قارن الطرق

	البرمجة الديناميكية العشوائية	التحسين العشوائي متعدد الأهداف
المجال	المحاكاة	المحاكاة
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1957	1990s–2000s
صاحب الطريقة	Bellman, R.; formalized for stochastic settings by Puterman, M. L.	Various (Fonseca, Fleming, Deb, Zitzler, and others)
النوع	Sequential optimization under uncertainty	Stochastic metaheuristic optimization
المصدر التأسيسي	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780486428093	Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester. ISBN: 9780471873396
الأسماء البديلة	SDP, Markov Decision Process, MDP, Stochastic DP	SMOO, Stochastic MOO, Multi-objective optimization under uncertainty, Robust multi-objective optimization
ذات صلة	6	5
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.	Stochastic Multi-Objective Optimization (SMOO) is a class of methods that simultaneously optimizes two or more conflicting objectives when parameters, costs, or constraints are uncertain or random. Rather than a single optimal solution, it produces a Pareto front of non-dominated solutions, each representing a different balance among objectives under the modeled uncertainty.