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 Minimize sum flow x distance TSP is a particular case of QAP Models many real world problems “NP-hard” problem known

QAP Example How to assign facilities to 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 1st best improvement Local Search

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

Ant Colony Optimization for QAP How important search guidance is?

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

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 70% optimum Avg.10 iterations

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!

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

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