قارن الطرق

	الماتْهُورِيسْتِيكس (Matheuristics): تهجين البرمجة الرياضية والميتاهُورِيسْتِيكس	البرمجة الصحيحة
المجال	التحسين	التحسين
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	2009	1958
صاحب الطريقة	Maniezzo, Stützle & Voß	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
النوع	Hybrid optimization framework	Mathematical optimisation — exact combinatorial method
المصدر التأسيسي	Maniezzo, V., Stützle, T., & Voß, S. (Eds.). (2009). Matheuristics: Hybridizing Metaheuristics and Mathematical Programming. Springer. ISBN: 978-1-4419-1305-0	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669
الأسماء البديلة	Hybrid Metaheuristics, MIP-based Heuristics, Math-Programming Hybrids, Matematiksel Sezgisel Yöntemler	IP, MIP, mixed-integer programming, mixed-integer linear programming
ذات صلة	3	4
الملخص	Matheuristics is a class of hybrid optimization methods that tightly couple exact mathematical programming components—such as mixed-integer programming (MIP) solvers—with metaheuristic search procedures. Formally introduced and named by Maniezzo, Stützle, and Voß in 2009, the framework leverages the global-search capability of metaheuristics and the structural exploitation of mathematical programming to tackle large-scale combinatorial optimization problems that neither approach can solve effectively alone.	Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems.