قارن الطرق

	البرمجة الخطية الصحيحة المختلطة البايزية	البرمجة الصحيحة المختلطة
المجال	المحاكاة	المحاكاة
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958	1958–1960
صاحب الطريقة	Baptista, R. & Poloczek, M. (formal Bayesian-BO-MIP formulation); mixed-integer programming roots in Gomory (1958)	Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960)
النوع	Surrogate-assisted combinatorial optimization	Mathematical optimization
المصدر التأسيسي	Baptista, R., Poloczek, M. (2018). Bayesian Optimization of Combinatorial Structures. Proceedings of the 35th International Conference on Machine Learning (ICML), PMLR 80:462–471.	Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432
الأسماء البديلة	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming
ذات صلة	5	6
الملخص	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.	Mixed-Integer Programming (MIP) is a mathematical optimization framework in which some decision variables must take integer values while others may be continuous. It generalizes linear programming and is widely used in operations research, logistics, scheduling, resource allocation, and engineering design, where indivisibility constraints — such as yes/no decisions or whole-unit quantities — arise naturally.