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

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 Quadratic Assignment Problem known

biggest flow: A - B QAP Example Locations Facilities How to assign facilities to locations ? Lower cost Higher 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 Pheromone laying facilities-location assignment Basic ACO algorithm Local Search 1 st best improvement

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

Ant Colony Optimization for QAP How important search guidance is?

Test problems tai12atai50akra30a Type of problem random Real-life Size 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

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: tai12a

Results: Real Life - Kra30a No LSWith LS No HeuristicConverges local minimum 72 % optimum Optimum Avg. 12 iterations With heuristicConverges 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

biggest flow: A - B Ants Path Locations Facilities Lower cost Higher cost (1,A) | (2,B) | (3,C) (1,C) | (2,B) | (3,A) Path