A Genetic Algorithm for Designing Materials:

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23 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

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A Genetic Algorithm for
Designing Materials:

Gene A. Tagliarini

Edward W. Page

M. Rene Surgi

The Problem:


Design materials
having desirable
physical properties


Limit the number of
materials assessed in
the laboratory

Key Technologies:


Group additivity models from
computational chemistry


Reid, Prausnitz, Poling


Joback


Genetic algorithms


Holland, Goldberg, DeJong, Davis


Adelsberger

What is a Genetic Algorithm?


A genetic algorithm is
a search method that
functions analogously
to an evolutionary
process in a biological
system.


They are often used to
find solutions to
optimization problems

Sample Applications:


Scheduling


Resource allocation


VLSI module placement


Machine learning


Signal processing filter design


Rocket nozzle design

Advantages of Genetic
Algorithms


Do not require strong mathematical
properties of the objective function


Solutions
--
of varying quality
--
are always
available


Independent operations are amenable to
parallel implementation


Uncomplicated and therefore, robust

Components of a Genetic
Algorithm:


A representation for possible solutions


Chromosomes, genes, and population


Fitness function


Operators


“Artificial” selection


Crossover and recombination


Mutation

Genetic Algorithm Pseudo
-
code:


Randomly create a population of solutions


Until a satisfactory solution emerges or the
“end of time”


Using the fitness measures, select (two) parents


Generate offspring


Mutate


Update the population


Example 1: Maximizing an
Unsigned Binary Value

0

1

1

0

0

0

1

1

1

0

0

0

1

1

0

0

1

0

1

0

1

0

0

1

0

0

0

0

0

1

1

0

Population

Example 1 (Continued):

A Fitness Function

Fitness Measure

99

0

1

1

0

0

0

1

1

Individual

Example 1 (Continued): Measure
the Fitness of Each Individual

0

1

1

0

0

0

1

1

1

0

0

0

1

1

0

0

1

0

1

0

1

0

0

1

0

0

0

0

0

1

1

0

Population

Fitness Measure

99

140

169

6

Example 1 (Continued):
“Artificial” Selection

0

1

1

0

0

0

1

1

1

0

0

0

1

1

0

0

Population

Fitness Measure

99

140



A random process



Favors “fit” individuals



Some individuals may be totally overlooked

Example 1 (Continued):
Crossover and Recombination

0

1

1

0

0

0

1

1

1

0

0

0

1

1

0

0

Parent 2; Fitness = 99

Parent 1; Fitness = 140

1

0

1

0

0

0

1

1

Offspring; Fitness = 163

Example 1 (Continued):
Mutation

1

0

1

0

0

0

1

1

Fitness = 163

1

0

1

1

0

0

1

0

Fitness after mutation = 178

Example 2: Traveling
Salesperson Problem

D

F

E

H

C

B

A

G

Example 2 (Continued):
Traveling Salesperson Problem

D

F

E

H

C

B

A

G

Example 2 (Continued):
Traveling Salesperson Problem

A

B

C

F

H

G

E

D

G

D

A

H

E

C

F

B

C

H

B

F

A

G

D

E

D

C

H

E

G

B

F

A

Population

D

F

E

H

C

B

A

G

Example 2 (Continued): Order
Sensitive Crossover #1

A

B

C

F

H

G

E

D

G

D

A

H

E

C

F

B

Parent 1

Parent 2

A

B

C

F

G

D

H

E

Offspring

Example 2 (Continued): Order
Sensitive Crossover #2

A

B

C

F

H

G

E

D

C

H

B

D

E

A

F

G

Parent 1

Parent 2

A

B

B

D

E

A

E

D

C

H

C

F

H

G

F

G

G

C

B

D

E

A

H

F

B

E

C

F

H

G

D

A

Example 2 (Continued): Order
Sensitive Crossover #2

A

B

C

F

H

G

E

D

G

D

A

H

E

C

F

B

Parent 1

Parent 2

A

B

A

H

E

C

E

D

G

D

C

F

H

G

F

B

C

B

A

F

E

G

H

D

C

D

A

F

E

G

H

B

Example 3: Designing Materials


Individual chemicals
and chemical
fragments contribute
to the properties of a
molecule


Propose fragments
likely to produce
molecules having
desirable properties

Example 3 (Continued):
Property Parameters

Example 3 (Continued):

Fitness Function



D
p

is the desired property value



J
p

is the predicted property value



p


{T
c
, P
c
, V
c
, T
b
, T
f
}

Example 3 (Continued): Joback
Group Additivity Constants

Example 3 (Continued):
Representation of Solutions

=C=

-
CH
3

-
CH
2
-

-
F

-
CH<

>C<

=CH
2

=CH
-

=C<


C
-


CH

-
Cl

-
Br

-
I

3

1

0

2

1

1

2

2

1

1

0

1

1

1

Cl

CH
3

CH
3

CH
3

CH
2

C

C

CH

CH
2

C

C

C

Br

I

C

C

CH

Individual

Example 3 (Continued): Sample
Results

CH
3

F

F

F

F

C

CH

Maximum error of 2.36%

was in T
c

F

F

F

F

F

C

CH

C

Maximum error of 3.65%

was in T
f

Conclusions


Genetic algorithms provide a robust tool for
finding solutions to search and optimization
problems.


Genetic algorithms can be used to propose
materials with specific properties.


The quality of the underlying model
strongly influences the outcome of genetic
algorithm searches

Related and Ongoing Work


Resource allocations in the weapon
-
to
-
target assignment problem


Design wavelets and “super
-
wavelets” to
highlight salient signatory features in sonar
signals as well as SAR and thermal
imagery.