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)