Efficient Construction of Feasible Solutions in Column Generation using Quantum Annealing

Abstract

Column generation (CG) has been used to solve constrained 0-1 quadratic programming problems. The pricing problem, which is iteratively solved in CG, can be reduced to an unconstrained 0-1 quadratic programming problem, allowing for the efficient application of quantum annealing (QA). The solutions obtained by CG are continuous relaxations, which cannot be practically used as feasible 0-1 solutions. In this paper, we propose a postprocessing method for constructing feasible 0-1 solutions from the continuous relaxations obtained through CG. The proposed technique consists of two phases: (i) mapping the continuous CG solution to a feasible 0-1 solution and (ii) applying a constraint-aware local search to improve that solution's quality. Numerical experiments on randomly generated problems demonstrate that CG with the proposed postprocessing yields solutions comparable to commercial solvers with significantly reduced computation time. Consequently, the postprocessing enables CG with QA to obtain high-quality approximate solutions faster.