Distributed MAP-Elites and its Application in Evolutionary Design

Abstract

Quality-Diversity search is the process of finding diverse solutions within the search space which do not sacrifice performance. MAP-Elites is a quality-diversity algorithm which measures n phenotypes/behaviours of a solution and places it into an $n$-dimensional hypercube based off its phenotype values. This thesis proposes an approach to addressing MAP-Elites' problem of exponential growth of hypercubes. The exponential growth of evaluation and computational time as the phenotypes/behaviours grow is potentially worse for optimization performance. The exponential growth in individuals results in the user being given too many candidate solutions at the end of processing. Therefore, MAP-Elites highlights diversity, but with the exponential growth, the said diversity is arguably impractical.

This research proposes an enhancement to MAP-Elites with Distributed island-model evolution. This will introduce a linear growth in population as well as a reasonable number of candidate solutions to consider. Each island consists of a two dimensional MAP which allows for a realistic analysis and visualization of these individuals. Since the system increases on a linear scale, and MAP-Elites on an exponential scale, high-dimensional problems will show an even greater decrease in total candidate solution counts, which aids in the realistic analysis of a run. This system will then be tested on procedural texture generation with multiple computer vision fitness functions. This Distributed MAP-Elites algorithm was tested against vanilla GP, island-model evolution, and traditional MAP-Elites on multiple fitness functions and target images. The proposed algorithm was found, at the very minimum, to be competitive in fitness to the other algorithms and in some cases outperformed them. On top of this performance, when visually observing the best solutions, the algorithm was found to have been able to produce visually interesting textures.