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Using Evolutionary Computation to explore geometry and topology without ground structures

Using Evolutionary Computation to explore geometry and topology without ground structures. IASS-IACM 2008 Ithaca, NY USA. Dr. –Ing. Peter von Buelow University of Michigan TCAUP 30 May 2008. What are ground structures?. Definition

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Using Evolutionary Computation to explore geometry and topology without ground structures

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  1. Using Evolutionary Computation to explore geometry and topology without ground structures IASS-IACM 2008 Ithaca, NY USA Dr. –Ing. Peter von Buelow University of Michigan TCAUP 30 May 2008 Peter von Buelow University of Michigan 1 / 37

  2. What are ground structures? Definition A set of all admissible bars connecting a set of admissible joints. (Dorn, et al. 1964) Peter von Buelow University of Michigan 2 / 37

  3. Examples of ground structures 12 nodes and 39 bars (Deb et al., 1999) 210 nodes and 21945 (max) bars (Klarbring, 1995) Peter von Buelow University of Michigan 3 / 37

  4. Effect of ground structure on results with EC • Ground structures have 2 effects on EC: • Results • Resolution • Geometry • Topology • Computation • Chromosome • Population • Analysis Peter von Buelow University of Michigan 4 / 37

  5. Effect of ground structure on results With ground structure (505 kg) without ground structure (322 kg) Other topologies found without using ground structure Peter von Buelow University of Michigan 5 / 37

  6. Effect of ground structure on GA computationGA computation depends on chromosome string length Length = 39 (actually used) Size of ground structure ½ of the incidence matrix Length = n(n-1)/2 = 45 Length = 21945 (all possible) Length = 153 Peter von Buelow University of Michigan 6 / 37

  7. Distinction of geometry and topology definitions Peter von Buelow University of Michigan 7 / 37

  8. Encoding Topology without ground structure ‘binary string’ from incidence matrix Peter von Buelow University of Michigan 8 / 37

  9. Breeding Topology one-point crossover Peter von Buelow University of Michigan 9 / 37

  10. Encoding Geometry without ground structure Array of real number nodal coordinates Peter von Buelow University of Michigan 10 / 37

  11. Breeding Geometry Half Uniform Crossover breeding Peter von Buelow University of Michigan 11 / 37

  12. Procedure M - the master sends and gathers all topologies S - each slave finds geometry for each topology Peter von Buelow University of Michigan 12 / 37

  13. Geometry Generations Random start with progenitor Peter von Buelow University of Michigan 13 / 37

  14. Geometry Generations Selection from generation 1 Peter von Buelow University of Michigan 14 / 37

  15. Geometry Generations Setup parents for generation 2 Peter von Buelow University of Michigan 15 / 37

  16. Geometry Generations Breed parents to fill generation 2 Peter von Buelow University of Michigan 16 / 37

  17. Geometry Generations Select best for parents in next generation Peter von Buelow University of Michigan 17 / 37

  18. Geometry Generations Setup parents for next generation Peter von Buelow University of Michigan 18 / 37

  19. Geometry Generations Breed parents for next generation Peter von Buelow University of Michigan 19 / 37

  20. Geometry Generations Cycle 1 Generations 4-6 Peter von Buelow University of Michigan 20 / 37

  21. Geometry Generations Cycle 1 Generations 26-28 Peter von Buelow University of Michigan 21 / 37

  22. Geometry GA Best from one cycle Peter von Buelow University of Michigan 22 / 37

  23. Topology Generations Mutate progenitor to start topology cycle Peter von Buelow University of Michigan 23 / 37

  24. Topology Generations Select best for next generation Peter von Buelow University of Michigan 24 / 37

  25. Topology Generations Set selection as parents for next generation Peter von Buelow University of Michigan 25 / 37

  26. Topology Generations Breed parents to obtain full generation Peter von Buelow University of Michigan 26 / 37

  27. Topology Generations Select best from full generation Peter von Buelow University of Michigan 27 / 37

  28. Topology Generations Set selection as parents for next generation Peter von Buelow University of Michigan 28 / 37

  29. Topology Generations Breed parents to obtain full generation Peter von Buelow University of Michigan 29 / 37

  30. Topology Best individuals from cycles 1- 4 All individualsfrom cycle 1 Peter von Buelow University of Michigan 30 / 37

  31. Topology selection list of ‘pretty good’ solutions Peter von Buelow University of Michigan 31 / 37

  32. Bridge Design automatic generation list of ‘pretty good’ solutions Peter von Buelow University of Michigan 32 / 37

  33. Interactive Group Design Idea generator Peter von Buelow University of Michigan 33 / 37

  34. User Selections Peter von Buelow University of Michigan 34 / 37

  35. Final Bridge Design Peter von Buelow University of Michigan 35 / 37

  36. 3D Trusses Peter von Buelow University of Michigan 36 / 37

  37. 3D Trusses Peter von Buelow University of Michigan 37 / 37

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