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Ant Colony OptimizationQuadratic Assignment Problem Hernan AGUIRRE, Adel BEN HAJ YEDDER, Andre DIAS and Pascalis RAPTIS Problem Leader: Marco Dorigo Team Leader: Marc Schoenauer
known 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
QAP Example Facilities Locations 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 heuristic • Choosing a Facility P(pheromone , heuristic) • Choosing a Location (solution quality) • Pheromone Update
Ant Colony Optimization for QAP • How important search guidance is?
Test problems • 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 Heuristicgets better minimun • With local search: always converges to optimum • Very quickly
Future Work Choosing a Facility Choosing a Location • Different strategies 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 Facilities Locations biggest flow: A - B Path Path (1,A) | (2,B) | (3,C) (1,C) | (2,B) | (3,A) Higher cost Lower cost