1 IE 607 Heuristic Optimization Ant Colony Optimization

2 Double Bridge Experiment

3 Behavior of Real Ants  Real Ants Find the Shortest Path to Food Resource  Pheromone Is Laid by Ants along the Trail  Pheromone Evaporates over Time  Pheromone Intensity Increases with Number of Ants Using Trail  Good Paths Are Reinforced And Bad Paths Gradually Disappear

4 ACO  Meta-Heuristic Optimization Method  Inspired by Real Ants  First published by Marco Dorigo (1992) as his dissertation  Is currently greatly expanding in applications and interest, mainly centered in Europe  Positive & Negative Feedback  Constructive Greedy Heuristic  Population-based Method

5 Application  TSP  QAP  VRP  Telecommunication Network  Scheduling  Graph Coloring  Water Distribution Network  etc

6 Methodology ACO Algorithm Set all parameters and initialize the pheromone trails Loop Sub-Loop Construct solutions based on the state transition rule Apply the online pheromone update rule Continue until all ants have been generated Apply Local Search Evaluate all solutions and record the best solution so far Apply the offline pheromone update rule Continue until the stopping criterion is reached ACO

7 Methodology  Each ant represents a complete solution  Online updating is performed each time after an ant constructed a solution: more chance to exploration  Local search is applied after all ants construct solutions  Offline updating is employed after the local search: allow good ants to contribute Overview of ACO Algorithm

8 Methodology : Pheromone trail of combination (i,j) : Local heuristic of combination (i,j) : Transition probability of combination (i,j) : Relative importance of pheromone trail : Relative importance of local heuristic : Determines the relative importance of exploitation versus exploration : Trail persistence Parameters of ACO Algorithm

9 Ant System (AS) – the earliest version of ACO State Transition Probability Pheromone Update Rule Methodology

10 AS elite AS rank Methodology

11 Ant-Q & Ant Colony System (ACS) Local Updating (Online Updating) Global Updating (Offline Updating) Exploitation Exploration Methodology

12 Max-Min Ant System (MMAS) ANTS Methodology

13 Website & Books   Bonabeau E., M. Dorigo & T. Theraulaz (1999). From Natural to Artificial Swarm Intelligence. New York: Oxford University Press.M. DorigoOxford University Press  Corne D., M. Dorigo & F. Glover, Editors (1999). New Ideas in Optimisation. McGraw-Hill.Corne D.M. DorigoF. GloverMcGraw-Hill