Swarm Intelligence

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 http://www.scs.carleton.ca/~arpwhite/courses/95590Y/notes/SI%20Lecture%203.pdf

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. 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    For each particle         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

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 = 1to n for k = 1 to m Choose the next city to move by applying a probabilistic state transition rule (to be described) end for end for Update pheromone trails Until End_condition

41. Pheromone Intensity

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

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

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