So sánh phương pháp

	Lập trình số nguyên hỗn hợp Bayes	Quy hoạch nguyên hỗn hợp ngẫu nhiên
Lĩnh vực	Mô phỏng	Mô phỏng
Họ	Process / pipeline	Process / pipeline
Năm ra đời	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958	1990s–2000s
Người khởi xướng	Baptista, R. & Poloczek, M. (formal Bayesian-BO-MIP formulation); mixed-integer programming roots in Gomory (1958)	Birge, J. R.; Louveaux, F.; Sen, S.
Loại	Surrogate-assisted combinatorial optimization	Stochastic optimization model
Công trình gốc	Baptista, R., Poloczek, M. (2018). Bayesian Optimization of Combinatorial Structures. Proceedings of the 35th International Conference on Machine Learning (ICML), PMLR 80:462–471.	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175
Tên gọi khác	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP
Liên quan	5	5
Tóm tắt	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.	Stochastic Mixed-Integer Programming (SMIP) is an optimization framework that finds the best mix of binary, integer, and continuous decisions when key parameters — costs, demands, capacities — are uncertain and modeled as probability distributions over a set of scenarios. It extends classical MIP by embedding scenario trees or expected-value objectives that hedge against uncertainty while respecting combinatorial constraints.