Large-scale controlled rounding using tabu search with strategic oscillation

When publishing tabular data, the United States Bureau of the Census must sometimes round fractional data to integer values of round integer data to multiples of a pre-specified base. Data integrity can be maintained by rounding tabular data subject to additivity constraints while minimizing the overall perturbation of the data. In this paper, the authors describe a heuristic based on tabu search with strategic oscillation for solving this NP-hard problem. A lower-bounding technique is developed in order to evaluate the quality of the solutions and provide a starting solution for the tabu search. Numerical results demonstrate the effectiveness of the procedure when applied to extremely large tables with up to 27,000 randomly generated entries. Additionally, the algorithm is shown to perform extremely well when applied to actual data obtained from the United States Bureau of the Census.