ant colony optimization algorithms : introduction and beyond
TRANSCRIPT
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??