เปรียบเทียบวิธี

	การโปรแกรมเชิงจำนวนเต็มแบบเบย์เซียน	การโปรแกรมจำนวนเต็มผสม
สาขาวิชา	การจำลอง	การจำลอง
ตระกูล	Process / pipeline	Process / pipeline
ปีกำเนิด	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958	1958–1960
ผู้ริเริ่ม	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)
ประเภท	Surrogate-assisted combinatorial optimization	Mathematical optimization
แหล่งต้นตำรับ	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
ชื่อเรียกอื่น	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming
ที่เกี่ยวข้อง	5	6
สรุป	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.