方法对比
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| 确定性整数规划× | 混合整数规划× | |
|---|---|---|
| 领域 | 仿真 | 仿真 |
| 方法族 | Process / pipeline | Process / pipeline |
| 起源年份≠ | 1958 | 1958–1960 |
| 提出者≠ | Ralph E. Gomory | Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960) |
| 类型≠ | Exact combinatorial optimization | Mathematical optimization |
| 开创性文献≠ | 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 ↗ | Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432 |
| 别名 | DIP, Integer Programming, IP, Integer Linear Programming | MIP, Mixed-Integer Linear Programming, MILP, Integer Programming |
| 相关≠ | 5 | 6 |
| 摘要≠ | 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. | 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. |
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