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Ant Colony Optimization

Ant Colony Optimization. Presenter: Chih-Yuan Chou. Outline. Introduction to ACO How do ants find the path random-proportional rule pseudo-random-proportional rule Pheromone updat e ACS performance Conclusion. Introduction to ACO.

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Ant Colony Optimization

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  1. Ant Colony Optimization Presenter: Chih-Yuan Chou

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

  3. 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

  4. How do ants find the path

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

  6. flow chart

  7. random-proportional rule • p is the probability with which ant k in city r chooses to move to the city s. • τ is the pheromone • η = 1/δ is the inverse of the distance δ • is the set of cities that remain to be visited by ant k positioned on city r • β is a parameter which determines the relative importance of pheromone versus distance

  8. pseudo-random-proportional rule • q is a random number uniformly distributed in [0…1] • is a parameter ( 0 ≦ ≦ 1) • S is a random variable selected according to the probability distribution given in random-proportional rule

  9. Pheromone update τ(r,s) : density of pheromone on edge (r,s) . 0 < α < 1 is a pheromone decay parameter.

  10. Pheromone update (cont.) • global update • local update

  11. 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.

  12. Local update

  13. ACS performance

  14. 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%

  15. Reference • Dorigo,M,maniezzo,v.,and colornj,A.,“the ant system:Optimization by a colony of cooperating agent”IEEE Transactions on Systems,Man,ad cybernetics-Part B,Vol26-1,PP.29-41. • Dorigo,M.and Gambardella,L.M.,”Ant colony system:A copperative learning approach to the traveling salesman problem”IEEE Transactions on Evoluationary Computation,Vo1.1-1,pp.53-66(1997)

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