方法对比

	分支定界法 (Branch and Bound)	动态规划	整数规划
领域	优化	优化	优化
方法族	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	1960	1957	1958
提出者	Ailsa Land & Alison Doig	Richard Bellman	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
类型	Exact combinatorial optimization algorithm	Exact combinatorial optimization via recursive decomposition	Mathematical optimisation — exact combinatorial method
开创性文献	Land, A. H., & Doig, A. G. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520.	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669
别名	B&B, Land-Doig Algorithm, Implicit Enumeration, Dal ve Sınır	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	IP, MIP, mixed-integer programming, mixed-integer linear programming
相关	3	3	4
摘要	Branch and Bound is a systematic exact algorithm for combinatorial and integer optimization problems, introduced by Ailsa Land and Alison Doig in 1960. It organizes the search space as a tree of subproblems, uses relaxation-derived upper bounds to prune branches that cannot improve the best known solution, and guarantees finding a globally optimal integer solution. It is the backbone of modern mixed-integer programming solvers used in operations research, logistics, scheduling, and engineering design.	Dynamic Programming (DP) is an exact optimization technique introduced by Richard Bellman in 1957 for solving multi-stage decision problems. It decomposes a complex problem into simpler, overlapping subproblems, solves each subproblem once, and stores the results to avoid redundant computation. Grounded in the Principle of Optimality, DP guarantees globally optimal solutions whenever the problem exhibits overlapping subproblems and optimal substructure.	Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems.