方法对比
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| 确定性混合整数规划× | 随机混合整数规划× | |
|---|---|---|
| 领域 | 仿真 | 仿真 |
| 方法族 | Process / pipeline | Process / pipeline |
| 起源年份≠ | 1958–1960 | 1990s–2000s |
| 提出者≠ | Gomory, R. E.; Dantzig, G. B.; Land, A. H.; Doig, A. G. | Birge, J. R.; Louveaux, F.; Sen, S. |
| 类型≠ | Mathematical programming / combinatorial optimization | Stochastic optimization model |
| 开创性文献≠ | Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. John Wiley & Sons, New York. ISBN: 9780471359432 | Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175 |
| 别名 | Deterministic MIP, Deterministic MILP/MIQP, Classical Mixed-Integer Programming, Deterministic MIP Optimization | SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP |
| 相关≠ | 6 | 5 |
| 摘要≠ | Deterministic Mixed-Integer Programming (MIP) is a mathematical optimization framework that finds the provably optimal solution to problems involving both continuous and integer decision variables under fully known, fixed coefficients and constraints. It is the foundational workhorse of operations research when all data are treated as certain. | Stochastic Mixed-Integer Programming (SMIP) is an optimization framework that finds the best mix of binary, integer, and continuous decisions when key parameters — costs, demands, capacities — are uncertain and modeled as probability distributions over a set of scenarios. It extends classical MIP by embedding scenario trees or expected-value objectives that hedge against uncertainty while respecting combinatorial constraints. |
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