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

i

iidFitness 2*

7

0

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 11 0 0 0 1 1 0 0

Parent 2; Fitness = 99Parent 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

DFE

H

C

BA

G

Example 2 (Continued): Traveling Salesperson Problem

DFE

H

C

BA

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 FE

H

CBA

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

12 ))(965.0584.0( cii

ii

ciibc TqTqTT

2)0032.0113.0( i

ciiAc PqnP

i

fiif TqT 122

i

biib TqT 198

i

ciic VqV 5.17

Example 3 (Continued):Fitness Function

• Dp is the desired property value

• Jp is the predicted property value

• p {Tc, Pc, Vc, Tb, Tf }

penaltyJDS pp

p 2)(

Example 3 (Continued): Joback Group Additivity Constants

Tc Pc Vc Tb Tf

-CH3 0.0141 -0.001 65 23.58 -5.10-CH2- 0.0189 0.0000 56 22.88 11.27-CH< 0.0164 0.0020 41 21.74 12.64>C< 0.0067 0.0043 27 18.25 46.43=CH2 0.0113 -0.003 56 18.18 -4.32

... ... ... ... ... ...

Example 3 (Continued): Representation of Solutions

=C

=

-CH

3

-CH

2-

-F

-CH

<

>C

<

=C

H2

=C

H-

=C

<

C

-

C

H

-Cl

-Br

-I

3 1 0 2 1 1 2 2 1 1 0 1 1 1

ClCH3

CH3

CH3

CH2 C C

CH

CH2

C C C

Br

IC

C

CH

Individual

Example 3 (Continued): Sample Results

CH3

F

F

F

F

C CH

Maximum error of 2.36%

was in Tc

F

F

F

F

F

C CH C

Maximum error of 3.65%

was in Tf

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.