قارن الطرق

	التحسين ثنائي المستوى (القائد-التابع)	البرمجة الصحيحة
المجال	التحسين	التحسين
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1998	1958
صاحب الطريقة	Jonathan Bard	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
النوع	Hierarchical mathematical programming	Mathematical optimisation — exact combinatorial method
المصدر التأسيسي	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
الأسماء البديلة	Stackelberg Optimization, Hierarchical Programming, Nested Optimization, İki Düzeyli Optimizasyon	IP, MIP, mixed-integer programming, mixed-integer linear programming
ذات صلة	3	4
الملخص	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.