1. Algorithms and their Applications CS2004 (2012-2013)
Dr Stephen Swift
14.1 Ant Colony Optimisation and Particle Swarm Optimisation

2. Previously On CS2004… So far we have looked at:
Concepts of computation and algorithms
Comparing algorithms
Some mathematical foundation
The Big-Oh notation
Computational complexity
Data structures
Sorting algorithms
Hill Climbing and Simulated Annealing
Tabu Search and Iterated Local Search
Applications and Optimisation
Genetic Algorithms
Evolutionary Computation and Related Topics
Ant Colony Optimisation and Particle Swarm Optimisation

3. This Lecture In this lecture we are going to cover: Swarm Intelligence
Ant Colony Optimisation
Particle Swarm Optimisation
Ant Colony Optimisation and Particle Swarm Optimisation

4. Swarm Intelligence A new field of study
<25 years old
Before the mid 80s Artificial Intelligence (AI) was:
Symbol based
Focused on reasoning, knowledge, planning, ...
New problem domains emerged that involved the environment changing dynamically
E.g. telecommunications and scheduling
These problems cannot be framed by calculations and simple algorithms
Holland’s Genetic Algorithm created a new way of thinking
Behaviour based AI
Intelligence is controlled by a set of independent semi autonomous modules
Ant Colony Optimisation and Particle Swarm Optimisation

5. Recap: Complexity
The interaction of many simple parts creating complex behaviour
Not to be confused with Computational Complexity) – but easily done!
The net effect is greater than the sum of the individuals, e.g. ant colonies
Emergent behaviour as a side effect of the system
Often incorporates elements of Chaos Theory, Artificial Life and Artificial Intelligence
Ant Colony Optimisation and Particle Swarm Optimisation

6. Social Insects Several million years of success
Efficient
Flexible
Robust
Can solve many problems:
Find food, feed the brood, defend the nest
Build a nest …
Ant Colony Optimisation and Particle Swarm Optimisation

7. Flocking “Boids” model created by Craig Reynolds in 1987
Boids =“bird-oid” objects (also schooling fish)
Video links:
Only three simple rules …
Ant Colony Optimisation and Particle Swarm Optimisation

8. Boid Rules Rule 1: Separation Rule 2: Alignment Rule 3: Cohesion
Steer to avoid crowding local flock-mates
Rule 2: Alignment
Steer towards the average heading of local flock-mates
Rule 3: Cohesion
Steer to move toward the average position of local flock-mates
Ant Colony Optimisation and Particle Swarm Optimisation

9. Swarm Intelligence – Part 1
First used by Beni, Hackwood and Wang in 1989 for work on cellular robotic systems
Later: for anything swarm inspired
Ant Colony Optimisation and Particle Swarm Optimisation

10. Swarm Intelligence – Part 2
Study of collective behaviour of decentralised, self-organised systems
No central control
Only simple rules for each individual
Simple but extremely powerful
The problems are usually difficult to define
Solutions result from the behaviour and interactions between individual agents
Solutions are emergent in the systems
Ant Colony Optimisation and Particle Swarm Optimisation

11. Swarm Intelligence Algorithms
Most Popular Algorithms
Ant Colony Optimisation (ACO)
Particle Swarm Optimisation (PSO)
More esoteric
Bacteria Colony Optimisation
Plant Propagation Algorithms
Strawberry Plant
Ant Colony Optimisation and Particle Swarm Optimisation

12. Ant Colony Optimisation
First proposed by Marco Dorigo in 1992
A Heuristic optimisation method inspired by biological systems
A multiple agent based approach for solving difficult combinatorial optimisation problems
Mainly Graph based problems
Traveling Salesman, vehicle routing, sequential ordering, graph colouring, routing in communications networks, etc…
Ant Colony Optimisation and Particle Swarm Optimisation

13. Ant Behavior Ants (blind) navigate from nest to food sources
The shortest path is discovered via pheromone trails
Each ant moves at random
Pheromone is deposited onto the path
Ants detect the lead ants path and are inclined to follow
More pheromone on the path means an increased probability of the path being followed
Pheromone upgrade: evaporation
Ant Colony Optimisation and Particle Swarm Optimisation

14. Dealing With Obstacles
The more ants follow a trail, the more attractive to follow that trail becomes
Ant Colony Optimisation and Particle Swarm Optimisation

15. Stigmergy
Indirect coordination/communication between agents or actions
Individual behaviour modifies the environment, which in turn modifies the behaviour of other individuals
Stimulates the performance of subsequent actions leading to the spontaneous emergence of coherent, apparently systematic activity
Reduces (or eliminates) communications between agents
Supports efficient collaboration between simple agents
Produces complex, seemingly intelligent structures, without need for any planning, control, or even direct communication between the agents
Ant Colony Optimisation and Particle Swarm Optimisation

16. Route Selection
At the beginning of the search process, a constant amount of pheromone is assigned to all arcs
When located at a node i an ant k uses the pheromone trail to compute the probability of choosing j as the next node:
The probability is zero for nodes that are unreachable from node i
Similar to Roulette Wheel Selection in a Genetic Algorithm
Ant Colony Optimisation and Particle Swarm Optimisation

17. Pheromone Update
The pheromone value of an arc (i,j) is updated when traversed by ant k as follows:
The probability of an arc being taken by subsequent ants is proportional to how “good” it was deemed by ants that have already traversed it
Ant Colony Optimisation and Particle Swarm Optimisation

18. Pheromone Evaporation
The pheromones “evaporate” by applying the following equation to all the arcs:
Here p  (0,1) is a parameter
An iteration is a complete cycle involving the ant’s movement, pheromone depositing and pheromone evaporation
Ant Colony Optimisation and Particle Swarm Optimisation

