Ant colonyoptimization

Ant Colony Optimization

GUIDED BY:- Mr. Deepak Kr. Mohanty Assistant. Professor Dept. of IT OEC

PRESENTED BY:-

Varun Kumar

Registration no:-1101211468

Roll no:-113036

Dept. of IT

3/2/2014 11:18 AM 2

CONTENT

• Introduction

• History

• Working Principle

• Applications of ACO

• Advantages and Disadvantages

• Summary

• Bibliography

Seminar Presentation on Ant Colony Optimization

3/2/2014 11:18 AM 3

INTRODUCTION

Seminar Presentation on Ant Colony Optimization

• The Ant Colony Optimization algorithm (ACO) is

a probabilistic technique for solving computational

problems which can be reduced to finding good

paths through graph.

• Searching for optimal path in the graph

based on behaviour of ants seeking a path

between their colony and source of food.

3/2/2014 11:18 AM Seminar Presentation on Ant Colony Optimization

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Ant Colony Optimization Concept

• Ants navigate from nest to food

source.

• Shortest path is discovered via

pheromone trails.

• Each ant moves at random

pheromone is deposited on path

• More pheromone on path increases

probability of path being followed


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.

•The majority of ants follow the short path

Double bridge experiments: different lengths


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Double bridge experiments: same lengths


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History

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

his PhD thesis in 1992.

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

in 1996

3. Ant Colony was developed by Gambardella Dorigo

in 1997


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Meta-heuristic Optimization

1. Heuristic method for solving a very general class of

computational problems by combining user-given

heuristics in the hope of obtaining a more efficient

procedure.

2. ACO is meta-heuristic

3. Soft computing technique for solving hard

discrete optimization problems


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The ACO Meta-heuristic

ACO Set Parameters, Initialize pheromone trails

SCHEDULE ACTIVITIES • Construct Ant Solutions

• Daemon Actions (optional)

• Update Pheromones

• Virtual trail accumulated on path segments


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Ants’ Foraging Behaviours and Optimization


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The ACO Met-heuristic Construct Ant Solutions

An ant will move from node i to node j with

probability(pseudorandom proportional rule)

where Tĳ is the amount of pheromone on edge if; j

𝛼 is a parameter to control the influence of ilk

Nͥͥĳ is the desirability of edge if; j (typically 1=dill )

𝛽 is a parameter to control the influence of ηij


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The ACO Met heuristic Pheromone Update

Amount of pheromone is updated according to the equation

Tĳ = 1 − 𝜌 𝑇ĳ + ∆𝑇ĳ

Where,

Tĳ is the amount of pheromone on a given edge ij

𝜌 is the rate of pheromone evaporation

∆Tĳ is the amount of pheromone deposited, typically given

by

∆Tĳͫ= 1/Lᶬ if ant m travels on edge ij

0 otherwise

Where

Lᶬ is the cost of the MTh ant’s tour (typically length).


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Ant Colony Optimization ACO System

Overview of the System • Path selected at random based on

amount of "trail" present on possible paths from starting node.

• Ant reaches next node, selects next path

• Continues until reaches starting node • Finished tour is a solution. • Tour is analysed for optimality


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Main ACO Algorithms ACO


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Algorithms Application

• For illustration, example problem used is Travelling

Salesman Problem.


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Ant System ACO - Ant System

• First ACO algorithm to be proposed (1992)

• Pheromone values are updated by all the ants that have completed

the tour. Tĳ ←(1-𝜌).Tĳ + ∆𝑇ĳᵐ𝑘

𝑚=1 (local pheromone update) Where 𝜌 is the evaporation rate k is the number of ants ∆Tĳᵐ is pheromone quantity laid on edge ( ij) by the Mth ∆Tĳᵐ = 1/Lᵐ if ant m travels on edge if ij 0 otherwise where Lᵐ is the tour length of the Mth ant


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Ant Colony System

ACO - Ant Colony System • First major improvement over Ant System • Differences with Ant System: 1 Decision Rule - Pseudorandom proportional rule 2 Local Pheromone Update 3 Best only offline Pheromone Update


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MAX-MIN Ant System

Differences with Ant System:

1. Best only offline Pheromone Update

2. Min and Max values of the pheromone are

explicitly limited

• Tĳ is constrained between Tmin𝑎𝑛𝑑 𝑇𝑚𝑎𝑥

(explicitly set by algorithm designer).

• After pheromone update, 𝑇ĳ is set to 𝑇𝑚𝑎𝑥

𝑖𝑓 𝑇ĳ > 𝑇𝑚𝑎𝑥

and to 𝑇ĳ < 𝑇𝑚𝑖𝑛.


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Applications of ACO

ACO

• Routing in telecommunication networks

• Traveling Salesman

• Graph Colouring

• Scheduling

• Constraint Satisfaction


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Advantages

• Inherent parallelism

• Positive Feedback accounts for rapid

discovery of good solutions

• Efficient for Traveling Salesman

Problem and similar problems

• Can be used in dynamic applications

(adapts to changes such as new

distances, etc.)


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• 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 is guaranteed!

Disadvantages


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Summary

• Artificial Intelligence technique used to develop a new

method to solve problems unsolvable since last many

years

• ACO is a recently proposed meta-heuristic approach for

solving hard combinatorial optimization problems.

• Artificial ants implement a randomized construction

heuristic which makes probabilistic decisions

• ACO shows great performance with the “ill-structured”

problems like network routing


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Bibliography

• M. Dorito, M. Brattain, T. Stutz, “Ant Colony

Optimization

• – Artificial Ants as a Computational Intelligence

• Technique”, IEEE Computationnel Intelligence

Magazine, 2006

• M. Dorito K. Sochi, “An Introduction to Ant Colony

• Optimization”, T. F. Gonzalez, Approximation

Algorithms and Meta-heuristics, CRC Press, 2007

• M. Dorito T. Stutz, “The Ant Colony Optimization

• Meta-heuristic: Algorithms, Applications, and

Advances”, *Handbook of Meta-heuristics, 2002

Thank You………….Questions…?


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Education

Ant colonyoptimization