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| Branch and Bound（ブランチ・アンド・バウンド法）× | 動的計画法× | |
|---|---|---|
| 分野 | 最適化 | 最適化 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1960 | 1957 |
| 提唱者≠ | Ailsa Land & Alison Doig | Richard Bellman |
| 種類≠ | Exact combinatorial optimization algorithm | Exact combinatorial optimization via recursive decomposition |
| 原典≠ | Land, A. H., & Doig, A. G. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520. DOI ↗ | Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6 |
| 別名 | B&B, Land-Doig Algorithm, Implicit Enumeration, Dal ve Sınır | DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama |
| 関連 | 3 | 3 |
| 概要≠ | 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. |
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