Increased adoption of distributed resources and renewables in distribution networks has led to a significant interest in local energy transactions at lower levels of the energy supply chain. Local energy markets (LM) are expected to play a crucial part in guaranteeing the balance between generation and consumption and contribute to the reduction of carbon emissions. Besides, LMs aim at increasing the participation of small end-users in energy transactions, setting the stage for transactive energy systems. In this work, we explore the use of evolutionary algorithms (EAs) to solve a bi-level optimization problem that arises when trading energy in an LM. We compare the performance of different EAs under a realistic case study with nine agents trading energy in the day-ahead LM. Results suggest that EAs can provide solutions in which all agents can improve their profits. It is shown the advantages in terms of profits that an LM can bring to market participants, thereby increasing the tolerable penetration of renewable resources and facilitating the energy transition.