This document discusses ant colony optimization (ACO), a metaheuristic technique for finding optimal paths or solutions. ACO is inspired by how ants find the shortest path to food. It can be used to solve complex optimization problems like routing parcels between cities. The algorithm works by simulating "pheromone trails" that ants leave to mark paths, and determining the next steps probabilistically based on the pheromone levels. Over multiple iterations, the paths with higher pheromone become more desirable, until the optimal solution emerges. As an example, the document outlines how ACO can be applied to solve the traveling salesman problem of finding the shortest route between multiple cities.

1. ANT COLONY OPTIMIZATION
(ACO)
DESIGN OPTIMIZATION TECHNIQUES
Presented by
K. Magesh
17ME325
I yr M.Tech. PDM
PONDICHERRY ENGINEERING COLLEGE
Subject handling Staff
Dr. V. Anandhan
Professor
Mechanical Engineering

2. WHY ACO IS DEVELOPED?
• We take an example of a courier company in
Germany which has to dispatch parcels in
various cities
Let no. of Parcels to be delivered = 40
• To save time, we need to find the fastest routes
between the cities
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3. • No. of possible routes interconnecting these
40 cities is found to be 815 Quattuordocillion
possibilities, i.e., numerically equal to one 8
followed by 47 zeros (8 x 1047)
• ACO serves as the best
optimization tool to find the
optimum in these complex
situations
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4. BIOLOGY BEHIND ACO
• Ants are blind
• Every ant has some liquid in their body, which
is called as a pheromone, similar to harmones
and enzymes in human body
• Ant secrete one type of pheromone when they
go in search of food
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5. CHARACTERISTICS OF
PHEROMONE
• Pheromone evaporates as time goes on
• It grows in density if ants travel repeatedly in
same path
• After finding the minimum distant path, the
pheromone in the other trails evaporate
completely
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6. TYPICAL EXAMPLE
Image courtesy : www.stuartreid.co.za
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7. ANT COLONY OPTIMIZATION
• ACO was first developed by Marco Dorigo in
1992
• ACO is a probabilistic technique for solving
highly computational problems
• It is based on foraging behaviour of ants
(Swarm Intelligence)
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8. SOLVING A TRAVELLING
SALESMAN PROBLEM USING
ACO

9. ASSUMPTIONS
• All the cities should be visited by the ants, but
only once., no repetition is allowed
• Initial Pheromone level is assumed to be
constant for every path
HOME DESTINATION
ONE TOUR
(ONE
ITERATION)
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10. ACO ALGORITHM FOR TSP
I. Randomly place all the ants in the cities. Let m
= no.of cities and n = no. of ants. ‘m’ may or
may not be equal to n
II. Assume initial pheromone level and problem
constants α, β. Let the initial pheromone level
τij =1
10
A
B
C
1
2
3
1
1
1
A
B
C

11. III. (i) For ant 1, choose an optimum ‘not yet visited’ city until
one tour is completed
ηij – Visibility (1/distance)
pk
ij – Probability of choosing a city ( for kth ant )
(ii) Calculate the cumulative probabilities and compare with
a random number ‘r’.
(iii) The path with immediately greater probability than ‘r’ is
chosen
(iv) Repeat the step III until the tour of ant 1 is completed
11
B
A
1
C

12. IV.Find the total length of the tour Lk for ant 1
Evaporate the pheromone level after ant 1
completes its tour
V. Update the pheromone level after ant 1
completes its tour
Where Δτk = Q/Lk
Q – constant ,usually equals to 1
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13. VI.Repeat all the steps for ant 2,3,…n. Find the
optimum path and update the pheromone
levels. The path with highest pheromone
level is the optimum path
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14. REFERENCES
• ‘Tutorial On Ant Colony Optimization’ by Budi Santosa,
Professor, Industrial Engineering, Institut Teknologi Sepuluh
Nopember, ITS, Surabaya
• Engineering Optimization – theory and Practice by Singaresu S
Rao – 4th Edition
• Solving travelling salesman problem by Ant Colony Algorithm
by Jayathra Majumdar, Barrackpore Rastraguru Sundaranath
College
• Practical Genetic algorithms by Randy L Haupt and Sue Ellen
Haupt
• Jinhui Yang, Xiaohu Shi, Mariso Marchese, Yanchun, ‘LiangAn
ant colony optimization method for generalized TSP problem’
Progress in Natural Science ( Elsevier) – 2008
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15. THANK YOU
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