Ant Colony System: A Cooperative Learning Approach to the

Traveling Salesman Problem

Paper by: Marco Dorigo and Luca Maria Gambardella

Presented by: Martyna KowalczykCSCI 658

Basic Idea

● nature-inspired● real ants are capable of finding the

shortest path from a food source to their nest

● no use of visual cues; exploit pheromone information

Basic Idea

Ant System

● first ACO procedure published in 1992 by Marco Dorigo

● has been improved since then

Ant System Process

● each ant generates complete tour by choosing cities according to a probabilistic state transition rule

● when all ants are done, global pheromone updating rule is applied

● long-term memory = pheromone

Ant Colony System

● improved efficiency when applied to TSP

● 3 major changes to AS:o new state transition ruleo global updating rule applied only to edges

belonging to the best ant touro local pheromone updating rule

ACS Algorithm

ACS State Transition Rule

AS State Transition Rule

(S in the ACS state transition rule)

ACS Local Updating Rule

ACS Global Updating Rule

ACS Parameter Settings

All experiments had parameters set to:● β = 2● α = ρ = 0.1● q0 = 0.9

● τ0 = (n Lnn)-1

● number of ants = m = 10● ants are initially placed randomly with at most 1

ant in each city

Cooperation Among Ants

● ACS effectively exploits pheromone-mediated cooperation

● cooperating vs. non cooperating ants

Cooperation Experiment 1

Cooperation Experiment 2

Comparison with Other Heuristics

● considered two sets of TSP problems:o five randomly generated 50-city problemso three geometric problems between 50 and

100 cities

Comparison with Other Heuristics

Comparison with Other Heuristics

Improvements To Be Made

● number of ants that should contribute to global updating rule

● move from current parallel local updating of pheromone to a sequential one

● add more effective local optimizer

Thank you!