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 and obtains good results for both constrained and unconstrained problems. We have also developed a more complex tabu search algorithm that obtains high quality results in moderate computing times. Finally, we have implemented a path relinking procedure to improve the final results of the above algorithms. For the computational results we have used the set of large-scale test problems collected and generated by Fayard et al. (J. Oper. Res. Soc. 49 (1998) 1270). Scope and purpose The two-dimensional cutting problem (TDC) consists of cutting a single rectangular stock sheet into a set of small rectangular pieces of given sizes and values to maximise the total value of the pieces cut. This problem has a wide range of commercial and industrial applications, whenever a sheet of wood, glass, paper or metal has to be cut. The TDC problem can also be considered as a subproblem of more general cutting problems, involving several available stock sheets of different sizes. In this paper we develop several heuristic algorithms for solving TDC problems. The computational results show that they produce high-quality results in short computing times.