Vertaile menetelmiä

	Branch and Bound	Rajoiteohjelmointi	Dynaaminen ohjelmointi	Kokonaislukualkio-ohjelmointi
Tieteenala	Optimointi	Optimointi	Optimointi	Optimointi
Menetelmäperhe	Process / pipeline	Process / pipeline	Process / pipeline	Process / pipeline
Syntyvuosi	1960	2006	1957	1958
Kehittäjä	Ailsa Land & Alison Doig	Rossi, van Beek & Walsh	Richard Bellman	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
Tyyppi	Exact combinatorial optimization algorithm	Declarative combinatorial optimization	Exact combinatorial optimization via recursive decomposition	Mathematical optimisation — exact combinatorial method
Alkuperäislähde	Land, A. H., & Doig, A. G. (1960). An automatic method of solving discrete programming problems. Econometrica, 28(3), 497–520.	Rossi, F., van Beek, P., & Walsh, T. (Eds.). (2006). Handbook of Constraint Programming. Elsevier. ISBN: 978-0-444-52726-4	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669
Rinnakkaisnimet	B&B, Land-Doig Algorithm, Implicit Enumeration, Dal ve Sınır	Constraint Satisfaction Programming, Constraint-Based Optimization, Kısıt Programlama, CSP Optimization	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	IP, MIP, mixed-integer programming, mixed-integer linear programming
Liittyvät	3	3	3	4
Tiivistelmä	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.	Dynamic Programming (DP) is an exact optimization technique introduced by Richard Bellman in 1957 for solving multi-stage decision problems. It decomposes a complex problem into simpler, overlapping subproblems, solves each subproblem once, and stores the results to avoid redundant computation. Grounded in the Principle of Optimality, DP guarantees globally optimal solutions whenever the problem exhibits overlapping subproblems and optimal substructure.	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.