Selecting cutting planes for solving Mixed-Integer Linear Programming (MILP) is a critical task as it directly impacts the efficiency and effectiveness of the optimization process. By carefully choosing a set of cuts, it becomes possible to significantly reduce the size of the search space, thereby enhancing the algorithm’s ability to find optimal or near-optimal solutions within a reasonable computational time frame. In this paper, we examine recent advancements in utilizing Machine Learning (ML) techniques for the selection of cutting planes (separation) in MILP. Despite the existence of various types of separations, the task of selecting a set of cuts to augment the Linear Programming (LP) relaxation at a particular node of the Branch-and-Bound (B&B) tree remains a challenge, both in terms of formal methods and heuristic approaches. ML presents a promising direction for enhancing the cut selection process by leveraging data to identify promising cuts that expedite the resolution of MILP problems. Focusing on recent developments in research, we investigate common methodologies for data gathering, evaluation techniques, and ML model architectures. We review empirical findings in the literature to assess the extent of progress achieved and conclude by suggesting potential directions for future investigation. In conclusion, the integration of ML techniques holds great promise for advancing the field of MILP by improving the efficiency and effectiveness of cut selection processes, ultimately leading to better solutions for complex optimization problems

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Learning Different Separations in Branch and Cut: A Survey

  • Chaima Ayachi Amar,
  • Khadra Bouanane,
  • Oussama Aiadi

摘要

Selecting cutting planes for solving Mixed-Integer Linear Programming (MILP) is a critical task as it directly impacts the efficiency and effectiveness of the optimization process. By carefully choosing a set of cuts, it becomes possible to significantly reduce the size of the search space, thereby enhancing the algorithm’s ability to find optimal or near-optimal solutions within a reasonable computational time frame. In this paper, we examine recent advancements in utilizing Machine Learning (ML) techniques for the selection of cutting planes (separation) in MILP. Despite the existence of various types of separations, the task of selecting a set of cuts to augment the Linear Programming (LP) relaxation at a particular node of the Branch-and-Bound (B&B) tree remains a challenge, both in terms of formal methods and heuristic approaches. ML presents a promising direction for enhancing the cut selection process by leveraging data to identify promising cuts that expedite the resolution of MILP problems. Focusing on recent developments in research, we investigate common methodologies for data gathering, evaluation techniques, and ML model architectures. We review empirical findings in the literature to assess the extent of progress achieved and conclude by suggesting potential directions for future investigation. In conclusion, the integration of ML techniques holds great promise for advancing the field of MILP by improving the efficiency and effectiveness of cut selection processes, ultimately leading to better solutions for complex optimization problems