قارن الطرق

	البرمجة الصحيحة المختلطة العشوائية	التحسين العشوائي متعدد الأهداف
المجال	المحاكاة	المحاكاة
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1990s–2000s	1990s–2000s
صاحب الطريقة	Birge, J. R.; Louveaux, F.; Sen, S.	Various (Fonseca, Fleming, Deb, Zitzler, and others)
النوع	Stochastic optimization model	Stochastic metaheuristic optimization
المصدر التأسيسي	Birge, J. R., & Louveaux, F. (1997). Introduction to Stochastic Programming. Springer Series in Operations Research. New York: Springer. ISBN: 9780387982175	Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester. ISBN: 9780471873396
الأسماء البديلة	SMIP, Stochastic MIP, Mixed-Integer Stochastic Programming, SMILP	SMOO, Stochastic MOO, Multi-objective optimization under uncertainty, Robust multi-objective optimization
ذات صلة	5	5
الملخص	Stochastic Mixed-Integer Programming (SMIP) is an optimization framework that finds the best mix of binary, integer, and continuous decisions when key parameters — costs, demands, capacities — are uncertain and modeled as probability distributions over a set of scenarios. It extends classical MIP by embedding scenario trees or expected-value objectives that hedge against uncertainty while respecting combinatorial constraints.	Stochastic Multi-Objective Optimization (SMOO) is a class of methods that simultaneously optimizes two or more conflicting objectives when parameters, costs, or constraints are uncertain or random. Rather than a single optimal solution, it produces a Pareto front of non-dominated solutions, each representing a different balance among objectives under the modeled uncertainty.