Constrained Molecular Dynamics: Optimization Inspired by Physical Interactions

1. Constrained Molecular Dynamics as a Search and Optimization Tool Riccardo Poli Department of Computer Science University of Essex Christopher R. Stephens Instituto de Ciencias Nucleares UNAM

2. R. Poli - University of Essex Introduction • Search and optimization algorithms take inspiration from many areas of science: • Evolutionary algorithms biological systems • Simulated annealing physics of cooling • Hopfield neural networks physics of spin glasses • Swarm algorithms social interactions

3. R. Poli - University of Essex Lots of other things in nature know how to optimise!

4. R. Poli - University of Essex Minimisation by Marbles

5. R. Poli - University of Essex Minimisation by Buckets of Water

6. R. Poli - University of Essex Minimisation by Buckets of Water

7. R. Poli - University of Essex Minimisation by Buckets of Water

8. R. Poli - University of Essex Minimisation by Buckets of Water

9. R. Poli - University of Essex Minimisation by Waterfalls

10. R. Poli - University of Essex Minimisation by Skiers

11. R. Poli - University of Essex Minimisation by Molecules

12. R. Poli - University of Essex Constrained Molecular Dynamics • CMDis an optimisation algorithm inspired to multi-body physical interactions (molecular dynamics). • A population of particles are constrained to slide on the fitness landscape • The particles are under the effects of gravity, friction, centripetalacceleration, and couplingforces (springs).

13. R. Poli - University of Essex Some math (because it looks good  ) • Kinetic energy of a particle

14. R. Poli - University of Essex Some more math • Equation of motion for a particle

15. R. Poli - University of Essex Forces for Courses: No forces • If v=0 then CMD=kind of random search

16. R. Poli - University of Essex Forces for Courses: No forces • If v0 then CMD=parallel search guided by curvature 1/6

17. R. Poli - University of Essex Forces for Courses: No forces • If v0 then CMD=parallel search guided by curvature 2/6

18. R. Poli - University of Essex Forces for Courses: No forces • If v0 then CMD=parallel search guided by curvature 3/6

19. R. Poli - University of Essex Forces for Courses: No forces • If v0 then CMD=parallel search guided by curvature 4/6

20. R. Poli - University of Essex Forces for Courses: No forces • If v0 then CMD=parallel search guided by curvature 5/6

21. R. Poli - University of Essex Forces for Courses: No forces • If v0 then CMD=parallel search guided by curvature. 6/6

22. R. Poli - University of Essex Forces for Courses: Gravity • Minimum seeking behaviour • If E small + friction  hillclimbing behaviour 1/5

23. R. Poli - University of Essex Forces for Courses: Gravity • Minimum seeking behaviour • If E small + friction  hillclimbing behaviour 2/5

24. R. Poli - University of Essex Forces for Courses: Gravity • Minimum seeking behaviour • If E small + friction  hillclimbing behaviour 3/5

25. R. Poli - University of Essex Forces for Courses: Gravity • Minimum seeking behaviour • If E small + friction  hillclimbing behaviour 4/5

26. R. Poli - University of Essex Forces for Courses: Gravity • Minimum seeking behaviour • If E small + friction  hillclimbing behaviour. 5/5

27. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 1/11

28. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 2/11

29. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 3/11

30. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 4/11

31. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 5/11

32. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 6/11

33. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 7/11

34. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 8/11

35. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 9/11

36. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour 10/11

37. R. Poli - University of Essex Forces for Courses: Gravity • If E big  skier-type,local-optima-avoiding behaviour. 11/11

38. R. Poli - University of Essex Forces for Courses: Interactions • Particle-particle interactions (springs) • Springs integrate information across the population of particles (a bit like crossover in a GA). • Without friction  oscillatory/exploratory search behaviour (similar to PSOs) • With friction  exploration focuses (like in a GA)

39. R. Poli - University of Essex Forces for Courses: Interactions 1/12

40. R. Poli - University of Essex Forces for Courses: Interactions 2/12

41. R. Poli - University of Essex Forces for Courses: Interactions 3/12

42. R. Poli - University of Essex Forces for Courses: Interactions 4/12

43. R. Poli - University of Essex Forces for Courses: Interactions 5/12

44. R. Poli - University of Essex Forces for Courses: Interactions 6/12

45. R. Poli - University of Essex Forces for Courses: Interactions 7/12

46. R. Poli - University of Essex Forces for Courses: Interactions 8/12

47. R. Poli - University of Essex Forces for Courses: Interactions 9/12

48. R. Poli - University of Essex Forces for Courses: Interactions 10/12

49. R. Poli - University of Essex Forces for Courses: Interactions 11/12

50. R. Poli - University of Essex Forces for Courses: Interactions. 12/12