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	Multi-Objective Dynamic Programming	確率的動的計画法
分野	シミュレーション	シミュレーション
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	Bellman, R.; formalized for stochastic settings by Puterman, M. L.
種類	Exact optimization — recursive multi-objective decomposition	Sequential optimization under uncertainty
原典	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780691079516	Bellman, R. (1957). Dynamic Programming. Princeton University Press, Princeton, NJ. ISBN: 9780486428093
別名	MODP, Multi-criteria dynamic programming, Vector dynamic programming, Pareto dynamic programming	SDP, Markov Decision Process, MDP, Stochastic DP
関連	5	6
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.	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.