مقایسهٔ روش‌ها

	برنامه‌ریزی پویا چندهدفه	بهینه‌سازی چندهدفه
حوزه	شبیه‌سازی	شبیه‌سازی
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	1957-1975	1896 (concept); 1989–2002 (evolutionary algorithms era)
پدیدآور	Extension of Bellman (1957); formalized by multiple authors from 1970s onward	Vilfredo Pareto (concept); modern computational formulation by Goldberg and Deb et al.
نوع	Exact optimization — recursive multi-objective decomposition	Optimization framework
منبع بنیادین	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780691079516	Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester. ISBN: 9780471873396
نام‌های دیگر	MODP, Multi-criteria dynamic programming, Vector dynamic programming, Pareto dynamic programming	MOO, Multi-Criteria Optimization, Vector Optimization, Pareto Optimization
مرتبط	5	3
خلاصه	Multi-Objective Dynamic Programming (MODP) extends Bellman's classical dynamic programming to settings where a decision-maker must optimize several competing objectives simultaneously across a sequence of stages. Rather than a single optimal policy, it produces a Pareto-optimal set of policies — each representing a distinct trade-off profile — by propagating vector-valued value functions backward through the state space.	Multi-Objective Optimization (MOO) is a mathematical and computational framework for finding solutions that simultaneously optimize two or more conflicting objective functions. Rather than collapsing all goals into a single scalar, MOO produces a set of trade-off solutions — the Pareto front — from which a decision-maker selects according to preference. It is widely used in engineering design, operations research, logistics, economics, and policy analysis.