The document discusses ant colony optimization, an algorithm inspired by the foraging behavior of ants. It describes how ants communicate indirectly via pheromone trails to find the shortest paths between their nests and food sources. The algorithm emulates this behavior in artificial ant colonies to solve discrete optimization problems. It outlines various applications of the algorithm to routing problems, assignment problems, scheduling problems, and machine learning. In conclusion, it praises ant colony optimization as an intuitive, effective algorithm with many successful applications and variants.

1. Introduction Biological Inspiration The Algorithm Applications Conclusions
ANT COLONY OPTIMIZATION: THE ALGORITHM
AND ITS APPLICATIONS
Muhammad Adil Raja
Roaming Researchers, Inc.
July 31, 2014

2. Introduction Biological Inspiration The Algorithm Applications Conclusions
OUTLINE
1 INTRODUCTION
2 BIOLOGICAL INSPIRATION
3 THE ALGORITHM
4 APPLICATIONS
5 CONCLUSIONS

3. Introduction Biological Inspiration The Algorithm Applications Conclusions
OUTLINE
1 INTRODUCTION
2 BIOLOGICAL INSPIRATION
3 THE ALGORITHM
4 APPLICATIONS
5 CONCLUSIONS

4. Introduction Biological Inspiration The Algorithm Applications Conclusions
OUTLINE
1 INTRODUCTION
2 BIOLOGICAL INSPIRATION
3 THE ALGORITHM
4 APPLICATIONS
5 CONCLUSIONS

5. Introduction Biological Inspiration The Algorithm Applications Conclusions
OUTLINE
1 INTRODUCTION
2 BIOLOGICAL INSPIRATION
3 THE ALGORITHM
4 APPLICATIONS
5 CONCLUSIONS

6. Introduction Biological Inspiration The Algorithm Applications Conclusions
OUTLINE
1 INTRODUCTION
2 BIOLOGICAL INSPIRATION
3 THE ALGORITHM
4 APPLICATIONS
5 CONCLUSIONS

7. Introduction Biological Inspiration The Algorithm Applications Conclusions
ANT COLONY OPTIMIZATION
A valuable technique for mathematical optimization.
Takes inspiration from foraging behavior of real ant
colonies.
Useful for discrete and continuous optimization problems.
In telecommunications: Routing and load balancing.

8. Introduction Biological Inspiration The Algorithm Applications Conclusions
BIOLOGICAL INSPIRATION
Inception – early 90’s.
Observation of Ant colonies.
Ants are social insects.
Driven by the goal of community survival rather than being
focused on survival of the individuals.
Ant’ foraging behavior: How ants can find shortest paths.
Shortest Paths: Between food sources and their nests.

9. Introduction Biological Inspiration The Algorithm Applications Conclusions
FORAGING BEHAVIOR OF ANTS
When searching for food ants:
1 Initially explore the area surrounding their nest in a random
manner.
2 Leave a chemical pheromone trail on the ground.
3 Ants can smell pheromone.
4 While choosing their way, they choose paths with strong
pheromone concentrations with strong probabilities.
5 Evaluate the quality and quantity of a food source as soon
as it is found.
6 Carry some of it back to the nest.
7 The quantity of pheromone that is left on the ground may
depend on the quantity and quality of the food source.
8 The pheromone trails guide other ants back to the food
source.

10. Introduction Biological Inspiration The Algorithm Applications Conclusions
BENEFITS
Indirect communication between ants enables them to find
shortest paths between nests and food sources.
Communication happens through pheromone trails.
Stigmergy: The Phenomenon
Enables them to find shortest paths between their nests
and food sources.

11. Introduction Biological Inspiration The Algorithm Applications Conclusions
THE ALGORITHM
1 Initialize trail.
2 Let each ant complete its tour.
3 Local trail update (evaporate pheromone).
4 Analyze tours.
5 Perform a global trail update.
6 Go back to step 2 and loop until your stopping criteria is
met.

12. Introduction Biological Inspiration The Algorithm Applications Conclusions
ROUTING PROBLEMS
One or more agents have to visit a predefined set of
locations.
Objective function depends on the ordering in which the
locations are visited.
Sequential ordering problem.
Vehicle routing problem.

13. Introduction Biological Inspiration The Algorithm Applications Conclusions
SEQUENTIAL ORDERING PROBLEM
To find a minimum weight Hamiltonian path on a directed
graph with weights on arcs and nodes subject to
precedence constraints.

