Transcript Ant Colony Optimization

Ant Colony Optimization
Quadratic Assignment Problem
Hernan AGUIRRE, Adel BEN HAJ YEDDER,
Andre DIAS and Pascalis RAPTIS
Problem Leader: Marco Dorigo
Team Leader:
Marc Schoenauer
Quadratic Assignment Problem
• Assign n facilities to n locations
– Distances between locations
– Flows between facilities
• Goal
known
Minimize sum flow x distance
• TSP is a particular case of QAP
– Models many real world problems
• “NP-hard” problem
QAP Example
Locations
Facilities
biggest flow: A - B
How to assign facilities to locations ?
Higher cost
Lower cost
Ant Colony Optimization (ACO)
• Ant Algorithms
– Inspired by observation of real ants
• Ant Colony Optimization (ACO)
– Inspiration from ant colonies’ foraging
behavior (actions of the colony finding
food)
– Colony of cooperating individuals
– Pheromone trail for stigmergic communication
– Sequence of moves to find shortest paths
– Stochastic decision using local information
Ant Colony Optimization for QAP
facilities-location
assignment
• Pheromone laying
• Basic ACO algorithm
• Local Search
1st
best
improvement
Ant Colony Optimization for QAP
• Basic ACO algorithm
Actions

Choosing a Facility

Choosing a Location

Pheromone Update
Strategies
heuristic
P(pheromone ,
heuristic)
(solution
quality)
Ant Colony Optimization for QAP
• How important search guidance is?
Test problems
Type of
problem
Size
tai12a
tai50a
kra30a
random
random
Real-life
12
50
30
• 12 facilities/positions should be easy to solve!
• What behavior with real life problems?
• QAP solved to optimality up to 30
Parameters for ACO: 500 ants, evaporation =0.9
Results: tai12a
• Without local search convergence to local
minimum
NOT ALWAYS the optimum
Heuristic gets better minimun
• With local search: always converges to
optimum
Very quickly
Results: Real Life - Kra30a
No LS
With LS
No Heuristic
Converges local
minimum
72 % optimum
Optimum
Avg.12 iterations
With heuristic
Converges local
minimum
70% optimum
Optimum
Avg.10 iterations
Future Work
• Different strategies
Choosing a Facility
Choosing a Location
Pheromone Update
• Remain fixed, all ants use the same!
• Performance of strategies varies
Problem
Stage of the search
Co-evolution
Let the ants find it!
Conclusions
Great Summer School!
The ants did find their way to the
Beach
Pool
Beer
Ants Path
Locations
Facilities
biggest flow: A - B
Path
Path
(1,A)
(1,C)
|
|
(2,B)
(2,B)
|
|
(3,C)
Higher cost
Lower cost
(3,A)