Optimization in Engineering Design Georgia Institute of Technology Systems Realization Laboratory 1 Modeling in Optimization

Optimization in Engineering Design

Georgia Institute of TechnologySystems Realization Laboratory

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Modeling in OptimizationModeling in Optimization



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ModelsModels

Questions:

What are “models”?

What is “modeling”?

What is a “good” model?

Questions:

What are “models”?

What is “modeling”?

What is a “good” model?

A model is a necessary ingredient to optimization.A model is a necessary ingredient to optimization.



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Models in ORModels in OR

“The essence of OR lies in the construction and use of models.”

A model is a simplified representation of something real.

There are different types of models.



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EcoSystem Landscape ModelsEcoSystem Landscape Models

Surface Water Height Difference (m) Between Release and Baseline due to Textile Mill in Location 2

Hydrology

Nutrients

DOM

Process Model Unit Model Spatial Landscape Model

Suppose we placed Interface’s factory in this ecosystem. What would happen?



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Facility “Eco-Dash”Facility “Eco-Dash”

ProductionData

User-Configurable Dashboard

AccountingData

Cost Data

PhysicalData

Every shift Every month As info changes As requested

ABC+M&EData

Engineers'Data

PlantLevel

DataLevel

DisplayLevel

Every day

M E $

Total

Per Yd2

M

T

Every second

Report

EstimationsCalculations

Cost SheetsGeneralLedger

Amount/Style

Produced

A

GF

EDCB

H

SensorsCollectingActivity Data

Daily DriverUpdate

Note: F & GReside in aSingle Database

Dashboard Modules

SplashScreen

Sensor ABCEM

H



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Paint Line ModelPaint Line Model

Purge VOC emissions by recovery % and batch size

5.06

3.80

3.04

2.532.17

1.901.69

3.04

2.28

1.821.52

1.301.14 1.011.01

0.76 0.61 0.51 0.43 0.38 0.340.00

1.00

2.00

3.00

4.00

5.00

6.00

0 1 2 3 4 5

Average Car Batch Size

To

tal

VO

C e

mis

sio

ns

(to

ns)

50% recovery

70% recovery

90% recovery

Paint Line Simulation Screenshots

ABCEM



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Gear ManufacturingGear Manufacturing

Dry Hob

Heat Treat

Teeth Grind

Final Wash

Pre-HT Wash

Dry Hob

Teeth Grind

Teeth Grind

Gear Blanks

Finished GearChamfer

ChamferDry Hob

Gear Blanks

Face Grind

Bore Hone

Teeth Grind

Pre-Grind Wash

RollFace Grind

Finished GearFinal

WashHeat Treat

Bore Hone

BurnishPre-HT Wash

Dry Hob

Dry Hob

Dry Hob

Gear Blanks

Gear Blanks

Predictive Model

Inventory(1)

Conversion(2)

Types and Quantity

Potential Process

Machine Database

Intermediate Outputs

Part DesignEnvironmental InventoryEnvironmental ImpactsFinancial Costs

Facility Parameters

Front End Back End

Cost Database

Eco-Indicators Database

Hard FinishGreen FinishunitsEnvironmental SPS 313.140 146.789 mpt / partFinancial Cost 2.083 0.919 $ / partWater Use 3.940 3.138 gal / partLandfill Waste 0.000 0.000 lb / partRecyclable Material 0.287 0.284 lb / partSpecial Waste 0.401 0.000 lb / partEnergy 10.091 4.850 kWh / partCO2 13.482 6.480 lb / part

Mai

nIn

vent

ory



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Gears are part of this…Gears are part of this…

How do you “model” this?



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Paper versus Plastic: B2B PackagingPaper versus Plastic: B2B Packaging

. Longbeach, CA

Detroit, MI .

From Shanghai, China

Transmission Part (aluminum)

New Packaging (plastic)

Regrind

Reprocessing into splash shields (parts)

Conventional Packaging (cardboard)

Modeling Interface Economic & Environmental Analysis Report

Data Library Total Cost Analysis

Life Cycle Analysis

Packaging Configuration

Part Configuration

Logistics Processes

Energy Consumption Analysis

MS Excel based decision support model



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Rethinking Sourcing Options

Rethinking Sourcing Options

• Packaging work led to rethinking of where to source from

• Environmental Sourcing Tool helps assessing emissions from

– Production in different localities with different electrical generation emissions.

