Solving Job-Shop Scheduling Problems with QUBO-Based Specialized Hardware

Abstract

The emergence of specialized hardware, such as quantum computers and Digital/CMOS annealers, and the slowing of performance growth of general-purpose hardware raises an important question for our community: how can the high-performance, specialized solvers be used for planning and scheduling problems? In this work, we focus on the job-shop scheduling problem (JSP) and Quadratic Unconstrained Binary Optimization (QUBO) models, the mathematical formulation shared by a number of novel hardware platforms. We study two direct QUBO models of JSP and propose a novel large neighborhood search (LNS) approach, that hybridizes a QUBO model with constraint programming (CP). Empirical results show that our LNS approach significantly outperforms classical CP-based LNS methods and a mixed integer programming model, while being competitive with CP for large problem instances. This work is the first approach that we are aware of that can solve non-trivial JSPs using QUBO hardware, albeit as part of a hybrid algorithm.

Diversifying Investments and Maximizing Sharpe Ratio: A Novel Quadratic Unconstrained Binary Optimization Formulation

“…Classical techniques for solving a portfolio optimization task with a term as in (20), or even more nonconvex items modeling additional needs, may become inefficient as the problem size scales. Also, with a suitable change of variables, one could reformulate the objective function in order to linearize the problem and solve it through linear programming strategies.…”

“…In industrial contexts, QUBO models are indispensable for addressing optimization challenges across different sectors. They are applied, for instance, in logistics for optimizing vehicle routing problems and traffic flow [18,19], as well as in resource allocation and scheduling tasks [20].…”