So sánh phương pháp

	Lập trình số nguyên hỗn hợp Bayes	Tối ưu hóa Bayes
Lĩnh vực	Mô phỏng	Tối ưu hóa
Họ	Process / pipeline	Process / pipeline
Năm ra đời	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958	1975 (foundational); 2012 (ML standard)
Người khởi xướng	Baptista, R. & Poloczek, M. (formal Bayesian-BO-MIP formulation); mixed-integer programming roots in Gomory (1958)	Mockus (1975); popularised for ML by Snoek, Larochelle & Adams (2012)
Loại	Surrogate-assisted combinatorial optimization	Sequential model-based black-box 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.	Snoek, J., Larochelle, H., & Adams, R.P. (2012). Practical Bayesian Optimization of Machine Learning Algorithms. Advances in Neural Information Processing Systems (NeurIPS), 25.
Tên gọi khác	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization	Bayesçi Optimizasyon (Hyperparameter Tuning), surrogate-based optimization, sequential model-based optimization, SMBO
Liên quan	5	2
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.	Bayesian Optimization is a sequential, model-based strategy for finding the optimum of expensive black-box functions with as few evaluations as possible. Rooted in the work of Mockus (1975) and brought to mainstream machine-learning practice by Snoek, Larochelle, and Adams (2012), it fits a probabilistic surrogate model — typically a Gaussian Process — to past observations and uses an acquisition function to decide where to probe next, balancing exploration of unknown regions with exploitation of promising ones.