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| 混合整数計画法× | 動的計画法× | |
|---|---|---|
| 分野≠ | シミュレーション | 最適化 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1958–1960 | 1957 |
| 提唱者≠ | Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960) | Richard Bellman |
| 種類≠ | Mathematical optimization | Exact combinatorial optimization via recursive decomposition |
| 原典≠ | Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432 | Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6 |
| 別名 | MIP, Mixed-Integer Linear Programming, MILP, Integer Programming | DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama |
| 関連≠ | 6 | 3 |
| 概要≠ | Mixed-Integer Programming (MIP) is a mathematical optimization framework in which some decision variables must take integer values while others may be continuous. It generalizes linear programming and is widely used in operations research, logistics, scheduling, resource allocation, and engineering design, where indivisibility constraints — such as yes/no decisions or whole-unit quantities — arise naturally. | 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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