手法を比較

	制約プログラミング	動的計画法	ゴールプログラミング
分野	最適化	最適化	意思決定
系統	Process / pipeline	Process / pipeline	MCDM
提唱年	2006	1957	1955
提唱者	Rossi, van Beek & Walsh	Richard Bellman	Charnes, A., Cooper, W. W.
種類	Declarative combinatorial optimization	Exact combinatorial optimization via recursive decomposition	Multi-objective optimisation — weighted/lexicographic goal deviation minimisation
原典	Rossi, F., van Beek, P., & Walsh, T. (Eds.). (2006). Handbook of Constraint Programming. Elsevier. ISBN: 978-0-444-52726-4	Bellman, R. (1957). Dynamic Programming. Princeton University Press. ISBN: 978-0-691-07951-6	Charnes, A., Cooper, W. W. (1955). Optimal estimation of executive compensation by linear programming. Management Science
別名	Constraint Satisfaction Programming, Constraint-Based Optimization, Kısıt Programlama, CSP Optimization	DP, Bellman's Principle of Optimality, Recursive Optimization, Dinamik Programlama	—
関連	3	3	8
概要	Constraint Programming (CP) is a declarative optimization paradigm in which a problem is formulated as a set of variables, finite domains, and constraints, and a solver systematically searches for assignments that satisfy all constraints. Formalized comprehensively by Rossi, van Beek, and Walsh in their 2006 Handbook of Constraint Programming, CP unifies propagation-based pruning with intelligent backtracking search to tackle combinatorial problems across scheduling, planning, and configuration domains.	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.	GOAL-PROGRAMMING (Goal Programming — Minimise deviations from multiple aspiration levels) is a ranking multi-criteria decision-making (MCDM) method introduced by Charnes, A., Cooper, W. W. in 1955. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.