Swarm Intelligence Technique ACO and Traveling Salesman Problem

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 04 Issue: 08 | Aug -2017 www.irjet.net p-ISSN: 2395-0072
© 2017, IRJET | Impact Factor value: 5.181 | ISO 9001:2008 Certified Journal | Page 1002
Swarm Intelligence Technique ACO and Traveling Salesman Problem
Harsh Bhalani1, Dr. Seema Mahajan2, Prof. Zalak Vyas3
1Student, Dept. of Computer Engineering, Indus University, Gujarat, India.
2Head of the Dept. , Dept. of Computer Engineering, Indus University, Gujarat, India.
3Assistant Professor , Dept. of Computer Engineering, Indus University, Gujarat, India.
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Abstract – A swarm is a large number of homogenous,
simple agents interacting locally among themselves, andtheir
environment. Swarm Intelligence (SI) can be defined as a
relatively new branch of Artificial Intelligence that is used to
model the collective behavior of social swarms in nature. The
inspiration often comes from nature, especially biological
systems. The social interactions among swarmindividuals can
be either direct or indirect. Examples of direct interaction are
through visual or audio contact, such as the waggle dance of
honey bees. Indirect interaction occurs when one individual
changes the environment and the other individualsrespond to
the new environment, such as the pheromone trails of ants
that they deposit on their way to search for food sources.
Examples in natural system SI include bacterial growth, ant
colonies, bird flocking, and microbiological intelligence. This
paper comprises a snapshot of ant colony optimization
algorithm with its application in Traveling Salesman problem
(TSP).
Key Words: Swarm Intelligence (SI), Artificial Intelligence
(AI), Ant Colony Optimization (ACO), and Traveling
Salesman Problem (TSP).
1. INTRODUCTION
The various techniques of swarm intelligence used by
researchers are as follows:
1. Particle Swarm Optimization
2. Ant Colony Optimization
3. Bees Algorithm
4. Artificial Bee Colony Algorithm
5. Differential evolution
6. Artificial Immune System
7. Bat Algorithm
8. Glowworm Swarm Optimization
9. Gravitational Search Algorithm
We mainly discuss the Ant Colony Optimization (A.C.O)
algorithm in this paper.
1.1 Ant Colony Optimization
In 1991, Ant Colony Optimization (ACO) was
introduced by M. Dorigo and colleagues for the solution of
hard combinatorial optimization (CO) problems.ACOdraws
inspiration from the social behavior of ant colonies. It is a
shown in Fig-1.
A. Ants in a pheromone trail between nest and food
B. An obstacle interrupts the trail
C. Ants find two paths to go around the obstacle
D. A new pheromone trail is formed along the shorter
path
Fig -1: Pattern of path following by Ants
1.1.1 Ant Colony Optimization Metaheuristic
As shown in the basic flow of ACO in Fig-2, the
objective of ACO’s third step is toconstructantsolutions(i.e.,
find the quality paths on the problem’s construction graph)
by stochastically moving through neighbor nodes of the
graph.

Fig -2: Basic Flow chart of ACO
Ants are driven by a probability rule to
sequentially choose the solution components that make use
of pheromone trail intensities and heuristic information.
Where:
 is the probability of the kth ant to move
from node i to node j at the tth
iteration/time step.
 is the set of nodes in the neighborhood of
the kth ant in the tth node.
 is the pheromone amount on the arc
connecting node i and node j,
weighted by α.
 is the heuristic value of the arc connecting
node i and node j, weighted by β.
 The heuristic value is usually a non-increasing
function in the moving cost
from node i to node j.
 α and β are weight parameters that control the
relative importance of the pheromone versus
heuristic information, and application depend
constant.
The pheromone trail updated by all ants in the iteration.
Ants select nextvertex bya stochasticfunction
which depends on both pheromone and problem-
specific heuristic .
1.1.2. ACO Example: Traveling Salesman Problem
In TSP, the goal is to find the shortest possible tour
from the salesman’s home city to a finite number of
customer cities with only one constraint that each city must
be visited just once before finally returning to the starting
home city.
There are many different ways to translate the
above principles into a computational system apt to solve
the TSP. In our ant colony system (ACS) an artificial ant k in
city r chooses the city s to move to among those whichdonot
belong to its working memory by applying the following
probabilistic formula:
where τ(r,u) is the amount of pheromone trail on edge (r,u),
ɲ(r,u) is a heuristic function, which was chosen to be the
inverse of the distance between cities r and u, β is a
parameter which weighs the relative importance of
pheromone trail and of closeness, q is a value chosen
randomly with uniform probability in [0,1], q0 (0≤q0≤1)isa
parameter, and S is a random variable selected according to
the following probability distribution, which favors edges
which are shorter and have a higher level of pheromone
trail:
where (r,s) is the probability with which ant k chooses
to move from city r to city s.
Local updating is intended to avoid a very strong
edge being chosen by all the ants: Every
time an edge is chosen by an ant its amount of pheromone is
changed by applying the local trail
updating formula:

where is a parameter. Local trail updating is also
motivated by trail evaporation in real ants.
Typical parameter settings for TSP are: m = n (i.e.,
number of ants = number of cities), α = 1, β=2 to 5, ρ=0.5,
and = .
1.2. ACS: Ant Colony System
Ant Colony System has been introduced to improve
Ant System’s performance. ACSdiffersin3mainfactorsfrom
Ant System. ACS uses a more aggressive action choice rule
than AS. Second is that, the pheromone is added only to arcs
that belong to global best solution. Third, wheneverantuses
an arc (i, j) to move from city i to city j, it removes some
pheromone from the arc.
In ACS, ants choose the next city by using the
pseudo-random-proportional action choice rule:
When located at city I, ant k moves, with probability q0, to
city l. It is the best possible move as decided by learned
pheromone trails and heuristic information.
In ACS, only global best ant is allowed to add
pheromone after every iteration. Thus, the update is
modified to
Here, it is important to note that the trail updateonlyapplies
to the arcs of the global-best tour.
Aditionally to the global updatingrule,theantsusea
local update rule that they apply after having crossed an arc
during the tour construction:
where is parameter.The effect of this is to
make an already chosen arc less desirable. So that
exploration of not yet visited arcs is increased.
2. CONCLUSIONS
This paper presents an approach for solving
Traveling Salesman Problem based on ant colony algorithm.
The improved version of ACO algorithmbasedonAntColony
System is also presented, which gives a better solution of
traveling salesman problem compared to ACO algorithm.
REFERENCES
[1] Ant colonies for Traveling Salesman Problem.
TR/IRIDIA/1996-3
- Marco Dorigo & Luca Gambardella
[2] M. Dorigo and T. Stützle. Ant Colony Optimization.
MIT press, Cambridge, MA, 2004
[3] M. Dorigo, M. Birattari, T. Stuzle, Ant Colony
Optimization, Artificial Ants as a Computational
Intelligence Technique, IEEE Computational
Intelligence Magazine, November 2006.
[4] Y. Zhang, Z-l.Pei, J-h.Yang, Y-c. Liang, An Improved
Ant Colony Optimization Algorithm Based onRoute
Optimization and Its Applications in Traveling
Salesman Problem, IEEE 2007. 1-42441509-8.
[5] Swarm Intelligence: Concepts, Models and
Application
-Hazem Ahmed & Janice I. Glasgow

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