A Genetic Algorithm-Based Methodology for the Structural Optimization of Voronoi Flat Roofs

Voronoi tessellations are a mathematical concept that appears in many examples in nature, such as the skin of giraffes, dry soil, and vegetable cells. In the context of biomimicry, these tessellations have been used to build impressive structures worldwide that are both aesthetically pleasing and structurally efficient. This paper proposes a methodology based on genetic algorithms (GA) to determine the structural topology of Voronoi flat roofs with tubular steel cross sections and a given boundary. The design variables correspond to the number and position of the Voronoi centers that form the tessellations within the roof, as well as the dimensions of the structural elements. This representation of the design variables creates an unstructured optimization problem. Such characteristic is addressed by an implicit redundant representation of possible solutions, which generates chromosomes with varying numbers of variables. The objective function relates to the weight of the roof, considering constraints raised in technical and constructive issues. The methodology was applied to four different roof boundaries: triangular, pentagonal, square, and rhombic. In general, the results provide optimal aesthetic solutions with a few Voronoi tessellations, based on the algorithm configuration and the multimodal nature of the search space. Convergence analysis indicates the possibility of the algorithm getting stuck in an optimum local and shows the progressive reduction of Voronoi centers. Lastly, it is observed that the maximum displacement constraint leads to the shape of the optimal roof.