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	Multi-Objective Dynamic Programming	動的計画法
分野	シミュレーション	最適化
系統	Process / pipeline	Process / pipeline
提唱年	1957-1975	1957
提唱者	Extension of Bellman (1957); formalized by multiple authors from 1970s onward	Richard Bellman
種類	Exact optimization — recursive multi-objective decomposition	Exact combinatorial optimization via recursive decomposition
原典	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
別名	MODP, Multi-criteria dynamic programming, Vector dynamic programming, Pareto dynamic programming	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama
関連	5	3
概要	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.