Column generation (CG) is a powerful technique for solving optimization
problems that involve a large number of variables or columns. This technique
begins by solving a smaller problem with a subset of columns and gradually
generates additional columns as needed. However, the generation of columns
often requires solving difficult subproblems repeatedly, which can be a
bottleneck for CG. To address this challenge, we propose a novel method called
machine learning enhanced ant colony optimization (MLACO), to efficiently
generate multiple high-quality columns from a subproblem. Specifically, we
train a ML model to predict the optimal solution of a subproblem, and then
integrate this ML prediction into the probabilistic model of ACO to sample
multiple high-quality columns. Our experimental results on the bin packing
problem with conflicts show that the MLACO method significantly improves the
performance of CG compared to several state-of-the-art methods. Furthermore,
when our method is incorporated into a Branch-and-Price method, it leads to a
significant reduction in solution time.

机器学习增强蚁群算法（MLACO）是一种用于列生成（CG）的有效方法，通过训练机器学习模型来预测子问题的最优解，并将该预测融入蚁群算法的概率模型中，以生成多个高质量的列。在解决冲突的装箱问题上，实验证明 MLACO 方法显著改善了 CG 的性能，并且当将该方法与分支定价法相结合时，能大幅缩短求解时间。