» E.g., hydro vs coal

– Transport modes and distances

1) Enter Energy/Part

2) Select Region (or US)

3) Select Country (or US State) 1

4) Total CO2 Emissions/Part

Country (state) CO2 Coefficient

1) Enter Transporation Data

Enter Weight per Conveyance

Enter Pieces per Conveyance

Enter Pieces per Unit Load

Enter Tare Weight per Unit Load

2) Select Transportation Modes (deselect for unused modes)TRUE

FALSE

FALSE3) Enter Total Mileage for Each Mode (miles)

By Truck 00

4) Inbound Trip Shipping Energy/partOutbound Trip Shipping Energy/partTotal Shipping Energy/part

5) Total CO2 Emissions/Part

Total Energy/part

Total CO2/part

Manufacturing 4,130.06 79

Transportation 309.39 15.35

Rank Source Country (or US State) Tot. Energy Tot. CO2 CO2 Coeff.

Saved CasesTo delete a case, select the entire row, right click, and select 'Delete'

MJ/part

(scroll up)

g/part

g/MJ

lbs

parts

parts

lbs

g/part

MJ/part

FEST

94.35

4439.45

15.35

24

1248

25409

25323453

79

4,130.06

52.28

158

Ford Environmental Sourcing Tool

Manufacturing Module

Transportation Module

150

3.6011.74

309.39

Case Results

MJ/part

MJ/part

MJ/part

g/part

North America

Canada

Truck

Train

Ship

CO2 Emmissions by Activity

(g of CO2/part)

0.001,000.002,000.003,000.004,000.005,000.00

Manufacturing Transportation

Energy Usage by Activity (MJ/part)

020406080

100

Manufacturing Transportation



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Decision SupportDecision Support

Analysis & Decision Support Models &Tools

Component

Material

Urban Region

Ecosystem

Product

Industry

Material Flows

Recycling

Land FillingPhysical Systems

Remanufacturing

A Goal: Integration of data, models, knowledge & learning to support high impact decision-making



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“The” Modeling Process (in OR)“The” Modeling Process (in OR)

Real system Model

Real conclusions Model conclusions

Formulation

Deduction

Interpretation



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FormulationFormulation

Formulation:

• Often considered to be an art.

• Typical questions to answer in formulating a model:

What aspects of the real system should be included, which can be ignored?

What assumptions can and should be made?



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DeductionDeduction

Deduction:

• Involves techniques that depend on the nature of the model.

• It may involve solving equations, running a computer program, expressing a sequence of logical statements – whatever it takes to solve the problem of interest relative to the model.

• It should not be subject to differences of opinion, provided that the assumptions are clearly stated and identified.



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InterpretationInterpretation

Interpretation:

• Again involves a large amount of human judgment.

• The model conclusions must be translated to the real world conclusions, in full cognizance of possible discrepancies between the model and its real-world referent.

Remember:

Ties between model and system are often only at best ties of plausible association,

SO BE CAREFUL WITH THE CONCLUSIONS!!!!

Remember:

Ties between model and system are often only at best ties of plausible association,

SO BE CAREFUL WITH THE CONCLUSIONS!!!!



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Validation – An IntroductionValidation – An Introduction

• The process of acquiring the conviction that a model actually works is commonly called validation.

• When people are persuaded or convinced that a model is useful in some basic context, they will speak of it as a valid model.

• However, the validity is often restricted to a certain context.

• Hence, it is vital to know the limitations of the model.

• Some people may never accept a model.

Validation is a considerably weaker term than "proof"Validation is a considerably weaker term than "proof"



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The Scientific Method (in natural science)The Scientific Method (in natural science)

“Real” system Hypothesis

“Real” conclusions Theory

Inductive generalization

Verification

Application

Testing and revision

Models are invented – Theories are discoveredModels are invented – Theories are discoveredModels are invented – Theories are discoveredModels are invented – Theories are discovered



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How about design?How about design?

What is the difference between designing, modeling, and OR?



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Difference between OR and designingDifference between OR and designing

Model

Model conclusions

Formulation

Deduction

Interpretation

Real system

Real conclusions

build

and test

Change the system's design



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Modeling and DesigningModeling and Designing

• Designing is very open-ended

• This openness is very unique

• Openness is troublesome, but a fact of life.

• Designing is very open-ended

• This openness is very unique

• Openness is troublesome, but a fact of life.

Ask yourself,

how would you model the process of configuring a general how would you model the process of configuring a general arrangement of parts, and solve it as a mathematical arrangement of parts, and solve it as a mathematical optimization problem?optimization problem?

