Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant colony Optimization Algorithms :Introduction and Beyond

Anirudh Shekhawat Pratik Poddar Dinesh Boswal

Indian Institute of Technology Bombay

Artificial Intelligence Seminar 2009

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Outline

1 IntroductionAnt Colony OptimizationMeta-heuristic OptimizationHistoryThe ACO Metaheuristic

2 Main ACO AlgorithmsMain ACO AlgorithmsAnt SystemAnt Colony SystemMAX-MIN Ant System

3 Applications of ACO4 Advantages and Disadvantages

AdvantagesDisadvanatges

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony Optimization

What is Ant Colony Optimization?

ACOProbabilistic technique.Searching for optimal path in the graph based onbehaviour of ants seeking a path between their colony andsource of food.Meta-heuristic optimization

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony Optimization

ACO Concept

Overview of the ConceptAnts navigate from nest to food source. Ants are blind!Shortest path is discovered via pheromone trails.Each ant moves at randomPheromone is deposited on pathMore pheromone on path increases probability of pathbeing followed

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony Optimization

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony Optimization

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony Optimization

ACO System

Overview of the SystemVirtual trail accumulated on path segmentsPath selected at random based on amount of "trail" presenton possible paths from starting node

Ant reaches next node, selects next pathContinues until reaches starting node

Finished tour is a solution.Tour is analyzed for optimality

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony Optimization

ACO System

Overview of the SystemVirtual trail accumulated on path segmentsPath selected at random based on amount of "trail" presenton possible paths from starting nodeAnt reaches next node, selects next pathContinues until reaches starting node

Finished tour is a solution.Tour is analyzed for optimality

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony Optimization

ACO System

Overview of the SystemVirtual trail accumulated on path segmentsPath selected at random based on amount of "trail" presenton possible paths from starting nodeAnt reaches next node, selects next pathContinues until reaches starting nodeFinished tour is a solution.Tour is analyzed for optimality

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Meta-heuristic Optimization

Meta-heuristic

1 Heuristic method for solving a very general class ofcomputational problems by combining user-given heuristicsin the hope of obtaining a more efficient procedure.

2 ACO is meta-heuristic3 Soft computing technique for solving hard discrete

optimization problems

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Meta-heuristic Optimization

Meta-heuristic

1 Heuristic method for solving a very general class ofcomputational problems by combining user-given heuristicsin the hope of obtaining a more efficient procedure.

2 ACO is meta-heuristic3 Soft computing technique for solving hard discrete

optimization problems

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

History

History

1 Ant System was developed by Marco Dorigo (Italy) in hisPhD thesis in 1992.

2 Max-Min Ant System developed by Hoos and Stützle in1996

3 Ant Colony was developed by Gambardella Dorigo in 1997

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

The ACO Metaheuristic

The ACO Meta-heuristic

ACOSet Parameters, Initialize pheromone trails

SCHEDULE ACTIVITIES1 Construct Ant Solutions2 Daemon Actions (optional)3 Update Pheromones

Virtual trail accumulated on path segments

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

The ACO Metaheuristic

ACO - Construct Ant Solutions

ACO - Construct Ant SolutionsAn ant will move from node i to node j with probability

pi,j =(ταi,j )(η

βi,j )P

(ταi,j )(ηβi,j )

whereτi,j is the amount of pheromone on edge i , jα is a parameter to control the influence of τi,jηi,j is the desirability of edge i , j (typically 1/di,j )β is a parameter to control the influence of ηi,j

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

The ACO Metaheuristic

ACO - Pheromone Update

ACO - Pheromone UpdateAmount of pheromone is updated according to the equation

τi,j = (1− ρ)τi,j + ∆τi,j

whereτi,j is the amount of pheromone on a given edge i , jρ is the rate of pheromone evaporation∆τi,j is the amount of pheromone deposited, typically given by

∆τ ki,j =

{1/Lk if ant k travels on edge i , j0 otherwise

where Lk is the cost of the k th ant’s tour (typically length).

