เปรียบเทียบวิธี

	การโปรแกรมจำนวนเต็มแบบเบย์ (Bayesian Integer Programming	การโปรแกรมเชิงจำนวนเต็มแบบเบย์เซียน
สาขาวิชา	การจำลอง	การจำลอง
ตระกูล	Process / pipeline	Process / pipeline
ปีกำเนิด	1990s–2000s	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958
ผู้ริเริ่ม	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)
ประเภท	Probabilistic combinatorial optimization	Surrogate-assisted combinatorial optimization
แหล่งต้นตำรับ	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.
ชื่อเรียกอื่น	BIP, Bayesian combinatorial optimization, Bayesian discrete optimization, probabilistic integer programming	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization
ที่เกี่ยวข้อง	6	5
สรุป	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.