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

TL;DR

This paper introduces a data mining approach to identify promising variable pairs for local search in large-scale binary integer programs, significantly improving solution quality and efficiency.

Contribution

It develops a novel 4-flip neighborhood local search algorithm that leverages variable associations to enhance performance on large-scale set covering and partitioning problems.

Findings

Improved solution quality for large-scale problems

Reduced computation time through variable association extraction

Effective adaptive penalty weight control

Abstract

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.