A Hybrid Approach of Dynamic Programming and Genetic Algorithm for Multi-criteria Optimization on Sustainable Architecture design

Abstract

This study deals with the design for manufacturing (DFM) of fractals created by a random walk called iterated function system (IFS). In particular, the DFM of an IFS-created fractal called Barnsley's fern-leaf is considered. The IFS dedicated for creating virtual models of a fern-leaf uses a set of four strictlycontracting affine mappings in the onto manner. The interactions among these mappings are studied in detail in order to identify some data structures. Based on the identified data structures, a DFM procedure is proposed. In the proposed DFM procedure, three out of the four mappings are employed in both the onto and one-to-one manner. The proposed DFM procedure is applied to the redesign of the shape (fern-leaf). Physical models of the redesigned fern-leaf are manufactured using both additive and subtractive manufacturing technologies (3-D printing and milling). The factors affecting accuracy of the physical models are also described. Although this study is limited to the shape of the fern-leaf, other IFS-created shapes can be redesigned using the proposed DFM procedure. Nevertheless, this study sheds some light on our understanding of how to develop more accurate physical models of IFS-created fractals.