Constrained two-dimensional cutting stock problems a best-first branch-and-bound algorithm

Abstract

In this paper, we develop a new version of the algorithm proposed in Hi® (Computers and Operations Research 24/8 (1997) 727±736) for solving exactly some variants of (un)weighted constrained twodimensional cutting stock problems. Performance of branch-and-bound procedure depends highly on particular implementation of that algorithm. Programs of this kind are often accelerated drastically by employing sophisticated techniques. In the new version of the algorithm, we start by enhancing the initial lower bound to limit initially the space search. This initial lower bound has already been used in Fayard et al. 1998 (Journal of the Operational Research Society, 49, 1270±1277), as a heuristic for solving the constrained and unconstrained cutting stock problems. Also, we try to improve the upper bound at each internal node of the developed tree, by applying some simple and ecient combinations. Finally, we introduce some new symmetric-strategies used for neglecting some unnecessary duplicate patterns. The performance of our algorithm is evaluated on some problem instances of the literature and other hard-randomly generated problem instances. 7 (M. Hi®). J (NV-pattern but not a NH-pattern) horizontal combination of the patterns A and

A Genetic Programming Hyper-Heuristic Approach for Evolving 2-D Strip Packing Heuristics

“…Tree search procedures have been employed to produce optimal solutions for small instances of the 2-D guillotine stock cutting problem [40] and 2-D nonguillotine stock cutting problem [41]. The method used in [40] has since been improved in [42] and [43]. Recent exact approaches can be found in [44]- [47].…”

Bidirectional best-fit heuristic considering compound placement for two dimensional orthogonal rectangular strip packing

“…Christofides & Whitlock (1977) and Beasley (1985) used methods based on tree-search to solve the guillotine and non-guillotine variants of the strip packing problems respectively. The approach of Christofides & Whitlock (1977) was improved by Hifi & Zissimopoulos (1997) and further by Cung et al (2000) however solving large instances was still impractical in a reasonable amount of time. Martello et al (2003) and Lesh et al (2004) both proposed variations of branch and bound techniques to solve small strip packing instances.…”

Multi-dimensional bin packing problems with guillotine constraints

“…Hifi [Hif97] improved the algorithm of Viswanathan and Bagchi by introducing improved upper and lower bounds based on the solution of one-dimensional bounded knapsack problems. Cung et al [CHC97] further improved the algorithm by adding symmetry detection for duplicate patterns, and using more eficient data structures. Hifi [Hif98] presented an exact algorithm for the strip packing problem with guillotine constraints.…”