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 ...

Column generation algorithms have been specially designed for solving mathematical programs with a huge number of variables. Unfortunately, this method suffers from slow convergence that limits its efficiency and usability. Several accelerating approaches are proposed in the literature such as stabilization-based techniques. A more classical approach, known as “intensification”, consists in ins...

The cutting and packing problem belongs to the combinatorial optimization problems; it covers a wide range of practical cases in industries. present paper investigates new real world needs be solved through daily operations foam blocks an industrial company. is considered as one non-classical problems area. It represents variant three dimensional Cutting Stock Problem. originality studied indic...

We review the most important mathematical models and algorithms developed for the exact solution of the one dimensional bin packing and cutting stock problems, and experimentally evaluate, on state-of-the art computers, the performance of the main available software tools.

This paper considers variants of the one-dimensional bin packing (and stock cutting) problem in which both the ordering and orientation of items in a container influences the validity and quality of a solution. Two new real-world problems of this type are introduced, the first that involves the creation of wooden trapezoidal-shaped trusses for use in the roofing industry, the second that requir...

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...

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...