Quantum Annealing With Integer Slack Variables for Grid Partitioning

Quantum annealing (QA) can be used to efficiently solve quadratic unconstrained binary optimization (QUBO) problems. Grid partitioning (GP), which is a classic NP-hard integer programming problem, can potentially be solved much faster using QA. However, inequality constraints in the GP optimization model are difficult to handle. In this study, a novel solution framework based on QA is proposed for GP problems. The integer slack (IS) and binary expansion methods are applied to transform GP problems into QUBO problems. Instead of introducing continuous variables in traditional slack methods, the proposed IS method can avoid complex iteration processes when using QA. The case study demonstrates that the IS method obtains accurate feasible solutions with less calculation time.