A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems

TL;DR

This paper introduces a new, simplified framework for deriving bounds in higher-dimensional orthogonal packing problems, enhancing existing bounds and facilitating the creation of new ones within a branch-and-bound optimization context.

Contribution

It presents a general, easy-to-apply approach for generating and verifying lower bounds, improving upon and unifying previous methods in higher-dimensional packing.

Findings

The new bounds improve upon existing bounds in accuracy.

The framework simplifies the process of proving bound correctness.

The approach is applicable to various higher-dimensional packing problems.

Abstract

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is of crucial importance to have good and easy bounds for an optimal solution. Previous efforts have produced a number of special classes of such bounds. Unfortunately, some of these bounds are somewhat complicated and hard to generalize. We present a new approach for obtaining classes of lower bounds for higher-dimensional packing problems; our bounds improve and simplify several well-known bounds from previous literature. In addition, our approach provides an easy framework for proving correctness of new bounds.