Swarm Intelligence and Optimization

A brief overview of the relationship between Swarm Intelligence and Mathematical Optimization

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1. Swarm Intelligence Doug Stephen Algorithms Monday, April 1, 13
2. A Brief Discussion on Swarm Intelligence Algorithms Monday, April 1, 13
3. A Brief Discussion on Swarm Intelligence Algorithms Optimization Theory Monday, April 1, 13
4. A Brief Discussion on Swarm Intelligence Algorithms Optimization Theory Biological motivation Monday, April 1, 13
5. A Brief Discussion on Swarm Intelligence Algorithms Optimization Theory Biological motivation Problem Mapping Monday, April 1, 13
6. Swarm Intelligence Algorithms are rooted in Optimization Theory Monday, April 1, 13
7. Monday, April 1, 13
8. Optimization Monday, April 1, 13
9. Optimization ➡ Minimize or maximize a value Monday, April 1, 13
10. Optimization ➡ Minimize or maximize a value ➡ Based on the objective(s) and contraint(s). Monday, April 1, 13
11. Optimization ➡ Minimize or maximize a value ➡ Based on the objective(s) and contraint(s). ➡ Has an uncountable number of applications Monday, April 1, 13
12. Optimization ➡ Minimize or maximize a value ➡ Based on the objective(s) and contraint(s). ➡ Has an uncountable number of applications ➡ Operations/Industrial Systems Monday, April 1, 13
13. Optimization ➡ Minimize or maximize a value ➡ Based on the objective(s) and contraint(s). ➡ Has an uncountable number of applications ➡ Operations/Industrial Systems ➡ Path planning Monday, April 1, 13
14. Optimization ➡ Minimize or maximize a value ➡ Based on the objective(s) and contraint(s). ➡ Has an uncountable number of applications ➡ Operations/Industrial Systems ➡ Path planning ➡ Simulation/Physics Monday, April 1, 13
15. Optimization ➡ Minimize or maximize a value ➡ Based on the objective(s) and contraint(s). ➡ Has an uncountable number of applications ➡ Operations/Industrial Systems ➡ Path planning ➡ Simulation/Physics ➡ Dynamical system analysis Monday, April 1, 13
16. Example Monday, April 1, 13
17. Example Monday, April 1, 13
18. Example Monday, April 1, 13
19. But Optimization is Tough Monday, April 1, 13
20. But Optimization is Tough Systems don’t always lend themselves to exploitable Matrix structures Monday, April 1, 13
21. But Optimization is Tough Monday, April 1, 13
22. But Optimization is Tough This means optimization can be very expensive; you may frequently see the quali ers “online” & “of ine” optimization Monday, April 1, 13
23. So how does all of this relate to swarms? Monday, April 1, 13
24. Nearly Perfectly. Monday, April 1, 13
25. Swarm workers frequently need to perform tasks that lend well to optimization Monday, April 1, 13
26. Swarm-type problems are also frequently related to search, another eld married to optimization. Monday, April 1, 13
27. However, swarm- type problems frequently need to leverage heuristics or metaheuristics Monday, April 1, 13
28. Costs Monday, April 1, 13
29. Costs Energy Use Monday, April 1, 13
30. Costs Monday, April 1, 13
31. Costs Time Monday, April 1, 13
32. Costs Monday, April 1, 13
33. Costs Path Length Monday, April 1, 13
34. Constraints Monday, April 1, 13
35. Constraints Energy Available Monday, April 1, 13
36. Constraints Monday, April 1, 13
37. Constraints Time to nish Monday, April 1, 13
38. Constraints Monday, April 1, 13
39. Constraints Articulation Monday, April 1, 13
40. Constraints Monday, April 1, 13
41. Constraints Behavior Monday, April 1, 13
42. Constraints Monday, April 1, 13
43. Constraints Collisions Monday, April 1, 13
44. For Example Monday, April 1, 13
45. Particle Swarm Optimization Monday, April 1, 13
46. Particle Swarm Optimization Given a search space de ned by a cost function and a collection of randomly initialized particles, attempt to converge the particles on the minimum. Monday, April 1, 13
47. Ant Colony Optimization Monday, April 1, 13
48. Ant Colony Optimization Find the shortest path in a graph using a decay and positive feedback Monday, April 1, 13
49. Problem Mapping Monday, April 1, 13
50. Problem Mapping The trick is to map a real optimization problem to the modeled behavior, like Ant Colony to Graph traversal. Monday, April 1, 13
51. Swarms are complex systems with trivial individual behavior that could lead to many solutions. So we try to nd the best one. In Essence… Monday, April 1, 13
52. We optimize by translating our cost in to “space”, our solutions in to “agents”, and then we prod them until they stumble on the answer. In Essence… Monday, April 1, 13
53. This can include actually moving around in space, solving a non- physical problem, or presenting a novel model for non-trivial analysis. In Essence… Monday, April 1, 13
54. Slides Available on Speaker Deck https://speakerdeck.com/dljsjr/swarm-intelligence-and-optimization Monday, April 1, 13