So sánh phương pháp

	Lập trình số nguyên Bayes	Lập trình số nguyên hỗn hợp Bayes
Lĩnh vực	Mô phỏng	Mô phỏng
Họ	Process / pipeline	Process / pipeline
Năm ra đời	1990s–2000s	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958
Người khởi xướng	Baptiste, Lassagne, Nuijten and others in Bayesian optimization community	Baptista, R. & Poloczek, M. (formal Bayesian-BO-MIP formulation); mixed-integer programming roots in Gomory (1958)
Loại	Probabilistic combinatorial optimization	Surrogate-assisted combinatorial optimization
Công trình gốc	Baptiste, P., Lassagne, I., & Nuijten, W. (2001). Bayesian reasoning in mixed integer programming. European Journal of Operational Research, 130(2), 293–313.	Baptista, R., Poloczek, M. (2018). Bayesian Optimization of Combinatorial Structures. Proceedings of the 35th International Conference on Machine Learning (ICML), PMLR 80:462–471.
Tên gọi khác	BIP, Bayesian combinatorial optimization, Bayesian discrete optimization, probabilistic integer programming	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization
Liên quan	6	5
Tóm tắt	Bayesian Integer Programming (BIP) integrates Bayesian probabilistic reasoning with integer programming to solve combinatorial optimization problems under uncertainty. Instead of treating parameters as fixed, it encodes prior beliefs about uncertain coefficients and updates them with observed data, producing a posterior-guided search over integer-feasible solutions. The approach is widely used in scheduling, resource allocation, and supply-chain planning where data are incomplete or noisy.	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.