Efficient partition of integer optimization problems with one-hot encoding

Abstract: Quantum annealing is a heuristic algorithm for solving combinatorial optimization problems, and D-Wave Systems Inc. has developed hardware for implementing this algorithm. The current version of the D-Wave quantum annealer can solve unconstrained binary optimization problems with a limited number of binary variables, although cost functions of many practical problems are defined by a large number of integer variables. To solve these problems with the quantum annealer, the integer variables are generally binarized with one-hot encoding, and the binarized problem is partitioned into small subproblems. However, the entire search space of the binarized problem is considerably extended compared to that of the original integer problem and is dominated by unfeasible solutions. Therefore, to efficiently solve large optimization problems with one-hot encoding, partitioning methods that extract subproblems with as many feasible solutions as possible are required.