and Games in Simulation Metamodeling Jirka Poropudas MSc Aalto University School of Science and Technology Systems Analysis Laboratory httpwwwsaltkkfien jirkaporopudastkkfi ID: 319420
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Slide1
Bayesian Networks, Influence Diagrams,and Games in Simulation Metamodeling
Jirka Poropudas (M.Sc.)Aalto UniversitySchool of Science and TechnologySystems Analysis Laboratoryhttp://www.sal.tkk.fi/en/jirka.poropudas@tkk.fi
Winter Simulation Conference 2010
Dec. 5.-8., Baltimore. MarylandSlide2
Contribution of the Thesis
SimulationMetamodeling
Influence Diagrams
Decision Analysis
with Multiple Criteria
Dynamic Bayesian Networks
Time Evolution
of Simulation
Games
Multiple Decision Makers
with Individual Objectives
Novel Approaches to Simulation MetamodelingSlide3
The Thesis
Consists of a summary article and six papers:Poropudas J., Virtanen K., 2010: Simulation Metamodeling with Dynamic Bayesian Networks, submitted for publicationPoropudas J., Virtanen K., 2010: Simulation Metamodeling in Continuous Time using Dynamic Bayesian Networks, Winter Simulation Conference 2010Poropudas J., Virtanen K., 2007: Analysis of Discrete Event Simulation Results using Dynamic Bayesian Networks, Winter Simulation Conference 2007
Poropudas J., Virtanen K., 2009: Influence Diagrams in Analysis of Discrete Event Simulation Data,
Winter Simulation Conference 2009
Poropudas J., Virtanen K., 2010: Game Theoretic Validation and Analysis of Air Combat Simulation Models,
Systems, Man, and Cybernetics – Part A: Systems and Humans
, Vol. 40, No. 5
Pousi J., Poropudas J., Virtanen K., 2010: Game Theoretic Simulation Metamodeling using Stochastic Kriging,
Winter Simulation Conference 2010
http://www.sal.tkk.fi/en/publications/Slide4
Dynamic Bayesian Networks and Discrete Event SimulationBayesian network
Joint probability distribution of discrete random variablesNodesSimulation state variablesDependenciesArcsConditional probability tablesDynamic Bayesian networkTime slices → Discrete time
Simulation state atSlide5
DBNs in Simulation MetamodelingTime evolution of simulation
Probability distribution of simulation state at discrete timesSimulation parametersIncluded as random variablesWhat-if analysisSimulation state at time t is fixed→ Conditional probability distributionsPoropudas J., Virtanen K., 2010. Simulation Metamodeling with Dynamic Bayesian Networks, submitted for publication.Slide6
Construction of DBN MetamodelSelection of variables
Collecting simulation dataOptimal selection of time instantsDetermination of network structureEstimation of probability tablesInclusion of simulation parametersValidation
Poropudas J., Virtanen K., 2010. Simulation Metamodeling with Dynamic Bayesian Networks,
submitted for publication
.Slide7
Approximative Reasoningin Continuous Time
DBN gives probabilities at discrete time instants → What-if analysis at these time instantsApproximative probabilities for all time instants with
Lagrange
interpolating polynomials
→ What-if analysis at arbitrary time instants
”Simple, yet effective!”
Poropudas J., Virtanen K., 2010. Simulation Metamodeling in Continuous Time using Dynamic Bayesian Networks,
WSC 2010
.
Monday 10:30 A.M. - 12:00 P.M.
Metamodeling
ISlide8
Air Combat Analysis
Poropudas J., Virtanen K., 2007. Analysis of Discrete Events Simulation Results Using Dynamic Bayesian Networks, WSC 2007.Poropudas J., Virtanen K., 2010. Simulation Metamodeling with Dynamic Bayesian Networks, submitted for publication.X-Brawler ̶ a discrete event simulation modelSlide9
Influence Diagrams (IDs) andDiscrete Event Simulation
Decision nodes”Controllable” simulation inputsChance nodesUncertain simulation inputsSimulation outputsConditional probability tablesUtility nodesDecision maker’s preferencesUtility functionsArcsDependenciesInformation
Poropudas J., Pousi J., Virtanen K., 2010. Simulation Metamodeling with Influence Diagrams,
manuscript
.Slide10
Construction of ID MetamodelSelection of variables
Collecting simulation dataDetermination of diagram structureEstimation of probability tablesPreference modelingValidation
Poropudas J., Pousi J., Virtanen K., 2010. Simulation Metamodeling with Influence Diagrams,
manuscript
.Slide11
IDs as MIMO Metamodels
Simulation parameters included as random variablesJoint probability distribution of simulation inputs and outputs
What-if analysis
using conditional probability distributions
Queueing model
Poropudas J., Pousi J., Virtanen K., 2010. Simulation Metamodeling with Influence Diagrams,
manuscript
.Slide12
Decision Making with Multiple Criteria
Decision maker’s preferencesOne or more criteriaAlternative utility functionsTool for simulation baseddecision supportOptimal decisionsNon-dominated decisionsSlide13
Air Combat AnalysisPoropudas J., Virtanen K., 2009. Influence Diagrams in Analysis of Discrete Event Simulation Data,
WSC 2009.
Consequences of decisions
Decision maker’s preferences
Optimal decisionsSlide14
Games andDiscrete Event Simulation
Poropudas J., Virtanen K., 2010. Game Theoretic Validation and Analysis of Air Combat Simulation Models, Systems, Man, and Cybernetics – Part A: Systems and Humans, Vol. 40, No. 5, pp.1057-1070.
Game setting
Players
Multiple decision makers with individual objectives
Players’ decisions
Simulation inputs
Players’ payoffs
Simulation outputsBest responsesEquilibrium solutionsSlide15
Construction ofGame Theoretic Metamodel
Definition of scenarioSimulation dataEstimation of payoffsRegression model, stochastic krigingANOVA
Poropudas J., Virtanen K., 2010. Game Theoretic Validation and Analysis of Air Combat Simulation Models,
Systems, Man, and Cybernetics – Part A: Systems and Humans
, Vol. 40, No. 5, pp.1057-1070.Slide16
Best Responses andEquilibirium Solutions
Best responses ̶ player’s optimal decisions against a given decision by the opponentEquilibrium solutions ̶ intersections of players’ best responses
Poropudas J., Virtanen K., 2010. Game Theoretic Validation and Analysis of Air Combat Simulation Models,
Systems, Man, and Cybernetics – Part A: Systems and Humans
, Vol. 40, No. 5, pp.1057-1070.Slide17
Games and Stochastic KrigingExtension to global response surface modeling
Pousi J., Poropudas J., Virtanen K., 2010. Game Theoretic Simulation Metamodeling Using Stochastic Kriging, WSC 2010.
Tuesday 1:30 P.M. - 3:00 P.M.
Advanced Modeling Techniques for Military ProblemsSlide18
Utilization ofGame Theoretic Metamodes
Validation of simulation modelGame properties compared with actual practicesFor example, best responses versus real-life air combat tacticsSimulation based optimizationBest responsesDominated and non-dominated decision alternativesAlternative objectives