Adaptive Stabilization Based on Machine Learning for Column Generation

TL;DR

This paper introduces a machine learning-based adaptive stabilization method for column generation, significantly improving convergence rates by accurately predicting dual solutions and reducing oscillations in large-scale linear programming.

Contribution

It presents a novel machine learning approach for early dual solution prediction combined with an adaptive stabilization technique in column generation.

Findings

Enhanced convergence rate on graph coloring problem

More accurate early dual solution predictions

Reduction in dual value oscillations

Abstract

Column generation (CG) is a well-established method for solving large-scale linear programs. It involves iteratively optimizing a subproblem containing a subset of columns and using its dual solution to generate new columns with negative reduced costs. This process continues until the dual values converge to the optimal dual solution to the original problem. A natural phenomenon in CG is the heavy oscillation of the dual values during iterations, which can lead to a substantial slowdown in the convergence rate. Stabilization techniques are devised to accelerate the convergence of dual values by using information beyond the state of the current subproblem. However, there remains a significant gap in obtaining more accurate dual values at an earlier stage. To further narrow this gap, this paper introduces a novel approach consisting of 1) a machine learning approach for accurate prediction of optimal dual solutions and 2) an adaptive stabilization technique that effectively capitalizes on accurate predictions. On the graph coloring problem, we show that our method achieves a significantly improved convergence rate compared to traditional methods.