Linganisha mbinu
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| Multi-objective mixed-integer programming× | Uratibu wa Malengo Mengi wa Kina× | |
|---|---|---|
| Nyanja | Uigaji | Uigaji |
| Familia | Process / pipeline | Process / pipeline |
| Mwaka wa asili≠ | 1980s–2000s | 1957-1975 |
| Mwanzilishi≠ | Ehrgott, M.; Mavrotas, G. and others in multi-criteria optimization | Extension of Bellman (1957); formalized by multiple authors from 1970s onward |
| Aina≠ | Mathematical optimization | Exact optimization — recursive multi-objective decomposition |
| Chanzo asilia≠ | Ehrgott, M. (2005). Multicriteria Optimization (2nd ed.). Springer, Berlin. ISBN: 9783540213987 | Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780691079516 |
| Majina mbadala | MO-MIP, Multi-criteria MIP, MOMIP, Multi-objective MILP | MODP, Multi-criteria dynamic programming, Vector dynamic programming, Pareto dynamic programming |
| Zinazohusiana | 5 | 5 |
| Muhtasari≠ | 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. | Multi-Objective Dynamic Programming (MODP) extends Bellman's classical dynamic programming to settings where a decision-maker must optimize several competing objectives simultaneously across a sequence of stages. Rather than a single optimal policy, it produces a Pareto-optimal set of policies — each representing a distinct trade-off profile — by propagating vector-valued value functions backward through the state space. |
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