Solving Large Break Minimization Problems in a Mirrored Double Round-robin Tournament Using Quantum Annealing

Quantum annealing (QA) has gained considerable attention because it can be applied to combinatorial optimization problems, which have numerous applications in logistics, scheduling, and finance. In recent years, research on solving practical combinatorial optimization problems using them has accelerated. However, researchers struggle to find practical combinatorial optimization problems, for which quantum annealers outperform other mathematical optimization solvers. Moreover, there are only a few studies that compare the performance of quantum annealers with one of the most sophisticated mathematical optimization solvers, such as Gurobi and CPLEX. In our study, we determine that QA demonstrates better performance than the solvers in the break minimization problem in a mirrored double round-robin tournament (MDRRT). We also explain the desirable performance of QA for the sparse interaction between variables and a problem without constraints. In this process, we demonstrate that the break minimization problem in an MDRRT can be expressed as a 4-regular graph. Through computational experiments, we solve this problem using our QA approach and two-integer programming approaches, which were performed using the latest quantum annealer D-Wave Advantage, and the sophisticated mathematical optimization solver, Gurobi, respectively. Further, we compare the quality of the solutions and the computational time. QA was able to determine the exact solution in 0.05 seconds for problems with 20 teams, which is a practical size. In the case of 36 teams, it took 84.8 s for the integer programming method to reach the objective function value, which was obtained by the quantum annealer in 0.05 s. These results not only present the break minimization problem in an MDRRT as an example of applying QA to practical optimization problems, but also contribute to find problems that can be effectively solved by QA.