Antnio GasparCunha - - PDF document

• Dept. Polymer Engineering

University of Minho

• António GasparCunha
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• Dept. Polymer Engineering

University of Minho

PORTUGAL

• Dept. Polymer Engineering

University of Minho

Schools

• School of Engineering (EENG)
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School of Engineering #$$ #% # # #! # Department of Polymer Engineering (DEP) # ! #"&"

UNIVERSITY OF MINHO

• Dept. Polymer Engineering

University of Minho

Engineering ' ($)* +#* $,$-$ ' ' $$ ' #"!" ' "& "! "".//" ' "! "/ ' "!,% *" '

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' Institute for Polymers and Composites (IPC) ' #! "!!"

RESEARCH CENTERS

Associate Labs ' $$ * $!$ ' I3N Institute of Nanostructures, Nanomodelling and Nanofabrication

• Dept. Polymer Engineering

University of Minho

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1st Cycle and Integrated Master Courses (15 000 Students)

TEACHING

• Dept. Polymer Engineering

University of Minho

GUIMARÃES

HISTORIC CITY CENTRE – Intramural Area (Classified UNESCO World Heritage Site)

• Dept. Polymer Engineering

University of Minho

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• Dept. Polymer Engineering

University of Minho

CONTENTS

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• Dept. Polymer Engineering

University of Minho

CONTENTS

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• Dept. Polymer Engineering

University of Minho

CONTENTS

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• Dept. Polymer Engineering

University of Minho

CONTENTS

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• Dept. Polymer Engineering

University of Minho

CONTENTS

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• Dept. Polymer Engineering

University of Minho

PEOPLE

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• Dept. Polymer Engineering

University of Minho

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António GasparCunha

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• Dept. Polymer Engineering

University of Minho

OUTLINE

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• Dept. Polymer Engineering

University of Minho

BIBLIOGRAPHY

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• Dept. Polymer Engineering

University of Minho

MOTIVATION

Sophisticated mathematical models are able to describe adequately a specific process

Governing equations Numerical methods Boundary conditions Heat transfer and flow behaviour Other models System geometry Material properties Operating conditions PROCESS PERFORMANCE

• Dept. Polymer Engineering

University of Minho

How are these tools can be used to: Set the operating conditions? Design the machine? ETC8

MOTIVATION

• Dept. Polymer Engineering

University of Minho

Approaches to optimize the processes (e.g., set the operating conditions, design machines, etc0): ' Use empirical knowledge; ' Use computational tools on a trial and error basis; ' Solve the inverse problem; ' Perform a partial process optimization; ' Develop a global optimization procedure.

MOTIVATION

• Dept. Polymer Engineering

University of Minho

Use computational tools on a trial and error basis

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• MOTIVATION

• Dept. Polymer Engineering

University of Minho

Use computational tools on a trial and error basis

A good performance may be distinct from the best performance

MOTIVATION

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• Dept. Polymer Engineering

University of Minho

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Direct problem: D !

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Inverse problem:

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Solve the inverse problem MOTIVATION

• Dept. Polymer Engineering

University of Minho

Perform a partial process optimization

• 1. Optimizing for output

' Melt conveying ' Melting (helix angle, number of flights, flight clearance, compression ratio) ' Solids conveying (channel depth, helix angle, number of flights, flight

clearance)

• 2. Optimizing for power consumption

(helix angle, flight clearance, flight width) EXAMPLE: Optimizing for output (Melt conveying)

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π       + +       + =

• π

θ

• C. Rauwendaal, Polymer Extrusion, Hanser (2001)

MOTIVATION

• Dept. Polymer Engineering

University of Minho

$ Objective Function Modelling Package

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• USER INTERFACE

Optimization Algorithm

RESULTS

Develop a global optimization procedure MOTIVATION

• Dept. Polymer Engineering

University of Minho

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1

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• In most optimization algorithms:

' The search is local ' If one local peak is found the search stops

Develop a global optimization procedure MOTIVATION

• Dept. Polymer Engineering

University of Minho

91E:

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MOTIVATION

• Dept. Polymer Engineering

University of Minho

91E:

