Optimal solving of a scheduling problem using quantum annealing metaheuristics on the D-Wave quantum solver

Abstract

<p>The main disadvantage of calculations on quantum computers is their non-determinism. For optimization problems, of course, it is possible to get surprisingly good results but without a guarantee of the actual optimality of the result, i.e, an assurance that there exists no better solution which could potentially be found by the quantum machine. In this paper, we propose an novel approach that provides such a guarantee of optimality. We generate a solution that is optimal in the strict mathematical sense, without probabilistic considerations. To accomplish this, we use the D-Wave quantum machine working as a sampler implementing quantum annealing -- an approach considered a hardware metaheuristic -- to obtain upper and lower bounds on the value of the objective function of the problem under consideration. Then, we use the Branch and Bound scheme controlled by quantum annealing. This allows us to obtain very quickly -- in constant time -- the boundaries of the considered subproblems. Our approach is a combination of calculations realized on a quantum machine controlled by procedures implemented on a classical computer, allowing us to generate optimal solutions to the NP-hard problems of task scheduling on a single machine with a total weighted tardiness criterion. The proposed quantum algorithm shows a significant advantage over the classical CPU approach both in terms of calculation time and the number of generated solution tree nodes.</p>

Optimal solving of a binary knapsack problem on a D-Wave quantum machine and its implementation in production systems

“…Bożejko et al (2022) proposed a distributed quantum annealing algorithm for a single-machine scheduling problem with total weighted tardiness criterion. In terms of optimal solving of optimization problems (Bożejko et al, 2024(Bożejko et al, , 2023 proposed exact algorithms for solving single-machine scheduling problems on a quantum machine in the CPU-QPU hybrid approach. In the work of Yarkoni et al (2022) is presented a review of the literature on the use of a quantum annealer, which can be used in combinatorial optimization.…”