1

IE 607 Heuristic Optimization

Ant Colony Optimization

2

Double Bridge Experiment

3

Behavior of Real Ants

Real Ants Find the Shortest Path to Food Resource

Pheromone Is Laid by Ants along the Trail

Pheromone Evaporates over Time

Pheromone Intensity Increases with Number of Ants

Using Trail

Good Paths Are Reinforced And Bad Paths Gradually

Disappear

4

ACO

Meta-Heuristic Optimization Method

Inspired by Real Ants

First published by Marco Dorigo (1992) as his dissertation

Is currently greatly expanding in applications and interest,

mainly centered in Europe

Positive & Negative Feedback

Constructive Greedy Heuristic

Population-based Method

5

Application

TSP QAP VRP Telecommunication Network Scheduling Graph Coloring Water Distribution Network etc

6

Methodology

ACO Algorithm

Set all parameters and initialize the pheromone trails

Loop

Sub-Loop

Construct solutions based on the state transition rule

Apply the online pheromone update rule

Continue until all ants have been generated

Apply Local Search

Evaluate all solutions and record the best solution so far

Apply the offline pheromone update rule

Continue until the stopping criterion is reached

ACO

7

Methodology

Each ant represents a complete solution Online updating is performed each time after an ant

constructed a solution: more chance to exploration Local search is applied after all ants construct

solutions Offline updating is employed after the local search:

allow good ants to contribute

Overview of ACO Algorithm

8

Methodology

: Pheromone trail of combination (i,j)

: Local heuristic of combination (i,j)

: Transition probability of combination (i,j)

: Relative importance of pheromone trail

: Relative importance of local heuristic

: Determines the relative importance of exploitation versus exploration

: Trail persistence

Parameters of ACO Algorithm

ij

ij

ijP

0q

9

Ant System (AS) – the earliest version of ACO

State Transition Probability

Pheromone Update Rule

Ulilil

ijijijP

)()(

)()(

NA

k

kij

oldij

newij

1

,Qkij

ij

kij d

Q k

kij L

Qor

Methodology

10

ASelite

ASrank

eij

NA

k

kij

oldij

newij

1

eij

e

r

rij

oldij

newij

1

1

eeij L

Qe

rrij L

Qre )(

Methodology

11

Ant-Q & Ant Colony System (ACS)

Local Updating

(Online Updating)

Global Updating

(Offline Updating)

V

vilil

Ul])()[(maxarg

0

0

qq

qq

Ulilil

ivivivP

)()(

)()(

0)1( oldij

newij

eij

oldij

newij )1(

Exploitation

Exploration

Methodology

12

Max-Min Ant System (MMAS)

ANTS

eij

oldij

newij maxmin ij

Ulilil

ijijijP ])1([

)1(

)1(0 LBL

LBL

avg

kkij

NA

k

kij

oldij

newij

1

Methodology

13

Website & Books

http://iridia.ulb.ac.be/~mdorigo/ACO/ACO.html Bonabeau E., M. Dorigo & T. Theraulaz (1999).

From Natural to Artificial Swarm Intelligence. New York: Oxford University Press.

Corne D., M. Dorigo & F. Glover, Editors (1999). New Ideas in Optimisation. McGraw-Hill .