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arXiv 2407.01546cs.NEcs.LGmath.OC

用于列生成的机器学习增强蚁群优化

Machine Learning-Enhanced Ant Colony Optimization for Column Generation

School of Computing Technologies, RMIT University（RMIT大学计算技术学院）；University of Technology Sydney（悉尼科技大学）；La Trobe Business School, La Trobe University（拉筹伯大学拉筹伯商学院）

Hongjie Xu, Yunzhuang Shen, Yuan Sun, Xiaodong Li

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AI总结：

针对列生成需反复求解困难子问题的瓶颈，提出MLACO，用机器学习预测引导蚁群优化采样高质量列，显著提升CG及Branch-and-Price效率。

摘要：

列生成（CG）是一种用于求解涉及大量变量或列的优化问题的强大技术。该技术首先求解一个包含列子集的较小问题，然后根据需要逐步生成额外的列。然而，列的生成通常需要反复求解困难的子问题，这可能成为CG的瓶颈。为应对这一挑战，我们提出了一种名为机器学习增强蚁群优化（MLACO）的新方法，以从子问题中高效生成多个高质量列。具体而言，我们训练一个ML模型来预测子问题的最优解，然后将该ML预测集成到ACO的概率模型中，以采样多个高质量列。我们在带冲突装箱问题上的实验结果表明，与若干最先进方法相比，MLACO方法显著提升了CG的性能。此外，当我们的方法被纳入Branch-and-Price方法时，它带来了求解时间的显著减少。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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