0000000000666874
AUTHOR
Antonio Parajón
A computational study of LP-based heuristic algorithms for two-dimensional guillotine cutting stock problems
In this paper we develop and compare several heuristic methods for solving the general two-dimensional cutting stock problem. We follow the Gilmore-Gomory column generation scheme in which at each iteration a new cutting pattern is obtained as the solution of a subproblem on one stock sheet. For solving this subproblem, in addition to classical dynamic programming, we have developed three heuristic procedures of increasing complexity, based on GRASP and Tabu Search techniques, producing solutions differing in quality and in time requirements. In order to obtain integer solutions from the fractional solutions of the Gilmore-Gomory process, we compare three rounding procedures, rounding up, t…
A tabu search algorithm for large-scale guillotine (un)constrained two-dimensional cutting problems
Abstract In this paper we develop several heuristic algorithms for the two-dimensional cutting problem (TDC) in which a single stock sheet has to be cut into a set of small pieces, while maximising the value of the pieces cut. They can be considered to be general purpose algorithms because they solve the four versions of the TDC: weighted and unweighted, constrained and unconstrained. We begin by proposing two constructive procedures based on simple bounds obtained by solving one-dimensional knapsack problems. We then use these constructive algorithms as building blocks for more complex procedures. We have developed a greedy randomised adaptive search procedure (GRASP) which is very fast an…
GRASP and Path Relinking for the Two-Dimensional Two-Stage Cutting-Stock Problem
We develop a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional two-stage 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 final pieces. We propose two different algorithms based on GRASP methodology. One is “piece-oriented” while the other is “strip-oriented.” Both procedures are fast and provide solutions of different structures to this cutting problem. We also propose a path-relinking algorithm, which operates on a set of elite soluti…