the master surface could contain defects. Some of them can be accepted (i.e., incorporated) in certain types of pieces, while other defected areas must be avoided. The pro...

In this article we solve a nonlinear cutting stock problem which represents a cutting stock problem that considers the minimization of, both, the number of objects used and setup. We use a linearization of the nonlinear objective function to make possible the generation of good columns with the Gilmore and Gomory procedure. Each time a new column is added to the problem, we solve the original n...