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	Programowanie mieszane całkowitoliczbowe bayesowskie	Programowanie stochastyczne z ograniczeniami całkowitoliczbowymi
Dziedzina	Symulacja	Symulacja
Rodzina	Process / pipeline	Process / pipeline
Rok powstania	2018 (surrogate-BO-MIP synthesis); MIP foundations 1958	1990s–2000s
Twórca	Baptista, R. & Poloczek, M. (formal Bayesian-BO-MIP formulation); mixed-integer programming roots in Gomory (1958)	Birge, J. R.; Louveaux, F.; Sen, S.
Typ	Surrogate-assisted combinatorial optimization	Stochastic optimization model
Źródło pierwotne	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
Inne nazwy	Bayesian MIP, BO-MIP, Bayesian Combinatorial Optimization, Mixed-Integer Bayesian Optimization	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP
Pokrewne	5	5
Podsumowanie	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.