Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Machine Learning-Enhanced Ant Colony Optimization for Column Generation

Hongjie Xu, Yunzhuang Shen, Yuan Sun, Xiaodong Li

TL;DR

The paper tackles the column generation pricing bottleneck in BPPC by introducing MLACO, a hybrid approach that trains an offline ML model to predict optimal pricing subproblem solutions and integrates these predictions into an Ant Colony Optimization framework to sample multiple high-quality columns. It introduces diversity-aware sampling and demonstrates that MLACO yields faster CG and improved Branch-and-Price performance on BPPC compared with state-of-the-art baselines. The key contributions include an offline predictive model for the pricing problem, a diversity-centric sampling strategy within ACO, and extensive empirical validation showing substantial speedups, especially as pricing problems grow in difficulty. The work has practical impact by enabling faster solution of BPPC and related decomposable problems, with potential extensions to other domains such as VRP and graph-based feature learning.

Abstract

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.

Machine Learning-Enhanced Ant Colony Optimization for Column Generation

TL;DR

The paper tackles the column generation pricing bottleneck in BPPC by introducing MLACO, a hybrid approach that trains an offline ML model to predict optimal pricing subproblem solutions and integrates these predictions into an Ant Colony Optimization framework to sample multiple high-quality columns. It introduces diversity-aware sampling and demonstrates that MLACO yields faster CG and improved Branch-and-Price performance on BPPC compared with state-of-the-art baselines. The key contributions include an offline predictive model for the pricing problem, a diversity-centric sampling strategy within ACO, and extensive empirical validation showing substantial speedups, especially as pricing problems grow in difficulty. The work has practical impact by enabling faster solution of BPPC and related decomposable problems, with potential extensions to other domains such as VRP and graph-based feature learning.

Abstract

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.
Paper Structure (14 sections, 12 equations, 3 figures, 5 tables, 3 algorithms)

This paper contains 14 sections, 12 equations, 3 figures, 5 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Problem Formulations
  4. Column Generation for BPPC
  5. Ant Colony Optimization
  6. Machine Learning for Optimization
  7. The Proposed Approach
  8. Optimal Solution Prediction
  9. MLACO for Column Generation
  10. Empirical Studies
  11. Experimental Setup
  12. Results for CG
  13. Results for Branch-and-Price
  14. Conclusion

Figures (3)

  • Figure 1: An illustration of our MLACO method as a pricing heuristic for CG. We train a ML model $\mathcal{M}$ on a set of solved pricing problem instances to learn a mapping from problem features to the optimal solutions. In the testing phase, we use the offline-trained ML model $\mathcal{M}$ to predict an optimal solution to an unseen pricing problem. The ML prediction is then incorporated into the ACO probabilistic model to sample multiple high-quality solutions, which are then iteratively improved in an online manner.
  • Figure 2: Number of instances solved by CG using different pricing methods. Each subfigure shows the results for a different bin capacity multipler.
  • Figure 3: Number of instances solved within an optimality gap by branch-and-price with various pricing methods.