Ant colony optimization is a metaheuristic algorithm that is inspired by the foraging behavior of ants. It is used to find optimal paths between locations. The algorithm works by simulating ants depositing and following virtual pheromone trails. As ants find food sources, they lay down more pheromone on shorter paths, which makes them more desirable for other ants to follow. This forms a positive feedback loop where the shortest paths become most prominent. The document discusses the key concepts of the ant colony optimization algorithm including edge selection, pheromone updating, and applications to problems like the travelling salesman problem.

1. Ant Colony Optimization
Medhini G Narasimhan
Department of Information Technology
National Institute of Technology, Karnataka

2. Contents
❖ Swarm Intelligence
❖ Ant Colony Optimization - Pheromone trails
❖ ACO Algorithm - Edge Selection
❖ ACO Algorithm - Pheromone Update
❖ ACO in Travelling Salesman Problem
❖ Other Applications
❖ Advantages and Disadvantages

3. Swarm Intelligence
● Discipline dealing with collective behaviour of decentralized self-organised
systems
● Natural systems : Bird Flocking, Fish Schooling
● Artificial systems : Robot Swarm
○ Jasmine Swarm Robots

4. Ant Colony Optimization
● Shortest path from the nest to their food source using Pheromone trails
● Ants - No vision
● Pheromone - behaviour altering chemical - STIGMERGY
● Ant decides to follow a pheromone trail with certain probability
● Reinforces the trail by laying more pheromone
● Pheromone strength decays over time
● Pheromone builds up along shorter path - more ants follow it - more
attractive

5. ● Population based search technique for solving combinatorial optimization
problems
○ Population based search : GA where entire population is evolved
○ Combinatorial Optimization : Optimal object in a set of finite objects
● ACO Algorithm
○ Edge Selection
○ Pheromone Update

6. ACO Algorithm - Edge Selection
● Ant - Computational Agent - k
● Iteratively construct solution for problem at hand
● In one iteration, each ant builds its own tour
● Final Solution is obtained from Intermediate Solutions
as the shortest tour
● Trail selection is based
○ Attractiveness of the trail
○ Thickness of the trail

7. ● Attractiveness : Desirability of that edge - Computed from a priori
knowledge - Usually Q/dxy
● Trail Level : Amount of pheromone deposited - How proficient it has
been
● 0 <= α : Parameter to control trail level
● >= 1: Parameter to control attractiveness
● and : Attractiveness and trail level for the other possible state
transitions

8. ACO - Pheromone Update
● When all ants have completed a solution, the trails are updated
● : amount of pheromone deposited for a state transition XY
● : Pheromone Evaporation Coefficient
○ Small - Slow adaptation
○ High - Fast adaptation
● : Amount of pheromone deposited by kth
ant

9. ● Q : Constant
● : Cost of kth
ant’s tour - Length travelled

10. ACO - Travelling Salesman Problem
● Minimum weighted Hamiltonian Cover
● Other approaches : Dynamic Programming, Minimum Spanning Tree (2
approximate ), Christofides algorithm (1.5 approximate )

11. ACO - Travelling Salesman Problem

12. Other Applications of ACO
● Bus routes, garbage collection, delivery routes
● Machine scheduling: Minimization of transport time for distant production
locations
● Feeding of lacquering machines
● Protein folding
● Telecommunication networks: Online optimization
● Personnel placement in airline companies
● Composition of products

13. Advantages
● Can be used in dynamic applications
● Positive Feedback leads to rapid discovery of good solutions
● Distributed computation avoids premature convergence
Disadvantages
● Convergence is guaranteed, but time to convergence is uncertain
● Coding is not straightforward

14. References
● https://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms#Convergence
● http://www.inf.ed.ac.uk/teaching/courses/nat/slides/lecture10_ACO.pdf
● https://bsantosa.files.wordpress.com/2015/03/aco-tutorial-english.pdf
● http://paginas.fe.up.
pt/~mac/ensino/docs/DS20102011/Presentations/PopulationalMetaheuristics/ACO_Nuno_
Muhammad_Zafeiris_Behdad.pdf
● http://www.codeproject.com/Articles/644067/Applying-Ant-Colony-Optimization-Algorithms-
to-Sol#_Toc364710426