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MOTIVATION

• Dept. Polymer Engineering

University of Minho

91E:

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MOTIVATION

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• Dept. Polymer Engineering

University of Minho

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MOTIVATION

• Dept. Polymer Engineering

University of Minho

RANDOM SEARCH ' " L #! selecting randomly # # % @ ' " L 1 one point each time, #% #! %% #@ ' Search is very slow L ! %- #-@ MOTIVATION

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• Dept. Polymer Engineering

University of Minho

GRADIENT METHODS These methods use information about the objective function gradient in

• rder

to establish the search direction.

y = f(x1,x2) starting point P(x1(0),x2(0))

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• MOTIVATION
• Dept. Polymer Engineering

University of Minho

SIMULATED ANNEALING

' 1 # way liquids freeze or metals recrystallize #@ ' 8 ! # ! , ! ! ##&! thermodynamic equilibrium@ ' " ! - progressively ordered ## 7 @ ' $! !, #7 one point randomly selected # 1 %@ ' " % - # improvement is obtained # #--! ## @

MOTIVATION

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• Dept. Polymer Engineering

University of Minho

ARTIFICIAL NEURAL NETWORKS

' * 1 ! input !

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layersM '

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P1 P2 Pi C1 ... C2 Cj ... Input Layer Output Layer Hidden Layer

' # -! ! # &- #- approximating an arbitrary complex functionM ' " builds a map - # #% #M

MOTIVATION

• Dept. Polymer Engineering

University of Minho

EXPERT SYSTEMS

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MOTIVATION

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• Dept. Polymer Engineering

University of Minho

SENSITIVITY ANALYSIS

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MOTIVATION

• Dept. Polymer Engineering

University of Minho

STATISTICAL METHODS

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MOTIVATION

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• Dept. Polymer Engineering

University of Minho

ANT COLONY OPTIMIZATION

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MOTIVATION

• Dept. Polymer Engineering

University of Minho

ANT COLONY OPTIMIZATION

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MOTIVATION

• Dept. Polymer Engineering

University of Minho Objective Function Parameter 2 Parameter 1 OPTIMUM Objective Function Parameter 2 Parameter 1 OPTIMUM Objective Function Parameter 2 Parameter 1 OPTIMUM

Initial Population 2nd Generation ithGeneration nth Generation

Objective Function Parameter 2 Parameter 1

OPTIMUM

' Search uses a population

• f points

' Able to distinguish between local and absolute maxima ' Do not require derivatives nor other knowledge on the process (BLACK BOX) ' Require significant computation resources

MOTIVATION EVOLUTIONARY ALGORITHMS

• Dept. Polymer Engineering

University of Minho

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f is the objective function of the n parameters xi, gj are the J (J≥ ≥ ≥ ≥0) inequality constraints, and k are the K (K≥ ≥ ≥ ≥0) equality constraints.

MOTIVATION

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• Dept. Polymer Engineering

University of Minho

Computational Intelligence MOTIVATION

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• Dept. Polymer Engineering

University of Minho

• Robust Search Methods

MOTIVATION

• Dept. Polymer Engineering

University of Minho

EVOLUTIONARY THEORY ' encodes the information % M ' identical % #M ' Small changes % ; *0 &#; , , @ @@@

Genes and DNA

• Dept. Polymer Engineering

University of Minho

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Genes and DNA

EVOLUTIONARY THEORY

• Dept. Polymer Engineering

University of Minho

' " 7 chromosomesM ' /( # , physical attributes %;

Human Reproduction

EVOLUTIONARY THEORY

• Dept. Polymer Engineering

University of Minho

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Reproductive Cells

EVOLUTIONARY THEORY

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University of Minho

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Crossover Before After

EVOLUTIONARY THEORY

• Dept. Polymer Engineering

University of Minho

Fertilization

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EVOLUTIONARY THEORY

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• Dept. Polymer Engineering

University of Minho

' # ! ! # mutation M ' " , #O, not inherited ! #M ' " #--! very lowM ' " #- %@

Mutation

EVOLUTIONARY THEORY

• Dept. Polymer Engineering

University of Minho

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Evolutionary Theory

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EVOLUTIONARY THEORY

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• Dept. Polymer Engineering

University of Minho

The evolutionary theory allows to explain that this slow change of genetic material through reproduction and mutation (and possibly crossover) enabled the possibility

