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| Column Generation (Dantzig-Wolfe)× | Phân rã Benders× | |
|---|---|---|
| Lĩnh vực | Vận trù học | Vận trù học |
| Họ | Machine learning | Machine learning |
| Năm ra đời≠ | 1960 | 1962 |
| Người khởi xướng≠ | George B. Dantzig and Philip Wolfe | Jacques F. Benders |
| Loại | algorithm | algorithm |
| Công trình gốc≠ | Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101-111. DOI ↗ | Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252. DOI ↗ |
| Tên gọi khác | Dantzig-Wolfe decomposition, column generation method | cutting plane method, constraint generation |
| Liên quan | 3 | 3 |
| Tóm tắt≠ | Column Generation, developed by George B. Dantzig and Philip Wolfe in 1960, is a powerful optimization technique for solving large-scale linear programming problems with special structure. Also known as Dantzig-Wolfe Decomposition, it decomposes the problem into a master problem (restricted to a subset of variables/columns) and a pricing subproblem (identifying new variables), iteratively improving the solution by introducing only relevant columns. | Benders Decomposition, introduced by Jacques F. Benders in 1962, is a powerful algorithmic framework for solving large-scale mixed-integer programming (MIP) problems. It decomposes the problem into a master problem (controlling complicating variables) and subproblems (handling remaining variables), using cutting planes generated from subproblem dual information to iteratively tighten the master problem. |
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