1. Swarm Intelligence
虞台文

2. Content Overview Swarm Particle Optimization (PSO)
Example
Ant Colony Optimization (ACO)

3. Swarm Intelligence
Overview

4. Swarm Intelligence
Collective system capable of accomplishing difficult tasks in dynamic and varied environments without any external guidance or control and with no central coordination
Achieving a collective performance which could not normally be achieved by an individual acting alone
Constituting a natural model particularly suited to distributed problem solving

5. Swarm Intelligence

6. Swarm Intelligence

7. Swarm Intelligence

8. Swarm Intelligence

9. Swarm Intelligence

10. Swarm Intelligence Particle Swarm Optimization (PSO)
Basic Concept

11. The Inventors Russell Eberhart James Kennedy electrical engineer
social-psychologist

12. Particle Swarm Optimization (PSO)
Developed in 1995 by James Kennedy and Russell Eberhart.
Particle Swarm Optimization (PSO)
PSO is a robust stochastic optimization technique based on the movement and intelligence of swarms.
PSO applies the concept of social interaction to problem solving.

13. PSO Search Scheme
It uses a number of agents, i.e., particles, that constitute a swarm moving around in the search space looking for the best solution.
Each particle is treated as a point in a N-dimensional space which adjusts its “flying” according to its own flying experience as well as the flying experience of other particles.

14. Particle Flying Model
pbest  the best solution achieved so far by that particle.
gbest  the best value obtained so far by any particle in the neighborhood of that particle.
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.

15. Particle Flying Model

16. Particle Flying Model
Each particle tries to modify its position using the following information:
the current positions,
the current velocities,
the distance between the current position and pbest,
the distance between the current position and the gbest.

17. Particle Flying Model

18. PSO Algorithm * ** For each particle Initialize particle END Do
        Calculate fitness value
        If the fitness value is better than the best fitness value (pbest) in history             set current value as the new pbest
   End
   Choose the particle with the best fitness value of all the particles as the gbest
   For each particle
        Calculate particle velocity according equation (*)
        Update particle position according equation (**)
   End
While maximum iterations or minimum error criteria is not attained

19. Swarm Intelligence Particle Swarm Optimization (PSO)
Examples

20. Schwefel's Function

21. Simulation  Initialization

22. Simulation  After 5 Generations

23. Simulation  After 10 Generations

24. Simulation  After 15 Generations

25. Simulation  After 20 Generations

26. Simulation  After 25 Generations

27. Simulation  After 100 Generations

28. Simulation  After 500 Generations

29. Summary Iterations gBest 416.245599 5 515.748796 10 759.404006 15 5 10 15 20
100
5000
Optimun

30. Exercises Compare PSO with GA
Can we use PSO to train neural networks? How?

31. Particle Swarm Optimization (PSO)
Ant Colony Optimization (ACO)

32. Facts
Many discrete optimization problems are difficult to solve, e.g., NP-Hard
Soft computing techniques to cope with these problems:
Simulated Annealing (SA)
Based on physical systems
Genetic algorithm (GA)
based on natural selection and genetics
Ant Colony Optimization (ACO)
modeling ant colony behavior

33. Ant Colony Optimization

34. Background
Introduced by Marco Dorigo (Milan, Italy), and others in early 1990s.
A probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs.
They are inspired by the behaviour of ants in finding paths from the colony to food.

35. Typical Applications TSP  Traveling Salesman Problem
Quadratic assignment problems
Scheduling problems
Dynamic routing problems in networks

36. Natural Behavior of Ant

37. ACO Concept Ants (blind) navigate from nest to food source
Shortest path is discovered via pheromone trails
each ant moves at random, probabilistically
pheromone is deposited on path
ants detect lead ant’s path, inclined to follow, i.e.,
more pheromone on path increases probability of path being followed

38. ACO System Virtual “trail” accumulated on path segments
Starting node selected at random
Path selection philosophy
based on amount of “trail” present on possible paths from starting node
higher probability for paths with more “trail”
Ant reaches next node, selects next path
Continues until goal, e.g., starting node for TSP, reached
Finished “tour” is a solution

39. ACO System , cont. A completed tour is analyzed for optimality
“Trail” amount adjusted to favor better solutions
better solutions receive more trail
worse solutions receive less trail
higher probability of ant selecting path that is part of a better-performing tour
New cycle is performed
Repeated until most ants select the same tour on every cycle (convergence to solution)

40. Ant Algorithm for TSP Randomly position m ants on n cities Loop
for step = 1 to n
for k = 1 to m
Choose the next city to move by applying
a probabilistic state transition rule (to be described)
end for
Update pheromone trails
Until End_condition

41. Pheromone Intensity

42. Ant Transition Rule visibility :
Probability of ant k going from city i to j:
visibility :
the set of nodes applicable
to ant k at city i

43. Ant Transition Rule Probability of ant k going from city i to j:
 = 0 : a greedy approach
 = 0 : a rapid selection of tours that may not be optimal.
Thus, a tradeoff is necessary.

44. Pheromone Update Q: a constant Tk(t): the tour of ant k at time t
Lk(t): the tour length for ant k at time t

45. Demonstration