手法を比較

	ベイズ混合整数計画法	多目的混合整数計画法
分野	シミュレーション	シミュレーション
系統	Process / pipeline	Process / pipeline
提唱年	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958	1980s–2000s
提唱者	Baptista, R. & Poloczek, M. (formal Bayesian-BO-MIP formulation); mixed-integer programming roots in Gomory (1958)	Ehrgott, M.; Mavrotas, G. and others in multi-criteria optimization
種類	Surrogate-assisted combinatorial optimization	Mathematical optimization
原典	Baptista, R., Poloczek, M. (2018). Bayesian Optimization of Combinatorial Structures. Proceedings of the 35th International Conference on Machine Learning (ICML), PMLR 80:462–471.	Ehrgott, M. (2005). Multicriteria Optimization (2nd ed.). Springer, Berlin. ISBN: 9783540213987
別名	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization	MO-MIP, Multi-criteria MIP, MOMIP, Multi-objective MILP
関連	5	5
概要	Bayesian Mixed-Integer Programming (BO-MIP) couples a probabilistic surrogate model — typically a Gaussian process — with a mixed-integer programming solver to efficiently optimize expensive black-box objectives defined over spaces that contain both continuous and discrete or integer-valued decision variables. It is especially valuable when each function evaluation is costly and exhaustive search is infeasible.	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.