Narahari Bharadwaj Songela Chen Chris Edgett Ishan Levy

Narahari Bharadwaj, Songela Chen, Chris Edgett, Ishan Levy, Agustey Mongia, Ruvini Navaratna, Martin Schneider, Claire Sheen, Nancy Wang, Justin Wong, Amy Zhou

What is global optimization? • What does it do? • How does it work? • Why use it? • Routing Problems • Biological Processes • Molecular Structure Prediction http: //www. mathworks. com/matlabcentral/fileexchange/scree nshots/4051/original. jpg

Would you like to try it? • Website allows users to query our solvers with custom input • Visual representations of the generated data • Unified theme for more effective presentation

How does the website work?

Traveling Salesman Problem (TSP) • No polynomial time algorithm exists What is the shortest path that traverses • every Focused city specifically in a graph once and returns to on Euclidean the beginning TSP (shortest Euclidean tour)?

TSP: Brute Force • Tests every possible route in order to find the shortest one • Has a runtime of O(n!) • n! ways to permute n distinct numbers

TSP: Ant Colony Optimization • Mimics ants’ pheromone system • Pheromone inversely related to total tour distance, determine the routes ants take • Final tour generated by always going along the route with the most pheromone

TSP: Fast/Wheel Dijkstra 1. Choose a random city 2. Find the closest city 3. Draw a route to the closest city 4. Repeat

TSP: Fast/Wheel Dijkstra

TSP: Gravitational • Works off of the idea that cities that are close to each other ‘attract’ and are favorable • Edges that connect two cities passing near the center of mass are considered unfavorable.

TSP: Gravitational

TSP: Simulated Annealing High Temperature "Redock: Docking Redone. " Redock: Docking Redone. N. p. , n. d. Web. 28 July 2014.

TSP: Simulated Annealing Medium Temperature "Redock: Docking Redone. " Redock: Docking Redone. N. p. , n. d. Web. 28 July 2014.

TSP: Simulated Annealing Low Temperature "Redock: Docking Redone. " Redock: Docking Redone. N. p. , n. d. Web. 28 July 2014.

TSP: Remove Line Intersections • Removes intersecting lines to reduce the length of the total path • Acts as a ‘helper’ algorithm • Resolve intersections by reversing order of nodes in between earliest and latest

Results for TSP

Protein Folding What is the secondary structure for a certain arrangement of hydrophobic and hydrophilic amino acids?

Protein Folding: Slithering Snake • Generates a randomized chain of amino acids that travel like a snake around a coordinate plane • Calculates all possible configurations and returns the one with the lowest energy state http: //www. physics. buffalo. edu/phy 410505/2011/topic 5/app 1/img/culdesac. png

Protein Folding: Slithering Snake A more negative potential energy is favorable

Protein Folding: Neural Network • Forms configurations that correspond to hydrophobic and hydrophilic behavior

Results for Protein Folding

Nanoparticle Configuration Metallic nanoparticles show promise in many fields, but are they stable? How do we determine the configuration with the lowest potential energy?

Nanoparticle Configuration: Simulated Annealing "Redock: Docking Redone. " Redock: Docking Redone. N. p. , n. d. Web. 28 July 2014.

Nanoparticle Configuration: Genetic Algorithm • Create many possible particles and select ones with lowest energy states • These are ‘bred’ and ‘mutated’ for several generations

Nanoparticle Configuration: Basin Hopping 1. Randomly changes positions of atoms 2. Finds most stable state 3. Randomly makes smaller changes to atom positions D. J. Wales, "Frontiers Article: Surveying a Complex Potential Energy Landscape: Overcoming Broken Ergodicity Using Basin-Sampling, " Chem. Phys. Lett. 584: 1 -9 (2013).

Results for Nanoparticles

Conclusion • Created a novel web interface for global optimization • Application: • Route Optimization • Drug Design • Fuel Cells

Acknowledgements Thank you to… • All the generous corporate and government sponsors who made PGSS possible • PGSS alumni for their passion in reviving PGSS • Zachary Pozun for his guidance and support • Jeff Conway for his unfailing help • Carnegie Mellon University for graciously providing educational and residential facilities • Dr. Barry Luokkala, faculty, and staff for making our PGSS experience unforgettable