In this paper, we propose a hybrid framework to solve large-scale
permutation-based combinatorial problems effectively using a high-performance
quadratic unconstrained binary optimization (QUBO) solver. To do so,
transformations are required to change a constrained optimization model to an
unconstrained model that involves parameter tuning. We propose techniques to
overcome the challenges in using a QUBO solver that typically comes with
limited numbers of bits. First, to smooth the energy landscape, we reduce the
magnitudes of the input without compromising optimality. We propose a machine
learning approach to tune the parameters for good performance effectively. To
handle possible infeasibility, we introduce a polynomial-time projection
algorithm. Finally, to solve large-scale problems, we introduce a
divide-and-conquer approach that calls the QUBO solver repeatedly on small
sub-problems. We tested our approach on provably hard Euclidean Traveling
Salesman (E-TSP) instances and Flow Shop Problem (FSP). Optimality gap that is
less than 10% and 11% are obtained respectively compared to the
best-known approach.Comment: 23 pages, 10 figure
