Solution and Fitness Evolution (SAFE): Coevolving Solutions and Their Objective Functions

Abstract: We recently highlighted a fundamental problem recognized to confound algorithmic optimization, namely, \textit{conflating} the objective with the objective function. Even when the former is well defined, the latter may not be obvious, e.g., in learning a strategy to navigate a maze to find a goal (objective), an effective objective function to \textit{evaluate} strategies may not be a simple function of the distance to the objective. We proposed to automate the means by which a good objective function may be discovered -- a proposal reified herein. We present \textbf{S}olution \textbf{A}nd \textbf{F}itness \textbf{E}volution (\textbf{SAFE}), a \textit{commensalistic} coevolutionary algorithm that maintains two coevolving populations: a population of candidate solutions and a population of candidate objective functions. As proof of principle of this concept, we show that SAFE successfully evolves not only solutions within a robotic maze domain, but also the objective functions needed to measure solution quality during evolution.