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 update ACS performance Conclusion

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 A

nt Colony System

How do ants find the path

Important term

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

flow chart

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

)(rJ k

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

0q 0q

Pheromone update

τ(r,s) : density of pheromone on edge (r,s) .

0 < α < 1 is a pheromone decay parameter.

Pheromone update (cont.)

global update local update

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.

Local update

ACS performance

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%

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)