方法对比
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| 混合整数规划× | 线性规划× | |
|---|---|---|
| 领域≠ | 仿真 | 优化 |
| 方法族 | Process / pipeline | Process / pipeline |
| 起源年份≠ | 1958–1960 | 1947 |
| 提出者≠ | Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960) | George B. Dantzig |
| 类型≠ | Mathematical optimization | Mathematical programming / continuous optimization |
| 开创性文献≠ | Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432 | Dantzig, G.B. (1963). Linear Programming and Extensions. Princeton University Press. ISBN: 9780691059136 |
| 别名≠ | MIP, Mixed-Integer Linear Programming, MILP, Integer Programming | LP, linear optimization, Doğrusal Programlama (LP) |
| 相关≠ | 6 | 4 |
| 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. | Linear programming (LP), pioneered by George B. Dantzig in 1947, is a mathematical method for finding the best value of a linear objective function — such as minimum cost or maximum profit — subject to a set of linear inequality and equality constraints. It is the foundational technique in operations research and underlies production planning, resource allocation, logistics, diet problems, and countless other decision-making scenarios across engineering, economics, and the natural sciences. |
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