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Constrained Molecular Dynamics as a Search and Optimization Tool

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. Introduction. Search and optimization algorithms take inspiration from many areas of science:

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Constrained Molecular Dynamics as a Search and Optimization Tool

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  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

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