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Optimization

Optimization. Group 2: Zak Estrada, Chandini Jain, Jonathan Lai. Problem. Hierarchy of optimization methods. Our Hamiltonian. r i is the position of bead i V k is the number of vertices for bead k V 0 is the actual number of vertices bead k should make.

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Optimization

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  1. Optimization Group 2: Zak Estrada, Chandini Jain, Jonathan Lai

  2. Problem

  3. Hierarchy of optimization methods

  4. Our Hamiltonian • ri is the position of beadi • Vk is the number of vertices for beadk • V0 is the actual number of vertices beadk should make. • Kb = 1, kv = 1024 are force constants

  5. Our systems (Replace with pictures) • HCP • Sheared HCP • HCP with bottom half shifted by δx +0.2 • HCP with lower triangular half shifted by δx +0.2 δy +0.2 • Square lattice • Random lattice

  6. Hexagonal lattice vs sheared hexagonal lattice

  7. Code implementation • Java – Heavylifting • Software Java 1.6 • Python – Analysis • Tcl – Analysis

  8. Simulated Annealing • A couple of slides explaining the method

  9. Ant Colony • A couple of slides explaining the method

  10. Genetic Algorithm • A couple of slides explaining the method

  11. Go With The Winners

  12. Simulated Annealing Reconstruction Hexagonal lattice Sheared hexagonal lattice

  13. Comparison • Runtime/Number of iterations • AvgFinal Energy • Standard Deviation

  14. Different solutions

  15. Conclusion

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