مقایسهٔ روش‌ها

	بهینه‌سازی چندهدفه	برنامه‌ریزی هدف	برنامه‌ریزی عدد صحیح مختلط
حوزه	شبیه‌سازی	تصمیم‌گیری	شبیه‌سازی
خانواده	Process / pipeline	MCDM	Process / pipeline
سال پیدایش	1896 (concept); 1989–2002 (evolutionary algorithms era)	1955	1958–1960
پدیدآور	Vilfredo Pareto (concept); modern computational formulation by Goldberg and Deb et al.	Charnes, A., Cooper, W. W.	Ralph Gomory (branch-and-bound cuts, 1958); Land & Doig (branch-and-bound, 1960)
نوع	Optimization framework	Multi-objective optimisation — weighted/lexicographic goal deviation minimisation	Mathematical optimization
منبع بنیادین	Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester. ISBN: 9780471873396	Charnes, A., Cooper, W. W. (1955). Optimal estimation of executive compensation by linear programming. Management Science	Nemhauser, G. L., Wolsey, L. A. (1988). Integer and Combinatorial Optimization. Wiley-Interscience, New York. ISBN: 9780471359432
نام‌های دیگر	MOO, Multi-Criteria Optimization, Vector Optimization, Pareto Optimization	—	MIP, Mixed-Integer Linear Programming, MILP, Integer Programming
مرتبط	3	8	6
خلاصه	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.	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.	Mixed-Integer Programming (MIP) is a mathematical optimization framework in which some decision variables must take integer values while others may be continuous. It generalizes linear programming and is widely used in operations research, logistics, scheduling, resource allocation, and engineering design, where indivisibility constraints — such as yes/no decisions or whole-unit quantities — arise naturally.