Evolutionary Optimum Shape Design

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Evolutionary Optimum Shape Design

• S. Avendano1, M. Nicolau2, P.Petrovic3 and
  M.Quintana4
• 1Scottish Agricultural College 2University of
  Limerick3Norwegian University of Science and
  Technology4The University of Birmingham

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Problem

• Topological Optimum Design
• Physical properties of material
• Example 2D cantilever problem

• min Weight
• with constraints Dload lt Dlim

• EA approach

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Simplified problem

• 2D shapes
• Computationally expensive
• -gt Fake fitness
• similarity with predefined shapes

Challenge explore representations for better
shape design
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Approaches Voronoi Diagrams

• Genotype variable-length list of points with 0/1
  label

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Approaches Holes Representations

• Genotype variable-length list of rectangles

Schoenauer, 1995
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Approaches Holes Representations
(2)
(1)
(3)

• Genotype variable-length set of points with
  shape label

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Approaches Tree dividers

• GP-based evolutionary algorithm

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Experiments
Purpose explore representations

• Voronoi x Holes (3) x GP
• 5 shapes
• 20 runs each
• 35000 evaluations

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Results

• 8x8

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Results

• 32 x 32

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Conclusion

• Holes representation (all 3) performed better
  than Voronoi representation
• Promising GP-representation
• Simplified problem need to test on real
  mechanical problem

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Thank you for your attention!
Thanks Marc!!!

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Results

• 16 x 16

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Statistical Analysis

• 95 confidence interval

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Test shapes