Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs

- A data mining approach for reducing the search space of local search algorithms.
- A lazy construction of a k-nearest neighbor graph by extracting variable associations.
- Identifying promising pairs of flipping variables in the 2-flip neighborhood search.
- A 4-flip neighborhood local search with an efficient incremental evaluation.

We present a data mining approach for reducing the search space of local search algorithms in a class of binary integer programs including the set covering and partitioning problems. The quality of locally optimal solutions typically improves if a larger neighborhood is used, while the computation time of searching the neighborhood increases exponentially. To overcome this, we extract variable associations from the instance to be solved in order to identify promising pairs of flipping variables in the neighborhood search. Based on this, we develop a 4-flip neighborhood local search algorithm that incorporates an efficient incremental evaluation of solutions and an adaptive control of penalty weights. Computational results show that the proposed method improves the performance of the local search algorithm for large-scale set covering and partitioning problems.