So sánh phương pháp

	Lập trình số nguyên hỗn hợp Bayes	Quy hoạch nguyên hỗn hợp đa mục tiêu
Lĩnh vực	Mô phỏng	Mô phỏng
Họ	Process / pipeline	Process / pipeline
Năm ra đời	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958	1980s–2000s
Người khởi xướng	Baptista, R. & Poloczek, M. (formal Bayesian-BO-MIP formulation); mixed-integer programming roots in Gomory (1958)	Ehrgott, M.; Mavrotas, G. and others in multi-criteria optimization
Loại	Surrogate-assisted combinatorial optimization	Mathematical optimization
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.	Ehrgott, M. (2005). Multicriteria Optimization (2nd ed.). Springer, Berlin. ISBN: 9783540213987
Tên gọi khác	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization	MO-MIP, Multi-criteria MIP, MOMIP, Multi-objective MILP
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.	Multi-Objective Mixed-Integer Programming (MO-MIP) is an optimization framework that simultaneously optimizes two or more conflicting objective functions subject to linear or nonlinear constraints, where some decision variables are restricted to integer values and others are continuous. It is widely applied in engineering design, supply chain planning, resource allocation, and scheduling problems that require discrete choices alongside continuous quantities.