قارن الطرق

	نموذج ماركوف متعدد الأهداف	نموذج ماركوف العشوائي
المجال	المحاكاة	المحاكاة
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	2006	1993
صاحب الطريقة	Chatterjee, K., Majumdar, R., Henzinger, T. A. (formal; survey: Roijers et al.)	Markov, A. A. (probabilistic extension developed by Sonnenberg & Beck and others)
النوع	Stochastic sequential decision model with multiple objectives	Probabilistic state-transition model with Monte Carlo uncertainty propagation
المصدر التأسيسي	Roijers, D. M., Vamplew, P., Whiteson, S., & Dazeley, R. (2013). A survey of multi-objective sequential decision-making. Journal of Artificial Intelligence Research, 48, 67–113.	Sonnenberg, F. A., & Beck, J. R. (1993). Markov models in medical decision making: A practical guide. Medical Decision Making, 13(4), 322–338.
الأسماء البديلة	MOMDP, Multi-objective MDP, Multi-criteria Markov Decision Process, MO-Markov Model	Probabilistic Markov Model, Stochastic Markov Chain, SMM, Monte Carlo Markov Model
ذات صلة	5	6
الملخص	A Multi-objective Markov Model (MOMDP) extends classical Markov Decision Processes to settings where an agent must optimize several reward signals simultaneously. Instead of a single optimal policy, the model produces a Pareto-optimal set of policies, enabling decision-makers to navigate trade-offs between competing goals such as cost, risk, and throughput over time.	A Stochastic Markov Model is a simulation technique that represents a system as a set of mutually exclusive health or decision states, moves a cohort (or individual agents) through those states using probabilistically sampled transition parameters, and aggregates outcomes across thousands of Monte Carlo iterations to produce full probability distributions over costs, outcomes, or rankings rather than single point estimates.