手法を比較

	Multi-Objective Dynamic Programming	多目的最適化
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	1896 (concept); 1989–2002 (evolutionary algorithms era)
提唱者	Extension of Bellman (1957); formalized by multiple authors from 1970s onward	Vilfredo Pareto (concept); modern computational formulation by Goldberg and Deb et al.
種類	Exact optimization — recursive multi-objective decomposition	Optimization framework
原典	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
別名	MODP, Multi-criteria dynamic programming, Vector dynamic programming, Pareto dynamic programming	MOO, Multi-Criteria Optimization, Vector Optimization, Pareto Optimization
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.	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.