Ant Colony Optimization

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Ant Colony Optimization

• Presenter Chih-Yuan Chou

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Outline

• Introduction to ACO
• How do ants find the path
• random-proportional rule
• pseudo-random-proportional rule
• Pheromone update
• ACS performance
• Conclusion

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Introduction to ACO

• 1991, M. Dorigo proposed the Ant System in his
  doctoral thesis (which was published in 1992).
• 1996, publication of the article on Ant System
• 1996, Hoos and Stützle invent the MAX-MIN Ant
  System
• 1997, Dorigo and Gambardella publish the Ant
  Colony System

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How do ants find the path
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Important term

• Ant System (AS)
• Ant Colony System (ACS)
• Ant Colony Optimization (ACO)
• artificial ants
• Pheromone
• Transition Probability
• Evaporation Mechanism

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flow chart
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random-proportional rule

• p is the probability with which ant k in city r
  chooses to move to the city s.
• t is the pheromone
• ? 1/d is the inverse of the distance d
• is the set of cities that remain to be
  visited by ant k positioned on city r
• ß is a parameter which determines the relative
  importance of pheromone versus distance

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pseudo-random-proportional rule

• q is a random number uniformly distributed in
  01
• is a parameter ( 0 ? ? 1)
• S is a random variable selected according to the
  probability distribution given in
  random-proportional rule

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Pheromone update
t(r,s) density of pheromone on edge (r,s) . 0
lt a lt 1 is a pheromone decay parameter.
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Pheromone update (cont.)

• global update
• local update

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Global update

• Global updating is performed after all ants have
  completed their tours.
• In ACS only the globally best ant is allowed to
  deposit pheromone.

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Local update
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ACS performance
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Conclusion

• The ACS is an interesting novel approach to
  parallel stochastic optimization of the TSP
• In ACS only the globally best ant is allowed to
  deposit pheromone.
• Relative error is smaller than 3.5

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Reference

• Dorigo,M,maniezzo,v.,and colornj,A.,the ant
  systemOptimization by a colony of cooperating
  agentIEEE Transactions on Systems,Man,ad
  cybernetics-Part B,Vol26-1,PP.29-41.
• Dorigo,M.and Gambardella,L.M.,Ant colony
  systemA copperative learning approach to the
  traveling salesman problemIEEE Transactions on
  Evoluationary Computation,Vo1.1-1,pp.53-66(1997)