方法对比
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| 混合整数规划× | 分支定界法 (Branch and Bound)× | |
|---|---|---|
| 领域≠ | 仿真 | 优化 |
| 方法族 | Process / pipeline | Process / pipeline |
| 起源年份≠ | 1958–1960 | 1960 |
| 提出者≠ | Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960) | Ailsa Land & Alison Doig |
| 类型≠ | Mathematical optimization | Exact combinatorial optimization algorithm |
| 开创性文献≠ | Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432 | Land, A. H., & Doig, A. G. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520. DOI ↗ |
| 别名 | MIP, Mixed-Integer Linear Programming, MILP, Integer Programming | B&B, Land-Doig Algorithm, Implicit Enumeration, Dal ve Sınır |
| 相关≠ | 6 | 3 |
| 摘要≠ | 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. | 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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