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.

翻译：列生成与Dantzig-Wolfe分解结合使用，尤其适用于具有可分解定价步骤的线性规划问题，该步骤需要求解大量独立的定价子问题。我们提出一种过滤方法，用于检测哪些定价子问题可能包含改进列，并在定价过程中仅求解这些子问题。该过滤通过利用列生成先前迭代中的对偶信息提供轻量级、可计算的界限来实现。实验表明，该方法对不同组合优化问题具有显著影响。