F unda me nta l Pro b le m tha t a ppe a rs in ma ny a pplic a tio - - PowerPoint PPT Presentation

 F

unda me nta l Pro b le m tha t a ppe a rs in ma ny a pplic a tio ns inc luding :

› T ra nspo rta tio n › Ro b o t Na vig a tio n › Urb a n T ra ffic Pla nning › Ro uting o f te le c o mmunic a tio n me ssa g e s

Pic ture So urc e : http:/ / www.visua lc o mple xity.c o m/ vc / pro je c t.c fm? id=610

 Gra ph Re pre se nta tio n o f diffe re nt pro b le ms a nd

• b je c tive func tio n o ptimiza tio n:

GRAPH VE RT ICE S E DGE S

F ina nc ia l Sto c ks, Curre nc y T ra nsa c tio n T ra nspo rta tio n Stre e t I nte rse c tio ns Hig hwa ys Ga me s Bo a rd Po sitio ns L e g a l Mo ve s Ne ura l Ne two rks Ne uro ns Syna pse s Pro te in Ne two rks Pro te ins Pro te in-Pro te in I nte ra c tio ns

 Cla ssic a l Appro a c he s:

› Be llma n-F

• rd

› Dijkstra › F lo yd-Wa rsha l

 T

he po ssib ility o f no t ha ving e xa c t

• ptima l so lutio n:

› Multiple Ob je c tive Optimiza tio n › No n-line a r Ob je c tive Optimiza tio n › Ne two rk F lo ws

 I

nput :

› Blue : Sta rt Po int › Bla c k : Ob sta c le s › Re d : T a rg e t Po int

 Output:

› Sho rte st Pa th fro m Blue to Re d

 Va ria b le le ng th c hro mo so me s ,

c o nsisting o f se q ue nc e o f c e lls, a re use d to e nc o de the pa ths.

 Admissib le c hro mo so me s a re the o ne s

whic h sta rt fro m b lue po int a nd e nd to the re d po int.

 T

he initia l po pula tio n o f a dmissib le c hro mo so me s a re g e ne ra te d ra ndo mly fro m the sta rting po int.

 Using re c ursio n fo r g o ing fro m b lue to re d

 T

he fitne ss func tio n o f the c hro mo so me s is c o mpute d b a se d o n the ir le ng th.

 T

he fitte st o ne s sho uld b e mo re like ly to b e c ho se n fo r c ro sso ve r ste p.

Pic ture So urc e : http:/ / thunda xso ftwa re .b lo g spo t.c a / 2010/ 11/ g e ne tic -a lg o rithms-g a .html

 F

• r e a c h c ro sso ve r we ne e d two

c hro mo so me s whic h ha ve inte rse c tio n a t so me inne r c e ll.

 F

• r this ste p a ra ndo m po int in a ra ndo m

c hro mo so me is c ho se n a nd the n a ra ndo m pa th is g e ne ra te d fro m tha t po int to the re d po int.

Ra ndo m Se le c tio n Chro mo so me Po o l

Ra ndo m Po int “ j” in c hro mo so me A ra ndo m pa th g e ne ra te d fro m po int “j” to the re d po int Pa th Ge ne ra tio n I nse rting ne w c hro mo so me to c hro mo so me po o l

Cro sso ve r

 F

• r ne xt g e ne ra tio n we se le c t the b e st

m(po pulatio n size ) c hro mo so me s fo r the ne xt g e ne ra tio n.

Chro mo so me Po o l Se le c te d Chro mo so me s Re sulte d Chro mo so me s I nitia l Ra ndo m Pa th g e ne ra tio n Se le c tio n Cro sso ve r a nd muta tio n So rting

 F

ina lly if the c ha ng e s in the fitne ss o f po pula tio n is le ss tha n a c e rta in thre sho ld a fte r so me ite ra tio ns we c a n c o nc lude tha t we ha ve re a c he d to a so lutio n.