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| Bilevel-Optimierung (Leader-Follower)× | Ganzzahlige Programmierung× | |
|---|---|---|
| Fachgebiet | Optimierung | Optimierung |
| Familie | Process / pipeline | Process / pipeline |
| Entstehungsjahr≠ | 1998 | 1958 |
| Urheber≠ | Jonathan Bard | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) |
| Typ≠ | Hierarchical mathematical programming | Mathematical optimisation — exact combinatorial method |
| Wegweisende Quelle≠ | Bard, J. F. (1998). Practical Bilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers. ISBN: 978-0-7923-5458-7 | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 |
| Aliasnamen≠ | Stackelberg Optimization, Hierarchical Programming, Nested Optimization, İki Düzeyli Optimizasyon | IP, MIP, mixed-integer programming, mixed-integer linear programming |
| Verwandt≠ | 3 | 4 |
| Zusammenfassung≠ | Bilevel optimization is a class of mathematical programming problems in which one optimization problem is nested inside another. The upper-level (leader) problem optimizes its objective subject to constraints that include the solution of a lower-level (follower) problem. Formalized comprehensively by Jonathan Bard in 1998, the framework models hierarchical decision-making where the leader anticipates and accounts for the rational response of the follower. | Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems. |
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