The concept of evolvability, that is the capacity to produce heritable and adaptive phenotypic variation, is crucial in the current understanding of evolution. However, while its meaning is intuitive, there is no consensus on how to quantitatively measure it. As a consequence, it is hard to evaluate the interplay between evolvability and fitness and its dependency on key factors like the evolutionary algorithm (EA) or the representation of the individuals. Here, we propose to use MAP-Elites, a well-established Quality Diversity EA, as a support structure for measuring evolvability and for highlighting its interplay with fitness. We map the solutions generated during the evolutionary process to a MAP-Elites-like grid and then visualize their fitness and evolvability as maps. This procedures does not affect the EA execution and can hence be applied to any EA: it only requires to have two descriptors for the solutions that can be used to meaningfully characterize them. We apply this general methodology to the case of Voxel-based Soft Robots, a kind of modular robots with a body composed of uniform elements whose volume is individually varied by the robot brain. Namely, we optimize the robots for the task of locomotion using evolutionary computation. We consider four representations, two for the brain only and two for both body and brain of the VSR, and two EAs (MAP-Elites and a simple evolutionary strategy) and examine the evolvability and fitness maps. The experiments suggest that our methodology permits to discover interesting patterns in the maps: fitness maps appear to depend more on the representation of the solution, whereas evolvability maps appear to depend more on the EA. As an aside, we find that MAP-Elites is particularly effective in the simultaneous evolution of the body and the brain of Voxel-based Soft Robots.