• You have to model and deal with geometrical forms, type of motions, force transmissions, etc.

• Combining all these issues in a single model is almost impossible

Ask yourself,

how would you model the process of configuring a general how would you model the process of configuring a general arrangement of parts, and solve it as a mathematical arrangement of parts, and solve it as a mathematical optimization problem?optimization problem?

• You have to model and deal with geometrical forms, type of motions, force transmissions, etc.

• Combining all these issues in a single model is almost impossible



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Types of DesignTypes of Design

Three types of design are often considered (e.g., Pahl and Beitz):

• Original Design – an original solution principle is determined for a desired system and used to create the design of a product.

• Adaptive Design – an existing design is adapted to different conditions or tasks; thus, the solution principle remains the same but the product will be sufficiently different so that it can meet the changed tasks that have been specified.

• Variant Design – the size and/or arrangement of parts or subsystems of the chosen system are varied. The desired tasks and solution principle are not changed.

Three types of design are often considered (e.g., Pahl and Beitz):

• Original Design – an original solution principle is determined for a desired system and used to create the design of a product.

• Adaptive Design – an existing design is adapted to different conditions or tasks; thus, the solution principle remains the same but the product will be sufficiently different so that it can meet the changed tasks that have been specified.

• Variant Design – the size and/or arrangement of parts or subsystems of the chosen system are varied. The desired tasks and solution principle are not changed.

Where do you think optimization is most used?Where do you think optimization is most used?Where do you think optimization is most used?Where do you think optimization is most used?



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Modeling and Optimization in Design

Modeling and Optimization in Design

Shape optimization is relatively frequently done.

Configuration optimization is difficult.

Invariably, you have to account for hierarchical interactions.

Questions to be asked when modeling designs:

• Does the problem contain identifiable components?

• How are the components linked?

• Can we identify component variables and system variables?

• Does the system interact with other systems at the same level and/or higher levels?



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Some Basic Principles of ModelingSome Basic Principles of Modeling



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Principles of ModelingPrinciples of Modeling

1. Do not build a complicated model when a simple one will suffice.

This can be contrary to traditional mathematics or when one wants to build a general, strong model. Typically, though, a useful model is a simple model.

2. Beware of molding the problem to fit the technique.

This happens often if somebody is an "expert" in a specific solution technique. However, optimization is just one of many decision support techniques.



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3. The deduction phase of modeling must be conducted rigorously.

If you do this and the conclusions are inconsistent with reality, then the fault lies in the assumptions.

Be extremely careful with computer programs which may contain hidden bugs.



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4. Models should be validated prior to implementation.

Some ways to do this:

• retrospective testing against historical data (especially for forecasting models).

• If the model is supposed to represent a class of things, test it against members of a class which was not used in the modeling (e.g., as in regression analysis).

• systematically vary parameters in the model and real system (if possible) and see whether the changes in behavior match.

• construct artificial tests, e.g., enter extreme values and see what happens (zero is always an interesting number to try).



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5. A model should never be taken too literally.

This sounds obvious, but is often forgotten as the model grows and is supposed to be more “accurate”

6. A models should neither be pressed to do, nor criticized for failing to do, that for which it was never intended.

Always remember and investigate the original context in which a model was made (e.g., a model for predicting the resistance of fishing vessels should not be used for aircraft carriers).



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7. Beware of overselling a model.

It is very tempting to state that your model can solve all problems in the world, but be truthful. Honesty goes a long way and keeps you out of lawsuits.

8. Some of the primary benefits of modeling are associated with the process of developing the model.

The model itself never contains the full knowledge and understanding of the real system that the builder must acquire in order to successfully model it.



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9. A model cannot be better than the information that goes into it.

Garbage In, Garbage Out (GIGO) is very applicable to modeling.

Also, models do not create information, but condense or convert information.

In some cases, instead of exerting one's efforts on model construction, one would be better off just gathering more information about the real system.

Be careful that you don't put in too much information.



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10.Models cannot replace decision makers

One of the most common misconceptions about the purpose of optimization and other OR models is that they are supposed to provide "optimal" solutions, free of human subjectivity and error.

There are so many decisions and assumptions to be made in the modeling, that only in a restricted and tight context we can speak of optimal solutions.

A human decision maker is always necessary, whether you like it or not.

Documents

Optimization in Engineering Design Georgia Institute of Technology Systems Realization Laboratory 1 Modeling in Optimization