方法对比
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| 混合整数规划× | 多目标混合整数规划× | |
|---|---|---|
| 领域 | 仿真 | 仿真 |
| 方法族 | Process / pipeline | Process / pipeline |
| 起源年份≠ | 1958–1960 | 1980s–2000s |
| 提出者≠ | Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960) | Ehrgott, M.; Mavrotas, G. and others in multi-criteria optimization |
| 类型 | Mathematical optimization | Mathematical optimization |
| 开创性文献≠ | Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432 | Ehrgott, M. (2005). Multicriteria Optimization (2nd ed.). Springer, Berlin. ISBN: 9783540213987 |
| 别名 | MIP, Mixed-Integer Linear Programming, MILP, Integer Programming | MO-MIP, Multi-criteria MIP, MOMIP, Multi-objective MILP |
| 相关≠ | 6 | 5 |
| 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. | Multi-Objective Mixed-Integer Programming (MO-MIP) is an optimization framework that simultaneously optimizes two or more conflicting objective functions subject to linear or nonlinear constraints, where some decision variables are restricted to integer values and others are continuous. It is widely applied in engineering design, supply chain planning, resource allocation, and scheduling problems that require discrete choices alongside continuous quantities. |
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