A Genetic Algorithm for Designing Materials:

1. A Genetic Algorithm for Designing Materials: Gene A. Tagliarini Edward W. Page M. Rene Surgi

2. The Problem: • Design materials having desirable physical properties • Limit the number of materials assessed in the laboratory

3. Key Technologies: • Group additivity models from computational chemistry • Reid, Prausnitz, Poling • Joback • Genetic algorithms • Holland, Goldberg, DeJong, Davis • Adelsberger

4. 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

5. Sample Applications: • Scheduling • Resource allocation • VLSI module placement • Machine learning • Signal processing filter design • Rocket nozzle design

6. 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

7. Components of a Genetic Algorithm: • A representation for possible solutions • Chromosomes, genes, and population • Fitness function • Operators • “Artificial” selection • Crossover and recombination • Mutation

8. 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

9. 0 1 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 Example 1: Maximizing an Unsigned Binary Value Population

10. 0 1 1 0 0 0 1 1 Individual Example 1 (Continued):A Fitness Function Fitness Measure 99

11. 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 Example 1 (Continued): Measure the Fitness of Each Individual Population Fitness Measure 99 140 169 6

12. 0 1 1 0 0 0 1 1 1 0 0 0 1 1 0 0 Example 1 (Continued): “Artificial” Selection Population Fitness Measure 99 140 • A random process • Favors “fit” individuals • Some individuals may be totally overlooked

13. 0 1 1 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 Example 1 (Continued): Crossover and Recombination Parent 1; Fitness = 140 Parent 2; Fitness = 99 Offspring; Fitness = 163

14. 1 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 Example 1 (Continued): Mutation Fitness = 163 Fitness after mutation = 178

15. B A C D E F G H Example 2: Traveling Salesperson Problem

16. B A C D E F G H Example 2 (Continued): Traveling Salesperson Problem

17. A C B H C B F F H A G G D E D E D G C D A H E H G E B C F F A B H G Example 2 (Continued): Traveling Salesperson Problem Population A B C E D F

18. A A B B C C F F G H G D E H E D G D A H E C F B Example 2 (Continued): Order Sensitive Crossover #1 Parent 1 Parent 2 Offspring

19. A A G B C B C B B D D F E H E G A A H E E D F D C C B E H H C B C F F D H E H A G G F D F A G G Example 2 (Continued): Order Sensitive Crossover #2 Parent 1 Parent 2

20. A A C B B B C A A F H F E H E G C G H E E D D D G G C D D D C A A F F H H E E C G G F H F B B B Example 2 (Continued): Order Sensitive Crossover #2 Parent 1 Parent 2

21. 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

22. Example 3 (Continued): Property Parameters

23. Example 3 (Continued):Fitness Function • Dp is the desired property value • Jp is the predicted property value • p  {Tc, Pc, Vc, Tb, Tf }

24. Example 3 (Continued): Joback Group Additivity Constants

25. 3 1 0 2 1 1 2 2 1 1 0 1 1 1 C C Example 3 (Continued): Representation of Solutions -CH3 -CH2- -CH< >C< =CH2 =CH- =C< C- -F -Cl -Br -I =C= CH Individual Cl Br CH3 CH3 CH2 C C C I CH3 C CH C CH2 CH

26. F F F C CH C F F Example 3 (Continued): Sample Results F F CH3 C CH F F Maximum error of 2.36% was in Tc Maximum error of 3.65% was in Tf

27. 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

28. 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.