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. Example 1: Maximizing an Unsigned Binary Value 01100011100011001010100100000110 Population

10. Example 1 (Continued): A Fitness Function Fitness Measure 99 01100011 Individual

11. Example 1 (Continued): Measure the Fitness of Each Individual 01100011100011001010100100000110 PopulationFitness Measure 99 140 169 6

12. Example 1 (Continued): “Artificial” Selection 0110001110001100 PopulationFitness Measure 99 140 A random process Favors “fit” individuals Some individuals may be totally overlooked

13. Example 1 (Continued): Crossover and Recombination 0110001110001100 Parent 2; Fitness = 99Parent 1; Fitness = 140 10100011 Offspring; Fitness = 163

14. Example 1 (Continued): Mutation 10100011 Fitness = 163 10110010 Fitness after mutation = 178

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

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

17. ABCFHGEDGDAHECFBCHBFAGDEDCHEGBFA Population D F E H C B A G

18. Example 2 (Continued): Order Sensitive Crossover #1 ABCFHGEDGDAHECFB Parent 1Parent 2 ABCFGDHE Offspring

19. Example 2 (Continued): Order Sensitive Crossover #2 ABCFHGEDCHBDEAFG Parent 1Parent 2 ABBDEAEDCHCFHGFGGCBDEAHFBECFHGDA

20. Example 2 (Continued): Order Sensitive Crossover #2 ABCFHGEDGDAHECFB Parent 1Parent 2 ABAHECEDGDCFHGFBCBAFEGHDCDAFEGHB

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 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 }

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

25. Example 3 (Continued): Representation of Solutions =C= -CH 3 -CH 2 --F-CH<>C<=CH 2 =CH-=C<  C-  CH -Cl-Br-I 31021122110111 Cl CH 3 CH 2 CC CH CH 2 C CC Br IC C CH Individual

26. Example 3 (Continued): Sample Results CH 3 F F F F CCH Maximum error of 2.36% was in T c F F F F F CCHC Maximum error of 3.65% was in T f

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.