مقایسهٔ روشها
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| برنامهریزی پویا چندهدفه× | برنامهریزی پویا× | |
|---|---|---|
| حوزه≠ | شبیهسازی | بهینهسازی |
| خانواده | Process / pipeline | Process / pipeline |
| سال پیدایش≠ | 1957-1975 | 1957 |
| پدیدآور≠ | Extension of Bellman (1957); formalized by multiple authors from 1970s onward | Richard Bellman |
| نوع≠ | Exact optimization — recursive multi-objective decomposition | Exact combinatorial optimization via recursive decomposition |
| منبع بنیادین≠ | Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780691079516 | Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6 |
| نامهای دیگر | MODP, Multi-criteria dynamic programming, Vector dynamic programming, Pareto dynamic programming | DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama |
| 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. | 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. |
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