方法对比

	列生成算法 (Dantzig-Wolfe)	Benders Decomposition	单纯形法
领域	运筹学	运筹学	运筹学
方法族	Machine learning	Machine learning	Machine learning
起源年份	1960	1962	1947
提出者	George B. Dantzig and Philip Wolfe	Jacques F. Benders	George Dantzig
类型	algorithm	algorithm	algorithm
开创性文献	Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8(1), 101-111.	Benders, J. F. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238-252.	Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press.
别名	Dantzig-Wolfe decomposition, column generation method	cutting plane method, constraint generation	simplex algorithm
相关	3	3	4
摘要	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.	The Simplex Method, developed by George Dantzig in 1947, is a foundational algorithm for solving linear programming problems. It systematically explores vertices of the feasible region to find the optimal solution where the objective function is maximized or minimized subject to linear constraints.