14. Introduction Biological Inspiration The Algorithm Applications Conclusions
VEHICLE ROUTING PROBLEM
A central problem in distribution management.
N customers have to be served from one central dept.
The customers are served by a fleet of vehicles of equal
capacity.
The goal is to find a set of routes that minimizes the total
travel time such that:
1 Each customer is served once by exactly one vehicle.
2 The route of each vehicle starts and ends at the depot.
3 The total demand covered by each vehicle does not exceed
its capacity.
VRP is is an NP-hard problem.
It contains TSP as a subproblem.

15. Introduction Biological Inspiration The Algorithm Applications Conclusions
ASSIGNMENT PROBLEMS
The task is to assign a set of items to a given number of
resources subject to some constraints.
Items: Objects, activities etc.
Resources: Locations, agents, etc.

16. Introduction Biological Inspiration The Algorithm Applications Conclusions
QUADRATIC ASSIGNMENT
Can be described as the problem of assigning a set of
facilities to a set of locations with given distances between
locations and given flows between the facilities.
The goal is to place the facilities on locations in such a way
that the sum of the products between flows and distances
is minimized.
Backboard wiring, campus and hospital layout, typewriter
keyboard design can all be formulated as QAPs.
QAP is an NP-hard optimization problem.

17. Introduction Biological Inspiration The Algorithm Applications Conclusions
GENERALIZED ASSIGNMENT
A set of tasks has to be assigned to a set of agents in such
a way that a cost function is minimized.

18. Introduction Biological Inspiration The Algorithm Applications Conclusions
FREQUENCY ASSIGNMENT
We have a set of links, a set of frequencies, and channel
separation constraints.
For each pair of links, channel separation constraints give
a minimum distance to be maintained between between
the frequencies assigned to the links.

19. Introduction Biological Inspiration The Algorithm Applications Conclusions
GRAPH COLORING PROBLEMS
Given an undirected graph the goal is to find the minimum
number of colors to assign to nodes such that no pair of
adjacent nodes is assigned the same color.

20. Introduction Biological Inspiration The Algorithm Applications Conclusions
UNIVERSITY COURSE TIMETABLING PROBLEMS
Given are a set of time slots, a set of events, a set of
rooms, a set of features, a set of students, and two types of
constraints; hard and soft constraints.
Hard constraints have to be satisfied by any feasible
solution.
Soft constraints do not concern the feasibility of a solution
but determine its quality.
The goal is to assign the events to the time slots and to the
rooms so that all hard constraints are satisfied
And an objective function, whose value depends on the
number of violated soft constraints, is optimized.

21. Introduction Biological Inspiration The Algorithm Applications Conclusions
SCHEDULING PROBLEMS
Scheduling is concerned with the allocation of scarce
resources to tasks over time.
Scheduling problems are central to production and
manufacturing industries, but also arise in a variety of other
settings.
Shop scheduling: where jobs have to processed on one or
several machines such that some objective function is
optimized.
In case jobs have to be processed on more than one
machine, the task to be performed on a machine for
completing a job is called an operation.
It is common for almost all the machine scheduling models
that:
1 The processing times of all jobs and operations are fixed
and known beforehand.
2 The processing of jobs and operations cannot be
interrupted (scheduling without preemption)

22. Introduction Biological Inspiration The Algorithm Applications Conclusions
SUBSET PROBLEMS
A solution to the problem under consideration is
represented as a subset of the set of available items
(components) subject to problem-specific constraints.

23. Introduction Biological Inspiration The Algorithm Applications Conclusions
APPLICATION OF ACO TO OTHER NP-HARD PROBLEMS
Shortest Common Super-sequence problem.
Bin Packing
2D-HP protein folding.
COnstraint satisfaction.

24. Introduction Biological Inspiration The Algorithm Applications Conclusions
APPLICATIONS TO MACHINE LEARNING PROBLEMS
Learning of classification rules.
Learning the structure of Bayesian networks.

25. Introduction Biological Inspiration The Algorithm Applications Conclusions
CONCLUSIONS
A great algorithm.
Bio-inspiration is the key.
Emulation of real ant foraging behavior to artificial ant
colonies.
Easy to comprehend.
Many variants.
Many applications.
Problem formulation is the real trick.
Inspiration (reference): Ant Colony Optimization, Marco
Dorigo and Thomas Stutzle.