S TOCHASTIC H ILL C LIMBING (C ONT D ) I. Ljubi and G. R. Raidl , An - PowerPoint PPT Presentation

A N A PPLICATION OF S TOCHASTIC H ILL C LIMBING O PTIMIZATION OF W EIGHTED P LANAR G RAPHS THROUGH M IRROR W ORLD M ODELING Thomas Slatton, Department of Computer Science Riley Turben, Department of Computer Science Craig Thompson, PhD, Department of Computer Science 4 th Annual FEP Honors Research Symposium 24 April, 2012

T HE P ROBLEM A REA  How can the University of Arkansas pathway system be redesigned to achieve an optimized configuration of paths? 2 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

O PTIMALITY  How can anyone be sure what they choose is better than another option?  Optimization  Making changes that increase the value of a system 3 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

D EFINING O PTIMALITY  A system that uses the same amount of pathway and has a lower average travel time  A system that has the same average travel time and a lower amount of pathway  A combination of lowered average time and lowered distance 4 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

R EPRESENTING THE U NIVERSITY OF A RKANSAS P ATHWAY S YSTEM  In what way can the University of Arkansas and its pathway system be represented virtually to allow for optimization? 5 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

G RAPHS  Node – A point at which edges meet  Intersections of pathways and building entrances  Edge – A connection between nodes  The paths themselves  Weight – The value assigned to an edge, often the length of that edge  The amount of time it takes to walk a path  Graph – A series of nodes and edges  The entire pathway system  Planar Graph – A graph that can be represented on a plane such that no edges cross  (Weisstein 1999) 12 7 5 7 6 7 5 5 6 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

B UILDING A G RAPH  Elevations Speed vs. Inclination  Building locations 3.5 (meters/second) 3  Path locations 2.5 Speed  Walking speed 2 1.5 1 0.5 0 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 Inclination (degrees) 7 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

O PTIMAL R OUTING  What is the most efficient way to walk from one place on the University of Arkansas campus to any other place using pedestrian walkways? 8 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

B READTH -F IRST S EARCH WITH P RIORITY Q UEUE 9 M. Barbehenn, "A Note on the Complexity of Dijkstra's Algorithm for Graphs with Weighted Vertices," in IEEE Transactions on Computers , IEEE Slatton, Turben. 4 th Annual FEP Honors Research Symposium Computer Society, 1998, vol. 47 pp. 263 .

O PTIMIZATION  How could the pathway system be redesigned to yield a more efficient model? 10 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

S TOCHASTIC H ILL C LIMBING  Hill Climbing  Making incremental changes to yield an increase in the output of the value function  Stochastic Hill Climbing  Changes do not necessarily yield the largest possible increase in value 11 S. Derbyshire. (2008, February 21). MaximumParabaloid.png [Online]. Available: http://en.wikipedia. org/wiki/File:MaximumParabo Slatton, Turben. 4 th Annual FEP Honors Research Symposium loid.png

S TOCHASTIC H ILL C LIMBING (C ONT ’ D ) I. Ljubić and G. R. Raidl , “An Evolutionary Algorithm with Stochastic Hill-Climbing for the 12 Edge-Biconnectivity Augmentation Problem” in Applications of Evolutionary Computing , Vol. 2037. Berlin, Germany, Springer-Verlag, 2001, Slatton, Turben. 4 th Annual FEP Honors Research Symposium ch. 3 , sec. 4, pp. 20-29 .

R ESULTS  University of Arkansas as it is  37.9 kilometers of pathway  305.5 second average travel time  Optimized graph  37.8 kilometers of pathway  277 second average travel time 13 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

A VERAGE T IME A S A F UNCTION OF T OTAL P ATHWAY L ENGTH Average Travel Time as a Function of Total Length 390 Average Travel Time 370 350 (seconds) 330 310 290 270 250 15000 20000 25000 30000 35000 40000 Total Pathway Length (meters) 14 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

O THER A PPLICATIONS  Related network analysis applications:  Roads and Highways  Virtual routing  Videogame artificial intelligence  Circuit design  Emergency evacuation simulations  Direct on-campus applications:  Optimal locations for bulletin boards, emergency phones, or other public-use devices  Adding new pathways 15 Slatton, Turben. 4 th Annual FEP Honors Research Symposium

R EFERENCES  I. Ljubić and G. R. Raidl , “An Evolutionary Algorithm with Stochastic Hill-Climbing for the Edge-Biconnectivity Augmentation Problem” in Applications of Evolutionary Computing , Vol. 2037. Berlin, Germany, Springer-Verlag, 2001, ch. 3 , sec. 4, pp. 20-29 .  M. Barbehenn, "A Note on the Complexity of Dijkstra's Algorithm for Graphs with Weighted Vertices," in IEEE Transactions on Computers , IEEE Computer Society, 1998, vol. 47 pp. 263 .  P. E. Boas et.al. , “Design and Implementation of an Efficient Priority Queue” in Theory of Computing Systems , Springer-Verlag, 1976, vol. 10. pp. 99-127.  D. Eppstein. (2002, March 8). Priority Dictionary [Online]. Available: http://code.activestate.com/recipes/117228- priority-dictionary/ 16 Slatton, Turben. 4 th Annual FEP Honors Research Symposium