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

▶

Feb 14, 2024 373 likes •542 views

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,

SLIDE 1

AN APPLICATION OF STOCHASTIC HILL CLIMBING OPTIMIZATION OF WEIGHTED PLANAR GRAPHS THROUGH MIRROR WORLD MODELING

Thomas Slatton, Department of Computer Science Riley Turben, Department of Computer Science Craig Thompson, PhD, Department of Computer Science 4th Annual FEP Honors Research Symposium 24 April, 2012

SLIDE 2

THE PROBLEM AREA

 How can the University of Arkansas pathway

system be redesigned to achieve an optimized configuration of paths?

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 3

OPTIMALITY

 How can anyone be sure what they choose is

better than another option?

 Optimization  Making changes that increase the value of a system

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 4

DEFINING OPTIMALITY

 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

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 5

REPRESENTING THE UNIVERSITY OF ARKANSAS PATHWAY SYSTEM

In what way can the University

f Arkansas and its pathway

system be represented virtually to allow for optimization?

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 6

GRAPHS

 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) 6

6 12 7 7 7 5 5 5

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 7

BUILDING A GRAPH

 Elevations  Building locations  Path locations  Walking speed

0.5 1 1.5 2 2.5 3 3.5

5 10 15 20 25 30 35

Speed (meters/second) Inclination (degrees)

Speed vs. Inclination

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 8

OPTIMAL ROUTING

What is the most efficient way to

walk from one place on the University of Arkansas campus to any other place using pedestrian walkways?

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 9

BREADTH-FIRST SEARCH WITH PRIORITY QUEUE

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.

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 10

OPTIMIZATION

How could the pathway system

be redesigned to yield a more efficient model?

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 11

 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

STOCHASTIC HILL CLIMBING

S. Derbyshire. (2008, February

21). MaximumParabaloid.png [Online]. Available: http://en.wikipedia.

rg/wiki/File:MaximumParabo

loid.png

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 12

STOCHASTIC HILL CLIMBING (CONT’D)

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.

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 13

RESULTS

 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

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 14

AVERAGE TIME AS A FUNCTION OF TOTAL PATHWAY LENGTH

Slatton, Turben. 4th Annual FEP Honors Research Symposium

250 270 290 310 330 350 370 390 15000 20000 25000 30000 35000 40000

Average Travel Time (seconds) Total Pathway Length (meters)

Average Travel Time as a Function of Total Length

SLIDE 15

OTHER APPLICATIONS

 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

Slatton, Turben. 4th Annual FEP Honors Research Symposium

SLIDE 16

REFERENCES

 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/

Slatton, Turben. 4th Annual FEP Honors Research Symposium