Swarm algorithms

1. Swarm algorithms COMP308

2. Swarming – The Definition • aggregation of similar animals, generally cruising in the same direction • Termites swarm to build colonies • Birds swarm to find food • Bees swarm to reproduce

3. Swarming is Powerful • Swarms can achieve things that an individual cannot

4. Powerful … but simple All evidence suggests: • No central control • Only simple rules for each individual • Emergent phenomena • Self-organization

5. Harness this Power out of Simplicity • Technical systems are getting larger and more complex • Global control hard to define and program • Larger systems lead to more errors • Swarm intelligence systems are: • Robust • Relatively simple (How to program a swarm?)

6. Swarming – Example • Bird Flocking • “Boids” model was proposed by Reynolds • Boids = Bird-oids (bird like) • Only three simple rules

7. Collision Avoidance • Rule 1: Avoid Collision with neighboring birds

8. Velocity Matching • Rule 2: Match the velocity of neighboring birds

9. Flock Centering • Rule 3: Stay near neighboring birds

10. Define the neighborhood • Model the view of a bird • Only local knowledge, only local interaction • Affects the swarm behavior (fish vs. birds)

11. Swarming - Characteristics • Simple rules for each individual • No central control • Decentralized and hence robust • Emergent • Performs complex functions

12. Ant Colony Optimization - Biological Inspiration • Inspired by foraging behavior of ants. • Ants find shortest path to food source from nest. • Ants deposit pheromone along traveled path which is used by other ants to follow the trail. • This kind of indirect communication via the local environment is called stigmergy. • Has adaptability, robustness and redundancy.

13. Foraging behavior of Ants • 2 ants start with equal probability of going on either path.

14. Foraging behavior of Ants • The ant on shorter path has a shorter to-and-fro time from it’s nest to the food.

15. Foraging behavior of Ants • The density of pheromone on the shorter path is higher because of 2 passes by the ant (as compared to 1 by the other).

16. Foraging behavior of Ants • The next ant takes the shorter route.

17. Foraging behavior of Ants • Over many iterations, more ants begin using the path with higher pheromone, thereby further reinforcing it.

18. Foraging behavior of Ants • After some time, the shorter path is almost exclusively used.

19. Generic ACO • Formalized into a metaheuristic. • Artificial ants build solutions to an optimization problem and exchange info on their quality vis-à-vis real ants. • A combinatorial optimization problem reduced to a construction graph. • Ants build partial solutions in each iteration and deposit pheromone on each vertex.

20. Ant Colony Metaheuristic • ConstructAntSolutions: Partial solution extended by adding an edge based on stochastic and pheromone considerations. • ApplyLocalSearch: problem-specific, used in state-of-art ACO algorithms. • UpdatePheromones: increase pheromone of good solutions, decrease that of bad solutions (pheromone evaporation).

21. Thinking is Social • Direct/Indirect communication • Social science can be used to perform combinatorial optimization • Adaptive Culture Model contains most of ingredients that will be used in the more sophisticated practical swarm algorithms • Similarity between pairs of individuals can result in spread of culture.

22. Culture Model (Axelrod, 1997) • Model of the spread of culture with social interactions • Individuals represented by symbolic strings (as in GAs), and arranged on a 2-D grid • Probability of agent interaction increases with agents’ similarity • Algorithm – Randomly select an agent – Randomly select a neighbor of the agent – Probability of interaction = (# shared string values)/(string length) – If interact, then copy value on one feature of neighbor’s string to the agent’s string • Behavior – Preservation of different cultures in same world – Increased local harmony over time – Similarity-based interaction creates distinct boundaries

24. Adaptive Culture Model (Kennedy & Eberhart, 1997) • Agents interact with each other based not on similarity, but on performance – Behavior is not only based on fads, but on results – “If neighbor’s sum is larger than my sum, then interact” -> “99999” – “If neighbor’s first 3 numbers are close to last 2 numbers (compared to my numbers), then interact” -> pockets of “17769” and “83193” • Can solve the Traveling salesman problem • Behavior – Preservation of different cultures in the same world – Increased local harmony over time

26. A Hard Function • Problem is considered intractable if the amount of time required to solve it increases at a faster-then-polynomial rate as the size of the problem increases. • For instance Travelling Salesman Problem (TCP) requires finding the shortest path through a set of nodes without passing through any node twice, and ending at the starting point • With each additional city the number of possible solutions grows exponentially: with N nodes there are NN possible combinations of nodes and N! “legal” tours. (NP-complete problem)