Modeling, Simulation and Optimization

Ammar Mushtaq Modeling, Simulation & Optimization Lecture 1: 1

Ammar Mushtaq [email protected]

Research Center for Modeling and Simulation (RCMS)National University of Sciences and Technology (NUST)

Islamabad, Pakistan

Course Outline


Comparison of System Designs

Analysis of Variance

Variance Reduction Techniques

Design of Experiments

Introduction to Simulations

Types of Simulation Models

Simulation Examples

Monte-Carlo Simulations

Response Surface Methods

Classical Optimization Theory

Unconstrained Optimization

Constrained Optimization

MODELING & SIMULATION

EVALUATION OF DESIGN

BEST SOLUTION


Probability & Statistics

Pre-requisites & Books

Discrete-Event Simulation (A first course)by S. Park & L. Leemis

Statistical Quality Controlby Douglas C. Montgomery

Simulation Modeling & Analysisby Averill M. Law

Linear Algebra & Calculus

Programming & MATLAB

Evaluation


Quizzes (06) 10-15%

Assignments (03) 05-10%

OHT’s (02) 30-40%

End Term 40-50%

3-0 Course (~ 45 Lec)

>75%

ATTENDANCE

MARKS DISTRIBUTION

Simulation has emerged as the

THIRD METHODOLOGY

of exploring the truth It would complement the theory and experimental

methodology

Simulation will never replace them!!

M & S?



Ways to Study?


System

Experiment with Actual System

Experiment with Model of the System

SimulationAnalytical Solution

Mathematical Model

Physical Model

Models Types


System model

Deterministic Stochastic

StaticDynamic Static Dynamic

ContinuousDiscrete Continuous Discrete

Monte Carlosimulation

Discrete-eventsimulation


ContinuoussimulationContinuoussimulation



ContinuoussimulationContinuoussimulation

Linear and Nonlinear

Models Types


Stochastic

• Model that contains random (probabilistic) elements,

• Examples

Inter-arrival time or service time of customers at a restaurant or store

Amount of time required to service a customer

• Output is a random quantity (multiple runs required analyze output)

Deterministic

• Model containing no random elements

• Examples

Simulation of a digital circuit

Simulation of a chemical reaction

• Output is deterministic for a given set of inputs

Models Types


Static

• Model where time is not a significant variable

• Examples

Determine the probability of a winning solitaire hand

• Static + stochastic = Monte Carlo simulation

Statistical sampling to develop approximate solutions to numerical problems

Dynamic

• Model focusing on the evolution of the system under investigation over time

Typically represented by differential equations.

Models Types


Discrete

• State of the system is viewed as changing at discrete points

in time

• An event is associated with each state transition

Events contain time stamp

Continuous

• State of the system is viewed as changing continuously

across time

Velocity of fluid in pipe flows

Temperatures and stresses in a solid


Define goals, objectives of study

Develop conceptual model

Develop specification of model

Develop computational model

Verify model

Validate model

Fundamentally an iterative process

Model Development Cycle


• What does you (or the customer) hope to accomplish with the model

Predict the weather

Train personnel to develop certain skills (e.g., driving)

Optimize a manufacturing process or develop the most cost effective means to reduce traffic congestion in some part of a city

• Often requires developing a business case to justify the cost

— Improved efficiency will save the company $$$

Example: electronics

• Objectives may not be known when you start the project!

— One often learns things along the way

Objective & Goals


• An abstract (i.e., not directly executable) representation of the

system

• What are state variables?

• How are they interrelated?

• Which variables should be included in model?

• What can be left out?

• Level of detail

• Appropriate choice depends on the purpose of the model

Conceptual Model


• A more detailed specification of the model including more

specifics

• Collect data to populate model

— Traffic example: Road geometry, signal timing, expected traffic demand,

driver behavior

— Empirical data or probability distributions often used

• Development of algorithms necessary to simulate the system

— Example: Path planning for vehicles

Specification Model


Computational Model

• Executable simulation model

• Software approach

— General purpose programming language

— Special purpose simulation language

— Simulation package

— Approach often depends on need for customization and economics

Where do you make your money?

Defense vs. commercial industry

• Other (non-functional) requirements

— Performance

— Interoperability with other models/tools/data

Verification


• Did I build the computational model right?

• Does the computational model match the specification model?

• Largely a software engineering activity (debugging)

• Not to be confused with correctness (see model validation)!

Validation


• Did I build the right model?

• Does the computational model match the actual (or envisioned)

system?

• Typically, compare against

― Measurements of actual system

― An analytic (mathematical) model of the system

― Another simulation model

• By necessity, always an incomplete activity!

— Often can only validate portions of the model

— If you can validate the simulation with 100% certainty, why build the

simulation?


Knowledge of the system under investigation (Domain Expert)

System analyst skills (model mathematical formulation)

Model building skills (model programming)

Data collection skills

Statistical skills (input data representation)

More statistical skills (output data analysis)

Even more statistical skills (Design of Experiments/ANOVA/Optimization)

Management skills (to get everyone pulling in the same directions)

M & S Team Skills

Summary


• Modeling and simulation is an important, widely used technique with

a wide range of applications

― Computation power increases (Moore’s law) have made it more universal

― In some cases, it has become essential (e.g., to be economically competitive)

― Rich variety of types of models, applications, uses

• As easy (actually, easier!) to get wrong or misleading answers as it is to

get useful results

• Appropriate methodologies required to protect against major mistakes

Documents

Modeling, Simulation and Optimization