قارن الطرق

	البرمجة الديناميكية العشوائية	البرمجة الديناميكية
المجال	المحاكاة	التحسين
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1957	1957
صاحب الطريقة	Bellman, R.; formalized for stochastic settings by Puterman, M. L.	Richard Bellman
النوع	Sequential optimization under uncertainty	Exact combinatorial optimization via recursive decomposition
المصدر التأسيسي	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780486428093	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6
الأسماء البديلة	SDP, Markov Decision Process, MDP, Stochastic DP	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama
ذات صلة	6	3
الملخص	Stochastic Dynamic Programming (SDP) is a mathematical optimization framework for sequential decision problems where outcomes are partly random. It extends Bellman's principle of optimality to stochastic environments, representing problems as Markov Decision Processes (MDPs) and computing optimal policies by solving recursive value equations over states and time periods.	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.