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2nd	
  Order	
  Swarm	
  Intelligence	
  
Vitorino	
  Ramos,	
  David	
  Rodrigues+,	
  and	
  Jorge	
  Louçã	
  
	
  
HAI...
Outline	
  
•  Present	
  an	
  algorithm	
  that	
  is	
  an	
  extension	
  to	
  
Ant	
  Colony	
  System	
  
•  Use	
 ...
Ant	
  Colony	
  OpSmisaSon	
  
•  ProbabilisSc	
  technique	
  
•  Searching	
  for	
  OpSmal	
  Path	
  in	
  the	
  gra...
ACO	
  Concept	
  	
  
•  Ants	
  navigate	
  from	
  nest	
  to	
  food	
  source.	
  
Blindly!	
  
•  Shortest	
  path	
...
ACO	
  IllustraSon	
  
TSP	
  Problem	
  
•  A	
  Salesman	
  must	
  visit	
  N	
  ciSes,	
  passing	
  
through	
  each	
  city	
  only	
  once...
History	
  
•  Ant	
  System	
  developed	
  by	
  Marco	
  Dorigo	
  (1992,	
  
PhD	
  thesis)	
  
•  Max-­‐Min	
  Ant	
 ...
Biology	
  Findings	
  of	
  non-­‐entry	
  singals	
  
•  Pharaoh's	
  ants	
  (Monomorium	
  pharaonis)	
  
deposit	
  a...
2nd	
  Order	
  Swarm	
  Intelligence	
  
•  Double	
  Pheromone	
  Model	
  on	
  top	
  of	
  
tradiSonal	
  ACS.	
  
– ...
State	
  TransiSon	
  Rule	
  
State	
  TransiSon	
  Rule	
  
Global	
  UpdaSng	
  Rule	
  
Local	
  UpdaSng	
  Rule	
  
2nd	
  Order	
  Reasoning	
  
2nd	
  Order	
  Response	
  Maps	
  
2nd	
  Order	
  AS	
  Results	
  
Influence	
  of	
  NegaSve	
  Pheromone	
  
kroA100.tsp	
  with	
  negaSve	
  pheromone	
  
performs	
  beHter	
  
NegaSve	
  Pheromone	
  Also	
  is	
  important	
  
for	
  bigger	
  problems.	
  
NegaSve	
  pheromone	
  can’t	
  dominate	
  
the	
  pheromone	
  maps.	
  
Take	
  Home	
  Message	
  
•  From	
  Biology	
  Findings:	
  use	
  of	
  negaSve	
  
pheromone	
  as	
  non-­‐entry	
  ...
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2nd Order Swarm Intelligence

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Presentation by David M.S. Rodrigues on a novel algorithm for Ant Colony System that includes a negative pheromone that acts as a non-entry signal for unrewarding paths in the Travelling Salesman Problem (TSP)

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2nd Order Swarm Intelligence

  1. 1. 2nd  Order  Swarm  Intelligence   Vitorino  Ramos,  David  Rodrigues+,  and  Jorge  Louçã     HAIS  2013,  Salamanca   September  11-­‐13,  2013   hHp://goo.gl/OXc0Oh     +  The  Open  University,  UK  –  david.rodrigues@open.ac.uk  
  2. 2. Outline   •  Present  an  algorithm  that  is  an  extension  to   Ant  Colony  System   •  Use  of  non-­‐entry  signal  via  a  negaSve   pheromone.   •  Use  of  2  pheromones  improves  quality  of   results  
  3. 3. Ant  Colony  OpSmisaSon   •  ProbabilisSc  technique   •  Searching  for  OpSmal  Path  in  the  graph   (Based  on  the  behaviour  of  ants  seeking  a   path  between  colony  and  source  of  food)   •  Mata-­‐heurisSc  opSmisaSon  
  4. 4. ACO  Concept     •  Ants  navigate  from  nest  to  food  source.   Blindly!   •  Shortest  path  is  discovered  via  pheromone   trails  deposited  by  other  ants.   •  Each  ant  moves  stochasScally   •  Pheromone  is  deposited  on  path   •  More  pheromone  implies  higher  probability  of   path  being  followed.  
  5. 5. ACO  IllustraSon  
  6. 6. TSP  Problem   •  A  Salesman  must  visit  N  ciSes,  passing   through  each  city  only  once,  and  returning  to   the  start  city.   •  The  cost  of  the  transportaSon  between  all   ciSes  is  known   •  The  ObjecSve  is  to  choose  the  order  of  the   tour  so  the  total  cost  is  minimum.  
  7. 7. History   •  Ant  System  developed  by  Marco  Dorigo  (1992,   PhD  thesis)   •  Max-­‐Min  Ant  System  by  Hoos  and  Stützle   (1996)   •  Ant  Colony  by  Gambardella,  Dorigo  (1997)  
  8. 8. Biology  Findings  of  non-­‐entry  singals   •  Pharaoh's  ants  (Monomorium  pharaonis)   deposit  a  pheromone  as  a  'no  entry'  signal  to   mark  unrewarding  foraging  paths.   [Robinson,  2005,  2007;  Grüter  2012]  
  9. 9. 2nd  Order  Swarm  Intelligence   •  Double  Pheromone  Model  on  top  of   tradiSonal  ACS.   – TradiSonal  posiSve  reinforcement  pheromone   – Use  of  NegaSve  Pheromone   •  Marker  for  forbidden  paths   •  Forbidden  paths  are  obtained  from  the  worse  ant  tour   of  each  iteraSon   •  This  Blockade  isn’t  permanent  as  the  pheromone   evaporates.  
  10. 10. State  TransiSon  Rule  
  11. 11. State  TransiSon  Rule  
  12. 12. Global  UpdaSng  Rule  
  13. 13. Local  UpdaSng  Rule  
  14. 14. 2nd  Order  Reasoning  
  15. 15. 2nd  Order  Response  Maps  
  16. 16. 2nd  Order  AS  Results  
  17. 17. Influence  of  NegaSve  Pheromone  
  18. 18. kroA100.tsp  with  negaSve  pheromone   performs  beHter  
  19. 19. NegaSve  Pheromone  Also  is  important   for  bigger  problems.  
  20. 20. NegaSve  pheromone  can’t  dominate   the  pheromone  maps.  
  21. 21. Take  Home  Message   •  From  Biology  Findings:  use  of  negaSve   pheromone  as  non-­‐entry  signal   •  New  algorithm  based  on  ACS  with  minimal   changes  to  tradiSonal  algorithm   •  BeHer  results  (faster  convergence  to  good   results/  faster     •  ApplicaSon  to  Dynamical  problems  for  faster   tracking  of  the  soluSons.  

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