Augmented neural networks and problem-structure based heuristics for the bin-packing problem

In this paper, we apply the Augmented-neural-networks (AugNN) approach for solving the classical bin-packing problem (BPP). AugNN is a metaheuristic that combines a priority- rule heuristic with the iterative search approach of neural networks to generate good solutions fast. This is the first time this approach has been applied to the BPP. We also propose a decomposition approach for solving harder BPP, in which sub problems are solved using a combination of AugNN approach and heuristics that exploit the problem structure. We discuss the characteristics of problems on which such problem-structure based heuristics could be applied. We empirically show the effectiveness of the AugNN and the decomposition approach on many benchmark problems in the literature. For the 1210 benchmark problems tested, 917 problems were solved to optimality and the average gap between the obtained solution and the upper bound for all the problems was reduced to under 0.66% and computation time averaged below 33 seconds per problem. We also discuss the computational complexity of our approach

Hybrid quantum-classical heuristic for the bin packing problem

Optimization problems is one of the most challenging applications of quantum computers, as well as one of the most relevants. As a consequence, it has attracted huge efforts to obtain a speedup over classical algorithms using quantum resources. Up to now, many problems of different nature have been addressed through the perspective of this revolutionary computation paradigm, but there are still many open questions. In this work, a hybrid classical-quantum approach is presented for dealing with the one-dimensional Bin Packing Problem (1dBPP). The algorithm comprises two modules, each one designed for being executed in different computational ecosystems. First, a quantum subroutine seeks a set of feasible bin configurations of the problem at hand. Secondly, a classical computation subroutine builds complete solutions to the problem from the subsets given by the quantum subroutine. Being a hybrid solver, we have called our method H-BPP. To test our algorithm, we have built 18 different 1dBPP instances as a benchmarking set, in which we analyse the fitness, the number of solutions and the performance of the QC subroutine. Based on these figures of merit we verify that H-BPP is a valid technique to address the 1dBPP.QUANTEK project (ELKARTEK program from the Basque Government, expedient no. KK-2021/00070) Spanish Ramón y Cajal Grant RYC-2020-030503- I QMiCS (820505) and OpenSuperQ (820363) of the EU Flagship on Quantum Technologies EU FET Open project Quromorphic (828826) and EPIQUS (899368

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

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.Comment: 14 pages, 4 figures, 1 tabl