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Slide 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
Slide 2 - 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
Slide 3 - biggest flow: A - B QAP Example Locations Facilities How to assign facilities to locations ? Lower cost Higher cost
Slide 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
Slide 5 - Ant Colony Optimization for QAP Pheromone laying facilities-location assignment Basic ACO algorithm Local Search 1st best improvement
Slide 6 - Ant Colony Optimization for QAP Actions Strategies Choosing a Facility heuristic Choosing a Location P(pheromone , heuristic) Pheromone Update (solution quality) Basic ACO algorithm
Slide 7 - Ant Colony Optimization for QAP How important search guidance is?
Slide 8 - 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
Slide 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
Slide 10 - Results: Real Life - Kra30a
Slide 11 - 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!
Slide 12 - Conclusions Great Summer School! The ants did find their way to the Beach Pool Beer
Slide 13 - 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 Path