Bin Completion Algorithms for Multicontainer Packing, Knapsack, and Covering Problems

TL;DR

This paper introduces bin completion, a branch-and-bound algorithmic framework for multicontainer packing problems, demonstrating significant performance improvements over previous methods for several problem types.

Contribution

The paper presents a novel bin completion approach with dominance-based pruning, achieving state-of-the-art results for multiple knapsack, bin covering, and min-cost covering problems.

Findings

Outperforms previous algorithms by orders of magnitude on hard instances

Achieves new best results for multiple knapsack, bin covering, and min-cost covering

Less competitive for bin packing compared to cutting-stock methods

Abstract

Many combinatorial optimization problems such as the bin packing and multiple knapsack problems involve assigning a set of discrete objects to multiple containers. These problems can be used to model task and resource allocation problems in multi-agent systems and distributed systms, and can also be found as subproblems of scheduling problems. We propose bin completion, a branch-and-bound strategy for one-dimensional, multicontainer packing problems. Bin completion combines a bin-oriented search space with a powerful dominance criterion that enables us to prune much of the space. The performance of the basic bin completion framework can be enhanced by using a number of extensions, including nogood-based pruning techniques that allow further exploitation of the dominance criterion. Bin completion is applied to four problems: multiple knapsack, bin covering, min-cost covering, and bin packing. We show that our bin completion algorithms yield new, state-of-the-art results for the multiple knapsack, bin covering, and min-cost covering problems, outperforming previous algorithms by several orders of magnitude with respect to runtime on some classes of hard, random problem instances. For the bin packing problem, we demonstrate significant improvements compared to most previous results, but show that bin completion is not competitive with current state-of-the-art cutting-stock based approaches.