Ant colony optimization (ACO) is a metaheuristic technique introduced in the 1990s based on the behavior of ants seeking food. The methodology involves ants probabilistically constructing solutions and adjusting pheromone trails based on solution quality over multiple iterations. ACO has proven effective for optimization problems like the traveling salesman problem by rapidly finding good solutions. While it works well experimentally, the theoretical analysis of ACO is difficult given its experimental nature.

1.  Swapnil S. Shahade

2.  Abstract
 Introduction
 History
 Methodology Of ACO
 Experiment on Ants
 How do Ants find the path
 Probability
 Update Pheromone
 Flow Chart
 Application
 Traveling Salesman Problem
 Advantages
 Disadvantage
 Conclusion
 References

3.  Ant colony optimization is a technique for optimization that
was introduced in the early 1990’s.
 Research on a new metaheuristic for optimization.
 After experimental work scientist has practical interest of the
method.
 Researchers try to deepen their understanding of the
method’s functioning not only through experiments but also
by building a theory.

4.  In the early 1990s, ant colony optimization (ACO) was introduced by M.
Dorigo.
 Metaheuristic for the solution of hard combinatorial optimization (CO)
problems.
 Using this method obtain good solutions to hard combinatorial
optimization (CO) problems in minimum time.
 For food, ants initially travel in a random manner.
 Ant finds a food source, during the return trip, the ant deposits a chemical
pheromone trail on the ground.
 The quantity of pheromone deposited, which may depend on the quantity
and quality of the food, will guide other ants to the food source.

5. 1991, M. Dorigo proposed the Ant System in his doctoral
thesis (which was published in 1992).
1996, Hoos and Stützle invent the MAX-MIN Ant System.
1997, Dorigo and Gambardella publish the Ant Colony
System.

6. Methodology Of ACO

7.  Equal length double bridge
 Different length double bridge

9. An ant will move from node i to
node j with probability
Where - τi,j is the amount of pheromone on edge i,j
α is a parameter to control the influence of τi,j
ηi,j is the desirability of edge i,j (typically 1/di,j)
β is a parameter to control the influence of ηi,j
 




ilil
ijij
ij
p

10. Amount of pheromone is updated
according to the equation
τi,j = (1−ρ)τi,j + ∆τi,j
k

12. Traveling salesman
Graph coloring
Multiple knapsack
Routing in telecommunication networks
Scheduling

14. Where, Xi & Yi -- Coordinates of i city.
Xj & Yj -- Coordinates of j city.
TSP is an problem and researchers have been studying
to develop efficient solving methods since 1950’s.
Because it is so easy to describe and so difficult to solve.
A complete weighted graph G = (N, E) can be used to
represent a TSP, where N is the set of n cities and E is the set of
edges (paths) fully connecting all cities. Each edge (i,j) ∈ E is
assigned a cost dij, which is the distance between cities i and j.
dij can be defined in the Euclidean space and is given as
follows.

16.  Rapid discovery of good solutions.
 Efficient for Traveling Salesman Problem and similar
problems.

17.  Theoretical analysis is difficult.
 Research is experimental rather than theoretical.

18. Ant colony optimization (ACO) is a heuristic algorithm
which has been proven a successful technique and applied to a
number of optimization problems and is taken as one of the high
performance computing methods for Traveling salesman problem
(TSP).

19. M. Dorigo, Stützle T. Ant Colony Optimization. MIT Press; 2004
M. Dorigo, M. Birattari, T. Stützle, “Ant Colony Optimization –
Artificial Ants as a Computational Intelligence Technique”, IEEE
Computational Intelligence Magazine, 2006.
M. Dorigo, “An Introduction to Ant Colony Optimization”, T. F.
Gonzalez, Approximation Algorithms and Meta-heuristics, CRC
Press, 2007