A Geometrical Branch-and-Price (GEOM-BP) Algorithm for Big Bin Packing Problems

TL;DR

This paper introduces a novel geometrical branch-and-price algorithm for big bin packing problems, improving solution efficiency by leveraging geometrical features and an implicit sectional pricing scheme, outperforming existing methods on benchmarks.

Contribution

The work presents a new approach to handle forbidden bins in two-dimensional knapsack problems and introduces diving criteria based on geometrical features to enhance column generation.

Findings

Outperforms state-of-the-art algorithms on benchmark instances

Solves more instances in less than one minute

Improves efficiency of column generation with implicit sectional pricing

Abstract

Bin packing problem examines the minimum number of identical bins needed to pack a set of items of various weights. This problem arises in various areas of the artificial intelligence demanding derivation of the exact solutions in the shortest amount of time. Employing branch-and-bound and column generation techniques to derive the exact solutions to this problem, usually requires designation of problem-specific branching rules compatible with the nature of the polluted pricing sub-problem of column generation. In this work, we present a new approach to deal with the forbidden bins which handles two-dimensional knapsack problems. Furthermore, a set of diving criteria are introduced which emphasize the importance of the geometrical features of the bins. It is further shown that efficiency of the column generation technique could significantly get improved using an implicit sectional pricing scheme. The proposed algorithm outperforms the current state-of-the-art algorithms in number of the benchmark instances solved in less than one minute.