手法を比較
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| 決定版整数計画法× | Branch and Bound（ブランチ・アンド・バウンド法）× | |
|---|---|---|
| 分野≠ | シミュレーション | 最適化 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1958 | 1960 |
| 提唱者≠ | Ralph E. Gomory | Ailsa Land & Alison Doig |
| 種類≠ | Exact combinatorial optimization | Exact combinatorial optimization algorithm |
| 原典≠ | Gomory, R. E. (1958). Outline of an algorithm for integer solutions to linear programs. Bulletin of the American Mathematical Society, 64(5), 275-278. DOI ↗ | Land, A. H., & Doig, A. G. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520. DOI ↗ |
| 別名 | DIP, Integer Programming, IP, Integer Linear Programming | B&B, Land-Doig Algorithm, Implicit Enumeration, Dal ve Sınır |
| 関連≠ | 5 | 3 |
| 概要≠ | Deterministic Integer Programming (DIP) is a mathematical optimization approach that finds the best solution to problems where some or all decision variables must take integer values, given fully known (deterministic) objective and constraint data. It is the classical, non-stochastic form of integer programming, foundational to operations research and combinatorial optimization since the late 1950s. | 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. |
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