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| 整数計画法× | 動的計画法× | |
|---|---|---|
| 分野 | 最適化 | 最適化 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1958 | 1957 |
| 提唱者≠ | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) | Richard Bellman |
| 種類≠ | Mathematical optimisation — exact combinatorial method | Exact combinatorial optimization via recursive decomposition |
| 原典≠ | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 | Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6 |
| 別名≠ | IP, MIP, mixed-integer programming, mixed-integer linear programming | DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama |
| 関連≠ | 4 | 3 |
| 概要≠ | 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. |
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