Linganisha mbinu

	Bayesian Mixed-Integer Programming	Mixed-Integer Programming
Nyanja	Uigaji	Uigaji
Familia	Process / pipeline	Process / pipeline
Mwaka wa asili	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958	1958–1960
Mwanzilishi	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)
Aina	Surrogate-assisted combinatorial optimization	Mathematical optimization
Chanzo asilia	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
Majina mbadala	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming
Zinazohusiana	5	6
Muhtasari	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.