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

We recently highlighted a fundamental problem recognized to confound algorithmic optimization, namely, $\mathit{\text{conflating}}$ 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 $\mathit{\text{evaluate}}$ 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 $\mathbf{\text{S}}$olution $\mathbf{\text{A}}$nd $\mathbf{\text{F}}$itness $\mathbf{\text{E}}$volution ($\mathbf{\text{SAFE}}$), a $\mathit{\text{commensalistic}}$ 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.