Pricing Filtering in Dantzig-Wolfe Decomposition

TL;DR

This paper introduces a filtering method for Dantzig-Wolfe decomposition that reduces computational effort by identifying which subproblems are likely to improve the solution, based on dual bounds from previous iterations.

Contribution

The paper presents a novel filtering technique that efficiently narrows down the set of subproblems solved during column generation, improving computational performance.

Findings

Significant reduction in computation time across various problems

Effective use of dual bounds for filtering subproblems

Maintains solution quality while reducing effort

Abstract

Column generation is used alongside Dantzig-Wolfe Decomposition, especially for linear programs having a decomposable pricing step requiring to solve numerous independent pricing subproblems. We propose a filtering method to detect which pricing subproblems may have improving columns, and only those subproblems are solved during pricing. This filtering is done by providing light, computable bounds using dual information from previous iterations of the column generation. The experiments show a significant impact on different combinatorial optimization problems.