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| Benders Decomposition× | 列生成算法 (Dantzig-Wolfe)× | |
|---|---|---|
| 领域 | 运筹学 | 运筹学 |
| 方法族 | Machine learning | Machine learning |
| 起源年份≠ | 1962 | 1960 |
| 提出者≠ | Jacques F. Benders | George B. Dantzig and Philip Wolfe |
| 类型 | algorithm | algorithm |
| 开创性文献≠ | Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252. DOI ↗ | Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101-111. DOI ↗ |
| 别名 | cutting plane method, constraint generation | Dantzig-Wolfe decomposition, column generation method |
| 相关 | 3 | 3 |
| 摘要≠ | 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. | 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. |
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