A new parallel approach to the constrained two-dimensional cutting stock problem

Abstract

In this paper we present a new parallelization of an efficient best-first branch-and-bound algorithm to solve the constrained two-dimensional single stock guillotine cutting stock problem (CSP) to optimality.

The underlying sequential branch-and-bound algorithm is based on an exact version of Wang's heuristic suggested by Viswanathan and Bagchi. In our algorithm we improve the upper bound and introduce duplicate pruning.

For an efficient parallelization we developed a special communication structure, as due to the unusual branching strategy and detection of duplicates a standard parallelization of the branch-and-bound approach cannot be applied to this problem. This structure allows a dynamic and fully distributed load-balancing using a direct neighbor strategy.

Computational results on two different parallel systems are presented. The implementation is system-independent using the portable parallel branch-and-bound library (PPBB-LIB) developed in Paderborn and can easily be ported to other systems.

This work was partly supported by the EU Human Capital and Mobility Project: ‘’SCOOP: Solving Combinatorial Optimization Problems in Parallel” and by the PARALOR Project of Federal German Ministry of Research (BMBF).