Topology optimization of conductive heat transfer problems using parametric L-systems

Generative encodings have the potential of improving the performance of evolutionary algorithms. In this work we apply parametric L-systems, which can be described as developmental recipes, to evolutionary topology optimization of widely studied two-dimensional steady-state heat conduction problems. We translate L-systems into geometries using the turtle interpretation, and evaluate their objective functions, i.e. average and maximum temperatures, using the Finite Volume Method (FVM). The method requires two orders of magnitude fewer function evaluations, and yields better results in 10 out of 12 tested optimization problems (the result is statistically significant), than a reference method using direct encoding. Further, our results indicate that the method yields designs with lower average temperatures than the widely used and well established SIMP (Solid Isotropic Material with Penalization) method in optimization problems where the product of volume fraction and the ratio of high and low conductive material is less or equal to 1. Finally, we demonstrate the ability of the methodology to tackle multi-objective optimization problems with relevant temperature and manufacturing related objectives.