Embodied evolutionary robotics is a sub-field of evolutionary robotics that employs evolutionary algorithms on the robotic hardware itself, during the operational period, i.e., in an on-line fashion. This enables robotic systems that continuously adapt, and are therefore capable of (readjusting g themselves to previously unknown or dynamically changing conditions autonomously, without human oversight. This paper addresses one of the major challenges that such systems face, viz. that the robots must satisfy two sets of requirements. Firstly, they must continue to operate reliably in their environment (viability), and secondly they must competently perform user-specified tasks (usefulness). The solution we propose exploits the fact that evolutionary methods have two basic selection mechanisms–survivor selection and parent selection. This allows evolution to tackle the two sets of requirements separately: survivor selection is driven by the environment and parent selection is based on task-performance. This idea is elaborated in the Multi-Objective aNd open-Ended Evolution (MONEE) framework, which we experimentally validate. Experiments with robotic swarms of 100 simulated e-pucks show that MONEE does indeed promote task-driven behaviour without compromising environmental adaptation. We also investigate an extension of the parent selection process with a 'market mechanism' that can ensure equitable distribution of effort over multiple tasks, a particularly pressing issue if the environment promotes specialisation in single tasks.