19. ACO Flowchart Have the stopping criteria been met?
START
Have the
stopping
criteria been
met?
Locate ants randomly
at different nodes
YES NO
Determine the shortest
tour until now and
update pheromone
STOP
Determine probabilistically
as to which node to visit next NO
Record the length of
tour
Is the
trail
complete?
Move to next node
YES
Ant Colony Optimisation and Particle Swarm Optimisation

20. ACO Advantages Can be used in dynamic applications
Adapts to changes such as new distances, etc…
Similar to GAs, good choice for constrained discrete problems
Not a gradient based algorithm
Performs better against other global optimisation techniques
Neural Networks, Genetic Algorithms, Simulated Annealing, under certain conditions
Convergence is “guaranteed”
Compared to GAs (Genetic Algorithms):
Retains memory of the colony instead of previous generation only
Less affected by poor initial solutions (due to combination of random path selection and colony memory)
Ant Colony Optimisation and Particle Swarm Optimisation

21. ACO Disadvantages Theoretical analysis is difficult
Due to sequences of random decisions (not independent)
Probability distribution changes by iteration
Research is experimental rather than theoretical
Time to convergence uncertain
Slower convergence sometimes than other Heuristics
Performed poorly for large scale problems
E.g. more than 75 cities when solving the TSP
No centralised processor to guide the ants towards good solutions
Ant Colony Optimisation and Particle Swarm Optimisation

22. ACO Applications
Graph based and combinatorial optimisation type problems, e.g.
TSP (Travelling Salesman Problem)
Vehicle Routing
Graph Colouring
Timetable Scheduling
Manufacturing Scheduling
Network Routing
Etc...
Ant Colony Optimisation and Particle Swarm Optimisation

23. Particle Swarm Optimisation (PSO)
It was developed in 1995 by James Kennedy (social psychologist) and Russell Eberhart (electrical engineer)
Population based stochastic optimisation technique
It uses a number of agents (particles) that constitute a swarm moving around in the search space looking for the best solution
Each particle is treated as a point in an n-dimensional space which adjusts its “flying” according to its own flying experience as well as the flying experience of other particles
Ant Colony Optimisation and Particle Swarm Optimisation

24. PSO Concepts – Part 1
Each particle keeps track of its coordinates in the solution space and associated fitness, along with the best solution and fitness it has achieved so far
This value is called the personal best, pbest
The PSO algorithm also tracks the best value obtained so far by any particle in swarm
This value is called the global best, gbest
The basic concept of PSO lies in accelerating each particle toward its pbest and the gbest locations, with a random weighted acceleration at each time step
Ant Colony Optimisation and Particle Swarm Optimisation

25. PSO Concepts – Part 2
Each particle tries to modify its position using the following information:
The current position
The current velocity
The distance between the current position and pbest
The distance between the current position and gbest
Ant Colony Optimisation and Particle Swarm Optimisation

26. PSO Concepts – Part 3 y x sk : current position in the search space
sk+1: modified position
vk: current velocity
vk+1: modified velocity
vpbest: velocity based on pbest
vgbest: velocity based on gbest
Ant Colony Optimisation and Particle Swarm Optimisation

27. PSO Update Formulae  (inertia), and  are parameters...
Particle i velocity at iteration k+1
Particle i best position
Particle i position at iteration k
Position of global best
 (inertia), and  are parameters...
Ant Colony Optimisation and Particle Swarm Optimisation

28. Loop until max iterations
PSO Flow Chart
START
Initialise particles with random position
and velocity vectors
For each particle’s position (p)
evaluate fitness
Loop until all particles exhausted
If fitness(p) better than
fitness(pbest) then pbest= p
Loop until max iterations
Update gbest
Update particles velocity and position
STOP: giving gbest, optimal solution
Ant Colony Optimisation and Particle Swarm Optimisation

29. PSO Simulation 1 max y min fitness x search space
Ant Colony Optimisation and Particle Swarm Optimisation

30. PSO Simulation 2 max y min fitness x search space
Ant Colony Optimisation and Particle Swarm Optimisation

31. PSO Simulation 3 max y min fitness x search space
Ant Colony Optimisation and Particle Swarm Optimisation

32. PSO Simulation 4 max y min fitness x search space
Ant Colony Optimisation and Particle Swarm Optimisation

33. PSO Simulation 5 max y min fitness x search space
Ant Colony Optimisation and Particle Swarm Optimisation

34. PSO Simulation 6 max y min fitness x search space
Ant Colony Optimisation and Particle Swarm Optimisation

35. PSO Simulation 7 max y min fitness x search space
Ant Colony Optimisation and Particle Swarm Optimisation

36. PSO Simulation 8 max y min fitness x search space
Ant Colony Optimisation and Particle Swarm Optimisation

37. PSO Comparison With EC No selection operation in PSO
All particles in PSO are kept as members of the population through the course of the run
PSO is the only algorithm (population based Heuristic search) that does not implement the survival of the fittest operator
No crossover operator in PSO
The PSO update formulae resembles mutation in EP (Evolutionary Programming)
In EP, the balance between the global and local search can be adjusted through a number of parameters, whilst in PSO the balance is achieved through the inertial weight factor ()
Ant Colony Optimisation and Particle Swarm Optimisation

38. Next Lecture We will be talking about:
Bin packing
Data clustering
The laboratory will involve looking at an number of simulations of ACO and PSO
Not assessed but useful revision!
Ant Colony Optimisation and Particle Swarm Optimisation