Bayesian Networks, Influence Diagrams, and Games in Simulation Metamodeling Jirka Poropudas (M.Sc.) Aalto University School of Science and Technology Systems Analysis Laboratory Winter Simulation Conference 2010 Dec , Baltimore. Maryland

Contribution of the Thesis Simulation Metamodeling Influence Diagrams Decision Analysis with Multiple Criteria Dynamic Bayesian Networks Time Evolution of Simulation Games Multiple Decision Makers with Individual Objectives

The Thesis Consists of a summary article and six papers: I.Poropudas J., Virtanen K., 2010: Simulation Metamodeling with Dynamic Bayesian Networks, submitted for publication II.Poropudas J., Virtanen K., 2010: Simulation Metamodeling in Continuous Time using Dynamic Bayesian Networks, Winter Simulation Conference 2010 III.Poropudas J., Virtanen K., 2007: Analysis of Discrete Event Simulation Results using Dynamic Bayesian Networks, Winter Simulation Conference 2007 IV.Poropudas J., Virtanen K., 2009: Influence Diagrams in Analysis of Discrete Event Simulation Data, Winter Simulation Conference 2009 V.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 VI.Pousi J., Poropudas J., Virtanen K., 2010: Game Theoretic Simulation Metamodeling using Stochastic Kriging, Winter Simulation Conference

Dynamic Bayesian Networks and Discrete Event Simulation Bayesian network –Joint probability distribution of discrete random variables Nodes –Simulation state variables Dependencies –Arcs –Conditional probability tables Dynamic Bayesian network –Time slices → Discrete time Simulation state at

DBNs in Simulation Metamodeling Time evolution of simulation –Probability distribution of simulation state at discrete times Simulation parameters –Included as random variables What-if analysis –Simulation state at time t is fixed → Conditional probability distributions Poropudas J., Virtanen K., Simulation Metamodeling with Dynamic Bayesian Networks, submitted for publication.

Construction of DBN Metamodel 1)Selection of variables 2)Collecting simulation data 3)Optimal selection of time instants 4)Determination of network structure 5)Estimation of probability tables 6)Inclusion of simulation parameters 7)Validation Poropudas J., Virtanen K., Simulation Metamodeling with Dynamic Bayesian Networks, submitted for publication.

Approximative Reasoning in Continuous Time DBN gives probabilities at discrete time instants → What-if analysis at these time instants Approximative probabilities for all time instants with Lagrange interpolating polynomials → What-if analysis at arbitrary time instants ”Simple, yet effective!” Poropudas J., Virtanen K., Simulation Metamodeling in Continuous Time using Dynamic Bayesian Networks, WSC Monday 10:30 A.M. - 12:00 P.M. Metamodeling I

Air Combat Analysis Poropudas J., Virtanen K., Analysis of Discrete Events Simulation Results Using Dynamic Bayesian Networks, WSC Poropudas J., Virtanen K., Simulation Metamodeling with Dynamic Bayesian Networks, submitted for publication. X-Brawler ̶ a discrete event simulation model

Influence Diagrams (IDs) and Discrete Event Simulation Decision nodes –”Controllable” simulation inputs Chance nodes –Uncertain simulation inputs –Simulation outputs –Conditional probability tables Utility nodes –Decision maker’s preferences –Utility functions Arcs –Dependencies –Information Poropudas J., Pousi J., Virtanen K., Simulation Metamodeling with Influence Diagrams, manuscript.

Construction of ID Metamodel 1)Selection of variables 2)Collecting simulation data 3)Determination of diagram structure 4)Estimation of probability tables 5)Preference modeling 6)Validation Poropudas J., Pousi J., Virtanen K., Simulation Metamodeling with Influence Diagrams, manuscript.

IDs as MIMO Metamodels Simulation parameters included as random variables Joint probability distribution of simulation inputs and outputs What-if analysis using conditional probability distributions Queueing model Poropudas J., Pousi J., Virtanen K., Simulation Metamodeling with Influence Diagrams, manuscript.

Decision Making with Multiple Criteria Decision maker’s preferences –One or more criteria –Alternative utility functions Tool for simulation based decision support –Optimal decisions –Non-dominated decisions

Air Combat Analysis Poropudas J., Virtanen K., Influence Diagrams in Analysis of Discrete Event Simulation Data, WSC Consequences of decisions Decision maker’s preferences Optimal decisions

Games and Discrete Event Simulation Poropudas J., Virtanen K., Game Theoretic Validation and Analysis of Air Combat Simulation Models, Systems, Man, and Cybernetics – Part A: Systems and Humans, Vol. 40, No. 5, pp Game setting Players –Multiple decision makers with individual objectives Players’ decisions –Simulation inputs Players’ payoffs –Simulation outputs Best responses Equilibrium solutions

Construction of Game Theoretic Metamodel 1)Definition of scenario 2)Simulation data 3)Estimation of payoffs Regression model, stochastic kriging ANOVA Poropudas J., Virtanen K., Game Theoretic Validation and Analysis of Air Combat Simulation Models, Systems, Man, and Cybernetics – Part A: Systems and Humans, Vol. 40, No. 5, pp

Best Responses and Equilibirium Solutions Best responses ̶ player’s optimal decisions against a given decision by the opponent Equilibrium solutions ̶ intersections of players’ best responses Poropudas J., Virtanen K., Game Theoretic Validation and Analysis of Air Combat Simulation Models, Systems, Man, and Cybernetics – Part A: Systems and Humans, Vol. 40, No. 5, pp

Games and Stochastic Kriging Extension to global response surface modeling Pousi J., Poropudas J., Virtanen K., Game Theoretic Simulation Metamodeling Using Stochastic Kriging, WSC Tuesday 1:30 P.M. - 3:00 P.M. Advanced Modeling Techniques for Military Problems

Utilization of Game Theoretic Metamodes Validation of simulation model –Game properties compared with actual practices For example, best responses versus real-life air combat tactics Simulation based optimization –Best responses –Dominated and non-dominated decision alternatives –Alternative objectives