Hybrid quantum-classical heuristic for the bin packing problem

Abstract

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.

Hybrid Approach for Solving Real-World Bin Packing Problem Instances Using Quantum Annealers

“…where (19) guarantees that items i placed inside the bin j are not outside of the last bin (n-th bin) along the x axis, (20) ensures that item i is located inside of its corresponding bin j along the x axis (activated if n > 1), (21) confirms that item i placed inside the bin j is not outside along the y axis, while (22) ensures that item i allocated inside the bin j is not outside along the z axis.…”

“…The pioneering work on BPP in the field of quantum computing presents a hybrid quantum-classical method for solving the 1dBPP 20 , whose solver is composed of two modules: i) a quantum subroutine with which to search a set of feasible configurations to fill one single bin and ii) a classical computational heuristic which builds complete solutions employing the subsets given by the quantum subroutine. To deepen the performance of the quantum subroutine developed, further tests were conducted against a random sampling and a random walk-based heuristic 21 .…”

BoxStacker: Deep Reinforcement Learning for 3D Bin Packing Problem in Virtual Environment of Logistics Systems

“…Many researchers have suggested various approximations or heuristic algorithms [ 2 , 5 ] due to the difficulties in achieving optimum bin packing problem solutions, including integer linear programming [ 9 ], space minimizing heuristics [ 10 ], genetic algorithms [ 11 , 12 ], quantum algorithms [ 13 , 14 ] and machine-learning-based smart heuristic selection [ 15 ]. Solving bin packing in a 3D environment is not an easy task.…”