مقایسهٔ روش‌ها

	برنامه‌ریزی محدودیت (Constraint Programming)	یادگیری تقویتی عمیق	برنامه‌ریزی عدد صحیح (IP) و برنامه‌ریزی عدد صحیح مختلط (MIP)
حوزه	بهینه‌سازی	یادگیری عمیق	بهینه‌سازی
خانواده	Process / pipeline	Machine learning	Process / pipeline
سال پیدایش	2006	2015	1958
پدیدآور	Rossi, van Beek & Walsh	Mnih, V. et al. (DQN)	Ralph Gomory (cutting planes, 1958); land-and-doig branch-and-bound (1960)
نوع	Declarative combinatorial optimization	Sequential decision-making (agent–environment interaction)	Mathematical optimisation — exact combinatorial method
منبع بنیادین	Rossi, F., van Beek, P., & Walsh, T. (Eds.). (2006). Handbook of Constraint Programming. Elsevier. ISBN: 978-0-444-52726-4	Mnih, V. et al. (2015). Human-Level Control through Deep Reinforcement Learning. Nature, 518, 529–533.	Wolsey, L.A. (1998). Integer Programming. Wiley. ISBN: 9780471283669
نام‌های دیگر	Constraint Satisfaction Programming, Constraint-Based Optimization, Kısıt Programlama, CSP Optimization	Derin Pekiştirmeli Öğrenme (DQN / PPO / A3C), derin pekiştirmeli öğrenme, deep RL, DRL	IP, MIP, mixed-integer programming, mixed-integer linear programming
مرتبط	3	4	4
خلاصه	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.	Deep Reinforcement Learning combines neural networks with reinforcement learning so an agent learns by interacting with an environment, popularised by Mnih and colleagues' 2015 Nature work on human-level Atari control. Instead of learning from a fixed labelled dataset, the agent takes actions, observes rewards, and gradually shapes a policy that maximises long-run return.	Integer programming (IP), also called mixed-integer programming (MIP) when only some variables are restricted to whole numbers, is a branch of mathematical optimisation in which some or all decision variables must take integer or binary values. Building on linear programming, it was formalised through Ralph Gomory's cutting-plane method (1958) and the Land-and-Doig branch-and-bound algorithm (1960), and it has since become the standard exact framework for scheduling, assignment, routing, and resource-allocation problems.