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LabelMover optimization benchmark

parametric analysis, finite element optimization

Here are LabelMover optimization benchmarks.

  • linear1.
    Move square's right edge to the right in order to get the maximal cross-section area. The movement range is 0..1.
    The optimized value is linearly dependent upon 1 optimization parameter.
    Reference: 2. QuickField: 1.9981 (0.1%)
    Maximal area =?


  • linear1_11.
    There are 11 squares. Move each square's right edge in order to get the maximal total cross-section area. Each edge can be moved independently.
    The optimized value is linearly dependent upon 11 optimization parameters.
    Reference: 22. QuickField: 21.928 (0.33%)
    Maximal total area =?


  • linear2.
    Move square's right and top edges right and up correspondingly in order to get the maximal cross-section area. The movement range for each edge is 0..1.
    The optimized value is linearly dependent upon 2 optimization parameters.
    Reference: 4. QuickField: 3.9836 (0.4%)
    Maximal area =?


  • linear3.
    Move square's 3 edges (right, left and top) in order to get the maximal cross-section area. The movement range for each edge is 0..1.
    The optimized value is linearly dependent upon 3 optimization parameters.
    Reference: 6. QuickField: 5.9674 (0.54%)
    Maximal area =?


  • linear1_2
    Move square's right edge by its two vertices moving right independently in order to get the maximal cross-section area. The movement range for each vertex is 0..1.
    The optimized value is linearly dependent upon 2 optimization parameter.
    Reference: 2. QuickField: 1.9967 (0.17%)
    Maximal area =?


  • square1.
    Move half-circle's right vertex in order to get the maximal cross-section area. The movement range is 0..1.
    The optimized value is square dependent upon 1 optimization parameter.
    Reference: 3.5343, QuickField: 3.5271 (0.2%)
    Maximal area =?


  • nonlinear1.
    Move common boundary 1-1 of rectangle and half-circle in order to get the minimal area.
    Half circle cross section is S1=π/2·(x/2)².
    The rectangle cross section is S2=0.5·(1-x).
    The optimal parameter value is x=2/π.
    Reference: 0.6366, QuickField: 0.6366 (0.0%)
    Maximal total area =?


  • cubic1.
    Move half-circle's right vertex in order to get the maximal volume. Axisymmetric model represents sphere. The sphere volume is calculated. The movement range is 0..1.
    The optimized value is cubic dependent on 1 optimization parameter
    Reference: 14.1372, QuickField: 14.094 (0.31%)
    Maximal volume =?


  • nonlinear2.
    Volume of sphere and cylinder is minimized
    The sphere volume is V1=4π/3·(x/2)³. Rectangle in axisymmetric model represents a cylinder. Its volume can be calculated as V2=π·0.5²·(1-x).
    The optimal parameter value is x=1/sqrt(2).
    Reference: 0.7071, QuickField: 0.7059 (0.17%)
    Minimal total volume =?
  • nonlinear3.
    Minimization of the total length of the lines connecting the internal point of the rectangle with its vertices. Optimal position of the internal point should be in the intersection of the diagonals.
    Reference: 5.6569, QuickField: 5.6569 (0%)
    Minimal lines length =?


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