1. 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

2. Quadratic Assignment Problem
Assign n facilities to n locations
Distances between locations
Flows between facilities
Goal Minimize sum flow x distance
TSP is a particular case of QAP
Models many real world problems
“NP-hard” problem
known

3. QAP Example How to assign facilities to locations ? Facilities
biggest flow: A - B
How to assign facilities to locations ?
Higher cost
Lower cost

4. 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

5. Ant Colony Optimization for QAP
facilities-location assignment
Pheromone laying
Basic ACO algorithm
1st
best
improvement
Local Search

6. Ant Colony Optimization for QAP
Basic ACO algorithm
Actions Strategies
Choosing a Facility
heuristic
P(pheromone , heuristic)
Choosing a Location
(solution quality)
Pheromone Update

7. Ant Colony Optimization for QAP
How important search guidance is?

8. Test problems tai12a tai50a kra30a Type of problem random Real-life
Size 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

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

10. Results: Real Life - Kra30a
No LS
With LS
No Heuristic
Converges local minimum
72 % optimum
Optimum
Avg.12 iterations
With heuristic
70% optimum
Avg.10 iterations

11. Future Work Choosing a Facility Different strategies
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!

12. The ants did find their way to the
Conclusions
Great Summer School!
The ants did find their way to the
Beach
Pool
Beer

13. Ants Path Facilities Locations biggest flow: A - B Path Path (1,A) |
Higher cost
Lower cost