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Main ACO Algorithms

ACO

ACOMany special cases of the ACO metaheuristic have beenproposed.The three most successful ones are: Ant System, AntColony System (ACS), and MAX-MIN Ant System (MMAS).For illustration, example problem used is TravellingSalesman Problem.

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant System

ACO - Ant System

ACO - Ant SystemFirst ACO algorithm to be proposed (1992)Pheromone values are updated by all the ants that havecompleted the tour.

τij ← (1− ρ) · τij +∑m

k=1 ∆τ kij ,

whereρ is the evaporation ratem is the number of ants∆τ k

ij is pheromone quantity laid on edge (i , j) by the k th ant

∆τ ki,j =

{1/Lk if ant k travels on edge i , j0 otherwise

where Lk is the tour length of the k th ant.

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony System

ACO - Ant Colony System

ACO - Ant Colony SystemFirst major improvement over Ant SystemDifferences with Ant System:

1 Decision Rule - Pseudorandom proportional rule2 Local Pheromone Update3 Best only offline Pheromone Update

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony System

ACO - Ant Colony System

ACO - Ant Colony SystemAnts in ACS use the pseudorandom proportional ruleProbability for an ant to move from city i to city j dependson a random variable q uniformly distributed over [0,1],and a parameter q0.If q ≤ q0, then, among the feasible components, thecomponent that maximizes the product τilη

βil is chosen,

otherwise the same equation as in Ant System is used.This rule favours exploitation of pheromone information

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony System

ACO - Ant Colony System

ACO - Ant Colony SystemDiversifying component against exploitation: localpheromone update.The local pheromone update is performed by all ants aftereach step.Each ant applies it only to the last edge traversed:

τij = (1− ϕ) · τij + ϕ · τ0

whereϕ ∈ (0,1] is the pheromone decay coefficientτ0 is the initial value of the pheromone (value kept smallWhy?)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Ant Colony System

ACO - Ant Colony System

ACO - Ant Colony SystemBest only offline pheromone update after constructionOffline pheromone update equation

τij ← (1− ρ) · τij + ρ ·∆τbestij

where

τbestij =

{1/Lbest if best ant k travels on edge i , j0 otherwise

Lbest can be set to the length of the best tour found in thecurrent iteration or the best solution found since the start ofthe algorithm.

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

MAX-MIN Ant System

ACO - MAX-MIN Ant System

ACO - MAX-MIN Ant SystemDifferences with Ant System:

1 Best only offline Pheromone Update2 Min and Max values of the pheromone are explicitly limited

τij is constrained between τmin and τmax (explicitly set byalgorithm designer).After pheromone update, τij is set to τmax if τij > τmax and toτmin if τij < τmin

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Applications of ACO

ACORouting in telecommunication networksTraveling SalesmanGraph ColoringSchedulingConstraint Satisfaction

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Advantages

Advantages of ACO

ACO

Inherent parallelism

Positive Feedback accounts for rapid discovery of goodsolutions

Efficient for Traveling Salesman Problem and similarproblems

Can be used in dynamic applications (adapts to changessuch as new distances, etc)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Advantages

Advantages of ACO

ACOInherent parallelism

Positive Feedback accounts for rapid discovery of goodsolutions

Efficient for Traveling Salesman Problem and similarproblems

Can be used in dynamic applications (adapts to changessuch as new distances, etc)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Advantages

Advantages of ACO

ACOInherent parallelismPositive Feedback accounts for rapid discovery of goodsolutions

Efficient for Traveling Salesman Problem and similarproblems

Can be used in dynamic applications (adapts to changessuch as new distances, etc)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Advantages

Advantages of ACO

ACOInherent parallelismPositive Feedback accounts for rapid discovery of goodsolutionsEfficient for Traveling Salesman Problem and similarproblems

Can be used in dynamic applications (adapts to changessuch as new distances, etc)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Advantages

