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| Branch and Bound（ブランチ・アンド・バウンド法）× | 整数計画法× | |
|---|---|---|
| 分野 | 最適化 | 最適化 |
| 系統 | Process / pipeline | Process / pipeline |
| 提唱年≠ | 1960 | 1958 |
| 提唱者≠ | Ailsa Land & Alison Doig | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) |
| 種類≠ | Exact combinatorial optimization algorithm | Mathematical optimisation — exact combinatorial method |
| 原典≠ | Land, A. H., & Doig, A. G. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520. DOI ↗ | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 |
| 別名≠ | B&B, Land-Doig Algorithm, Implicit Enumeration, Dal ve Sınır | IP, MIP, mixed-integer programming, mixed-integer linear programming |
| 関連≠ | 3 | 4 |
| 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. | 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. |
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