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generating all species

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plants and animals EVOLUTIONARY THEORY

Evolutionary Theory

• Dept. Polymer Engineering

University of Minho

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Evolutionary Algorithms

EVOLUTIONARY ALGORITHMS

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• Dept. Polymer Engineering

University of Minho

Evolutionary Computation – THE METAPHOR

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• EVOLUTIONARY ALGORITHMS
• Dept. Polymer Engineering

University of Minho

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Evolutionary Equation

EC = GA + ES + EP + GP

Evolutionary Computing Genetic Algorithms Evolution Strategies Evolutionary Programming Genetic Programming ,59KD +-,59K( 0,3, 8,59AA E7,599/

EVOLUTIONARY ALGORITHMS

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• Dept. Polymer Engineering

University of Minho

The Computational Cycle

Random initialization (or semi random) of the population of candidate solutions (Generation 0) Evaluation of the performance of population individuals Generation of a new population from members with more performance through genetic

• perations (recombination and

mutation) Evolutionary computation is an iterative technique, i.e., successively new populations are generated until a good solution is found

EVOLUTIONARY ALGORITHMS

• Dept. Polymer Engineering

University of Minho

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EVOLUTIONARY ALGORITHMS

The Evolutionary Cycle

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• Dept. Polymer Engineering

University of Minho

SCHEMA THEOREM

Schema Theorem: John Holland

Objective Q #% % #@ ## #- 1 7 -! ##7 -! -@ " #% &# %%, ! # @ ; ' $! #-M ' 0& %, M ' 0 # M ' %M ' @

• Dept. Polymer Engineering

University of Minho

Definition 1 Q ,*;

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#*@ )#-)B 2 #-,2R)!- !%@ @@-!#-)∈ SI,5,2T2∈ SI,5T SCHEMA THEOREM

• Dept. Polymer Engineering

University of Minho

Example 0 -! % L SI 5 5 5 I I IT, ! % , ? U2 5 5 2 I 2 2V " ? UI 5 2 5 2V , I 5 I 5 I I 5 I 5 5 I 5 5 5 I I 5 5 5 5 SCHEMA THEOREM

• Dept. Polymer Engineering

University of Minho

Definition 2 Q 3, *; , @, - R2) *@ Example, 2 2 2 I 2 2 2 ? 5 Definition 3 Q , δ*; , δ*, - R2) @ Example, δ2 2 2 I 2 2 2 ? C Q C ? I SCHEMA THEOREM

• Dept. Polymer Engineering

University of Minho

" #% # %

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Schemata theory

• (H) Scheme order (number of fixed positions):
• (1*01*) = 3 and o(*1**0) = 2

δ δ δ δ(H) Scheme length (distance between the first and the last fixed positions) δ δ δ δ(1*01*) = 3 and δ δ δ δ(*1**0) = 3

DEFINITIONS:

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#

chromossomes

SCHEMA THEOREM

• Dept. Polymer Engineering

University of Minho

" &# - # *, & >5, % -!;

( ) ( ) ( ) ( ) ( )

     − − − ≥ +

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+ *,>5*,-#>5M + *%-F%% #-!*M * %-F%##M * $ #--%#%!@

• Schemata theory

SCHEMA THEOREM

• Dept. Polymer Engineering

University of Minho

APLICATION EXAMPLE EXAMPLE OF APPLICATION: To minimize the cost of material used to manufacture a can

• Dept. Polymer Engineering

University of Minho

APLICATION EXAMPLE To minimize the cost of material used to manufacture a can

• Caracteristic dimensions:

h heigth d diameter

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= ≤ ≤ ≤ ≤ ≤ ≤ ≤ ≤ ≥ ≡         + = π π π

