方法对比

	整数规划	动态规划	线性规划
领域	优化	优化	优化
方法族	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	1958	1957	1947
提出者	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Richard Bellman	George B. Dantzig
类型	Mathematical optimisation — exact combinatorial method	Exact combinatorial optimization via recursive decomposition	Mathematical programming / continuous optimization
开创性文献	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136
别名	IP, MIP, mixed-integer programming, mixed-integer linear programming	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	LP, linear optimization, Doğrusal Programlama (LP)
相关	4	3	4
摘要	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.	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.	Linear programming (LP), pioneered by George B. Dantzig in 1947, is a mathematical method for finding the best value of a linear objective function — such as minimum cost or maximum profit — subject to a set of linear inequality and equality constraints. It is the foundational technique in operations research and underlies production planning, resource allocation, logistics, diet problems, and countless other decision-making scenarios across engineering, economics, and the natural sciences.