手法を比較

	ベイズ線形計画法	ベイズ混合整数計画法
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	1970s–1980s	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958
提唱者	Integrated from Dantzig (LP) and Zellner/Bayesian econometrics traditions	Baptista, R. & Poloczek, M. (formal Bayesian-BO-MIP formulation); mixed-integer programming roots in Gomory (1958)
種類	Optimization under Bayesian uncertainty	Surrogate-assisted combinatorial optimization
原典	Dantzig, G. B. (1963). Linear Programming and Extensions. Princeton University Press, Princeton, NJ. ISBN: 9780691059136	Baptista, R., Poloczek, M. (2018). Bayesian Optimization of Combinatorial Structures. Proceedings of the 35th International Conference on Machine Learning (ICML), PMLR 80:462–471.
別名	BLP, Bayesian LP, Bayesian stochastic linear programming, prior-posterior LP	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization
関連	6	5
概要	Bayesian Linear Programming (BLP) integrates Bayesian statistical inference with classical linear programming to handle uncertainty in model parameters such as objective function coefficients, constraint coefficients, or right-hand-side values. Instead of treating parameters as fixed or governed by worst-case bounds, BLP uses prior beliefs updated by data to form posterior distributions, which then guide the LP formulation and solution, producing decisions that are optimal in a probabilistic, data-informed sense.	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.