手法を比較

	二レベル最適化（リーダー・フォロワー）	整数計画法	ロバスト最適化
分野	最適化	最適化	最適化
系統	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1998	1958	1970s theoretical roots; modern tractable form from late 1990s–2004
提唱者	Jonathan Bard	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)	Ben-Tal, El Ghaoui & Nemirovski (seminal book, 2009); Bertsimas & Sim (tractable polyhedral formulation, 2004)
種類	Hierarchical mathematical programming	Mathematical optimisation — exact combinatorial method	Mathematical programming framework
原典	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	Ben-Tal, A., El Ghaoui, L. & Nemirovski, A. (2009). Robust Optimization. Princeton University Press. ISBN: 9780691143682
別名	Stackelberg Optimization, Hierarchical Programming, Nested Optimization, İki Düzeyli Optimizasyon	IP, MIP, mixed-integer programming, mixed-integer linear programming	minimax optimization, worst-case optimization, Gürbüz Optimizasyon (Robust Optimization)
関連	3	4	5
概要	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.	Robust optimization is a mathematical programming framework, formalised by Ben-Tal and Nemirovski in the late 1990s and made broadly tractable by Bertsimas and Sim (2004), that finds decisions guaranteed to perform acceptably under every scenario within a predefined uncertainty set — rather than assuming parameter values are known exactly. Instead of optimising for a single expected outcome, it minimises the worst-case objective across all plausible realisations of uncertain data.