方法对比

	整数规划	约束规划	动态规划
领域	优化	优化	优化
方法族	Process / pipeline	Process / pipeline	Process / pipeline
起源年份	1958	2006	1957
提出者	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Rossi, van Beek & Walsh	Richard Bellman
类型	Mathematical optimisation — exact combinatorial method	Declarative combinatorial optimization	Exact combinatorial optimization via recursive decomposition
开创性文献	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669	Rossi, F., van Beek, P., & Walsh, T. (Eds.). (2006). Handbook of Constraint Programming. Elsevier. ISBN: 978-0-444-52726-4	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6
别名	IP, MIP, mixed-integer programming, mixed-integer linear programming	Constraint Satisfaction Programming, Constraint-Based Optimization, Kısıt Programlama, CSP Optimization	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama
相关	4	3	3
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.	Constraint Programming (CP) is a declarative optimization paradigm in which a problem is formulated as a set of variables, finite domains, and constraints, and a solver systematically searches for assignments that satisfy all constraints. Formalized comprehensively by Rossi, van Beek, and Walsh in their 2006 Handbook of Constraint Programming, CP unifies propagation-based pruning with intelligent backtracking search to tackle combinatorial problems across scheduling, planning, and configuration domains.	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.