Advantages of ACO

ACOInherent parallelismPositive Feedback accounts for rapid discovery of goodsolutionsEfficient for Traveling Salesman Problem and similarproblemsCan be used in dynamic applications (adapts to changessuch as new distances, etc)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Disadvanatges

Disadvantages of ACO

ACO

Theoretical analysis is difficult

Sequences of random decisions (not independent)

Probability distribution changes by iteration

Research is experimental rather than theoretical

Time to convergence uncertain (but convergence isgauranteed!)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Disadvanatges

Disadvantages of ACO

ACOTheoretical analysis is difficult

Sequences of random decisions (not independent)

Probability distribution changes by iteration

Research is experimental rather than theoretical

Time to convergence uncertain (but convergence isgauranteed!)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Disadvanatges

Disadvantages of ACO

ACOTheoretical analysis is difficultSequences of random decisions (not independent)

Probability distribution changes by iteration

Research is experimental rather than theoretical

Time to convergence uncertain (but convergence isgauranteed!)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Disadvanatges

Disadvantages of ACO

ACOTheoretical analysis is difficultSequences of random decisions (not independent)Probability distribution changes by iteration

Research is experimental rather than theoretical

Time to convergence uncertain (but convergence isgauranteed!)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Disadvanatges

Disadvantages of ACO

ACOTheoretical analysis is difficultSequences of random decisions (not independent)Probability distribution changes by iterationResearch is experimental rather than theoretical

Time to convergence uncertain (but convergence isgauranteed!)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Disadvanatges

Disadvantages of ACO

ACOTheoretical analysis is difficultSequences of random decisions (not independent)Probability distribution changes by iterationResearch is experimental rather than theoreticalTime to convergence uncertain (but convergence isgauranteed!)

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Summary

Artificial Intelligence technique used to develop a newmethod to solve problems unsolvable since last manyyears

ACO is a recently proposed metaheuristic approach forsolving hard combinatorial optimization problems.

Artificial ants implement a randomized constructionheuristic which makes probabilistic decisions

ACO shows great performance with the “ill-structured”problems like network routing

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Summary

Artificial Intelligence technique used to develop a newmethod to solve problems unsolvable since last manyyears

ACO is a recently proposed metaheuristic approach forsolving hard combinatorial optimization problems.

Artificial ants implement a randomized constructionheuristic which makes probabilistic decisions

ACO shows great performance with the “ill-structured”problems like network routing

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Summary

Artificial Intelligence technique used to develop a newmethod to solve problems unsolvable since last manyyearsACO is a recently proposed metaheuristic approach forsolving hard combinatorial optimization problems.

Artificial ants implement a randomized constructionheuristic which makes probabilistic decisions

ACO shows great performance with the “ill-structured”problems like network routing

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Summary

Artificial Intelligence technique used to develop a newmethod to solve problems unsolvable since last manyyearsACO is a recently proposed metaheuristic approach forsolving hard combinatorial optimization problems.Artificial ants implement a randomized constructionheuristic which makes probabilistic decisions

ACO shows great performance with the “ill-structured”problems like network routing

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Summary

Artificial Intelligence technique used to develop a newmethod to solve problems unsolvable since last manyyearsACO is a recently proposed metaheuristic approach forsolving hard combinatorial optimization problems.Artificial ants implement a randomized constructionheuristic which makes probabilistic decisionsACO shows great performance with the “ill-structured”problems like network routing

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

References

M. Dorigo, M. Birattari, T. Stützle, “Ant Colony Optimization– Artificial Ants as a Computational IntelligenceTechnique”, IEEE Computational Intelligence Magazine,2006M. Dorigo K. Socha, “An Introduction to Ant ColonyOptimization”, T. F. Gonzalez, Approximation Algorithmsand Metaheuristics, CRC Press, 2007M. Dorigo T. Stützle, “The Ant Colony OptimizationMetaheuristic: Algorithms, Applications, and Advances”,Handbook of Metaheuristics, 2002

Introduction Main ACO Algorithms Applications of ACO Advantages and Disadvantages Summary References

Thank You.. Questions??