Problem Formulation:

c is the cost of can material per squared cm

• Dept. Polymer Engineering

University of Minho

Chromosome Representation

!-* #

CHROMOSOME GENE

5II-## APLICATION EXAMPLE

1 1 1 1

• Dept. Polymer Engineering

University of Minho

Solution Representation

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Example – binary codification:

* d [5.0, 15.0] with a single decimal place (c) * length: l = 15 5 = 10 * number of intervals (NI) = l * 10^c = 10 * 10^1 = 100 * number of bits (nb): [8] 2^6 = 64 < 100 < 2^7 = 128 * 5.0 is represented by (00 000 000) * 15.0 is represented by (11 111 111) * using a direct binary representation 8.0 (80) is (01 010 000) * while using the present representation (01 010 000) is 8.1

=+W6 APLICATION EXAMPLE

• Dept. Polymer Engineering

University of Minho

Conversion of binary string from base 2 to base 10

∑

− =

= ′

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• K

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− + =

• &
• Example:

* d [5.0, 15.0] * l = 10 * NI = 100 * nb = 8 * x´ = (01 100 001) = 97 * x = 8.803922

APLICATION EXAMPLE

• &O

& I I I I I I I I I D@II I I I I I I I 5 5 D@IC I I I I I I 5 I / D@I: I I I I I I I 5 ( D@5/ 5 5 5 5 5 5 I I /D/ 5C@:: 5 5 5 5 5 5 5 I /DC 5C@9A 5 5 5 5 5 5 5 5 /DD 5D@II

• Dept. Polymer Engineering

University of Minho

APLICATION EXAMPLE Decimal Binary Gray Code

I III III 5 II5 II5 / I5I I55 ( I55 I5I C 5II 55I D 5I5 555 A 55I 5I5 K 555 5II Gray codes have the property that adjacent integers only differ in one bit position.

GRAY CODE

7

• Dept. Polymer Engineering

University of Minho

Chromosome Fitness Evaluation

' %# #!-!.@ ' % # @

APLICATION EXAMPLE

• Dept. Polymer Engineering

University of Minho

Calculation of objective function

( )

• $

7

• I

C I

• C

I

• E
• =

        + = π π

• Initialization of the population (randomly)
• RANDOM NUMBER GENERATION ALGORITHMS

APLICATION EXAMPLE

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• Dept. Polymer Engineering

University of Minho

Choosing Parents to Reproduce

' "#; Q ! ##@ Q 8% #@

APLICATION EXAMPLE

• Dept. Polymer Engineering

University of Minho

Recombination operator (selection of solutions for reproduction)

• Mating pool

APLICATION EXAMPLE

B

• Dept. Polymer Engineering

University of Minho

Producing a child by Recombination

' + ; I I 5 I 5 I 5 5 5 I 5 5 I I 5 5 I 5 I 5 I 5 5 5

• 3#

APLICATION EXAMPLE

• Dept. Polymer Engineering

University of Minho

Mutation

I 5 I 5 I 5 5 5 I 5 I I I 5 5 5 ' 3!## ,&#;5.

• APLICATION EXAMPLE

C

• Dept. Polymer Engineering

University of Minho

Replacement

' "

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L, !,

• #
• &
• ;

Q + ##@ Q @

APLICATION EXAMPLE

• Dept. Polymer Engineering

University of Minho

APLICATION EXAMPLE

)!

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<&# ' 6 )&! The evolution cycle

*

• Dept. Polymer Engineering

University of Minho

New Population

• Fitness average of initial population = 32.4

Fitness average of new population = 28.0

APLICATION EXAMPLE

• Dept. Polymer Engineering

University of Minho

CONCLUSIONS

The Evolution Mechanism

' %!#; Q Q - ' "%!-!# #@

• Dept. Polymer Engineering

University of Minho

Real World EC

Tends to include: ' #& # # ' B

• #-

# 1

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CONCLUSIONS

• Dept. Polymer Engineering

University of Minho

Advantages

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CONCLUSIONS

• Dept. Polymer Engineering

University of Minho

Disadvantages

' #- # ' 81- ' !&%# ' 3#!&#%,! #7#-

CONCLUSIONS