QAL-BP: An Augmented Lagrangian Quantum Approach for Bin Packing

TL;DR

This paper introduces QAL-BP, a quantum-optimized bin packing formulation using Augmented Lagrangian methods, demonstrating its effectiveness on real quantum hardware and classical solvers, advancing quantum combinatorial optimization.

Contribution

The paper presents a novel QUBO formulation for bin packing that incorporates constraints via Augmented Lagrangian, eliminating the need for instance-dependent penalty tuning.

Findings

Quantum annealing effectively solves bin packing instances.

The formulation is correct and adaptable to quantum hardware.

Quantum approaches show promise compared to classical methods.

Abstract

The bin packing is a well-known NP-Hard problem in the domain of artificial intelligence, posing significant challenges in finding efficient solutions. Conversely, recent advancements in quantum technologies have shown promising potential for achieving substantial computational speedup, particularly in certain problem classes, such as combinatorial optimization. In this study, we introduce QAL-BP, a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation designed specifically for bin packing and suitable for quantum computation. QAL-BP utilizes the Augmented Lagrangian method to incorporate the bin packing constraints into the objective function while also facilitating an analytical estimation of heuristic, but empirically robust, penalty multipliers. This approach leads to a more versatile and generalizable model that eliminates the need for empirically calculating instance-dependent Lagrangian coefficients, a requirement commonly encountered in alternative QUBO formulations for similar problems. To assess the effectiveness of our proposed approach, we conduct experiments on a set of bin packing instances using a real Quantum Annealing device. Additionally, we compare the results with those obtained from two different classical solvers, namely simulated annealing and Gurobi. The experimental findings not only confirm the correctness of the proposed formulation but also demonstrate the potential of quantum computation in effectively solving the bin packing problem, particularly as more reliable quantum technology becomes available.