مقایسهٔ روشها
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| الگوریتم انشعاب و کران (Branch and Bound)× | برنامهریزی محدودیت (Constraint Programming)× | برنامهریزی عدد صحیح (IP) و برنامهریزی عدد صحیح مختلط (MIP)× | |
|---|---|---|---|
| حوزه | بهینهسازی | بهینهسازی | بهینهسازی |
| خانواده | Process / pipeline | Process / pipeline | Process / pipeline |
| سال پیدایش≠ | 1960 | 2006 | 1958 |
| پدیدآور≠ | Ailsa Land & Alison Doig | Rossi, van Beek & Walsh | Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960) |
| نوع≠ | Exact combinatorial optimization algorithm | Declarative combinatorial optimization | Mathematical optimisation — exact combinatorial method |
| منبع بنیادین≠ | Land, A. H., & Doig, A. G. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520. DOI ↗ | Rossi, F., van Beek, P., & Walsh, T. (Eds.). (2006). Handbook of Constraint Programming. Elsevier. ISBN: 978-0-444-52726-4 | Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669 |
| نامهای دیگر≠ | B&B, Land-Doig Algorithm, Implicit Enumeration, Dal ve Sınır | Constraint Satisfaction Programming, Constraint-Based Optimization, Kısıt Programlama, CSP Optimization | IP, MIP, mixed-integer programming, mixed-integer linear programming |
| مرتبط≠ | 3 | 3 | 4 |
| خلاصه≠ | Branch and Bound is a systematic exact algorithm for combinatorial and integer optimization problems, introduced by Ailsa Land and Alison Doig in 1960. It organizes the search space as a tree of subproblems, uses relaxation-derived upper bounds to prune branches that cannot improve the best known solution, and guarantees finding a globally optimal integer solution. It is the backbone of modern mixed-integer programming solvers used in operations research, logistics, scheduling, and engineering design. | Constraint Programming (CP) is a declarative optimization paradigm in which a problem is formulated as a set of variables, finite domains, and constraints, and a solver systematically searches for assignments that satisfy all constraints. Formalized comprehensively by Rossi, van Beek, and Walsh in their 2006 Handbook of Constraint Programming, CP unifies propagation-based pruning with intelligent backtracking search to tackle combinatorial problems across scheduling, planning, and configuration domains. | 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. |
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