2. What is Software Reliability ?
Reliability is usually defined in terms of a
statistical measure for the operation of a software
system without a failure occurring
Software reliability is a measure for the
probability of a software failure occurring

3. Swarm Intelligence
• “Swarm intelligence (SI) is artificial intelligence
based on the collective behaviour of
decentralized, self-organized systems”

4. Ant Colony Optimization (Li et al., 2010) is a
technique which uses probability to solve problems
where the computations are reduced with the help of
graphs to get efficient paths. Observing the behavior of
ants when they search for a path from their colony to the
food source, this algorithm was used to find the optimal
path. This concept has been expanded in solving a wide
variety of numerical problems. Many solutions have
been suggested based on different aspects of ant
behavior. ACO is a bionic simulated evolutionary
algorithm. ACO was applied to many optimization

5. Natural behavior of an ant
Foraging modes
•
•
•
•
•
•
Wander mode
Search mode
Return mode
Attracted mode
Trace mode
Carry mode

6. Natural behavior of ant

7. • The first ant finds the food source (F), via any way
(a), then returns to the nest (N), leaving behind a trail
pheromone (b)

8. Applications
•
•
•
•
Traveling Salesman Problem
Quadratic Assignment Problem
Network Model Problem
Vehicle routing

9. RELATING NATURE TO COMPUTER SCIENCE
NATURE
COMPUTER SCIENCE
Natural habitat
Graph (nodes and edges)
Nest and Food
Nodes in graph
Ants
Agents
Visibility
Reciprocal of distance
Pheromone
Artificial pheromone
Foraging behavior
Random walk through graph

10. ACO for the Traveling Salesman Problem
The TSP is a very important problem in the context
of Ant Colony Optimization because it is the
problem to which the original AS was first applied,
and it has later often been used as a benchmark to
test a new idea and algorithmic variants.
• It is a metaphor problem for the ant colony
• It is one of the most studied NP-hard problems in the combinatorial
optimization
• It is very easily to explain. So that the algorithm behavior is not
obscured by too many technicalities.

11. ACO Algorithm for TSP
Initialize
Place each ant in a randomly chosen city
For Each Ant
Choose NextCity(For Each Ant)
yes
more cities
to visit
No
Return to the initial cities
Update trace level using the tour cost for each ant
No
Stopping
criteria
yes
Print Best tour

12. Ant Colony Optimization (ACO) for TSP
Graph (N,E): where N = cities(nodes), E = edges
dij
= the tour cost from city i to city j (edge weight)
Ant move from one city i to the next j with some transition
probability.
B
A
D
C

13. [ ij ( t )] [
k
ij
p (t )
[
k allowed k
ik
ij
]
( t )] [
ik
if j allowedk
]
0
ij
otherwise
(t 1)
k
i, j
ij
(t )
ij
Q
if (i, j ) bestTour
Lk
0
otherwise

14. Some inherent advantages
• Positive Feedback accounts for rapid discovery of
good solutions
• The collective interaction of a population of agents.
Disadvantages in Ant Systems
• Slower convergence than other Heuristics
• Performed poorly for TSP problems larger than
75 cities.

15. Conclusion
• ACO is a relatively new meta heuristic approach for
solving hard combinatorial optimization problems.
• Artificial ants implement a randomized construction
heuristic which makes probabilistic decisions.
• The cumulated search experience is taken into account by
the adaptation of the pheromone trail.
• ACO shows great performance with the “ill-structured”
problems like network routing.
• In ACO local search is important to obtain good results.