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These terms allow to control global perimeter constraint and the occurrence of the intermediate solution values.
In order to have an efficient implementation and to make sure the strict satisfaction of such an upper-bound perimeter constraint, a diagonal quadratic approximation of the perimeter constraint is used in the construction of each explicit optimization subproblem.
Both the dual convex programming method and perimeter constraint scheme are used to optimize the 2D and 3D microstructures.
CMA-ES optimizes level set functions as design variables to minimize the fitness value that is regularized to avoid the ill-posedness of topology optimization using a perimeter constraint.
In addition to this, it is found that successive relaxations of the perimeter constraint by increasing the upper-bound tend to regularize the topology solution and result in a checkerboard free and satisfactory design solution without grey regions.
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We consider various objective functions with weight and perimeter constraints.
Then, a genetic algorithm was used to find an ellipse containing the maximum number of hypothesis points in an offset of its perimeter, considering some constraints.
In the form finding problem, we use the total length of cables as the objective functional and minimize it without or with considering the constraint condition of perimeter.
In the stiffness maximization problem, the compliance is used as the objective functional and minimized under the constraint condition of perimeter and total length of cables considering large deformation and small strain.
Then, we perform shape optimization of cable membrane structures in the stiffness maximization problem under the constraint conditions of total length of cables, membrane area, and membrane perimeter.
The reason Figure 4 contains data outside the perimeter of white dashed lines is that our implementation of SParSE does not utilize the parametric constraints other than to generate initial sets of reaction rates.
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