On Solving the Oriented Two-Dimensional Bin Packing Problem under Free Guillotine Cutting: Exploiting the Power of Probabilistic Solution Construction

TL;DR

This paper introduces a probabilistic approach combining a randomized heuristic and an evolutionary algorithm to effectively solve the oriented two-dimensional bin packing problem under free guillotine cutting, outperforming existing methods.

Contribution

It presents a novel randomized multi-start heuristic and an evolutionary algorithm that significantly improve solution quality for this complex packing problem.

Findings

The evolutionary algorithm outperforms current state-of-the-art methods.

Optimal solutions found for four previously unsolved instances.

The proposed methods are competitive and effective in minimizing the number of bins.

Abstract

Two-dimensional bin packing problems are highly relevant combinatorial optimization problems. They find a large number of applications, for example, in the context of transportation or warehousing, and for the cutting of different materials such as glass, wood or metal. In this work we deal with the oriented two-dimensional bin packing problem under free guillotine cutting. In this specific problem a set of oriented rectangular items is given which must be packed into a minimum number of bins of equal size. The first algorithm proposed in this work is a randomized multi-start version of a constructive one-pass heuristic from the literature. Additionally we propose the use of this randomized one-pass heuristic within an evolutionary algorithm. The results of the two proposed algorithms are compared to the best approaches from the literature. In particular the evolutionary algorithm compares very favorably to current state-of-the-art approaches. The optimal solution for 4 previously unsolved instances could be found.