This work presents a novel genetic algorithm (GA) for optimizing the few-group energy grid structure used for full-core nodal calculations in lead-cooled fast reactors. The optimization is started considering a set of group constants computed on a reference 61-group structure from which the GA selects an optimal subset of groups. Compared to existing works in the literature, the number of groups is not defined a priori but varies within a user-defined range, allowing a better exploration of the solution space. This feature requires one to develop an adequate representation of the chromosomes used in the evolution process, which is examined with different definitions of the chromosomes. The work also proposes a suitable combination of physics-driven fitness functions (FFs) related to the effective multiplication factor, the power density, and the neutron flux. Different weights based on the adjoint flux are also studied for the flux FF, with the aim of improving the convergence of the evolution process. All the studies are performed focusing on a three-dimensional model of the Advanced Lead Fast Reactor European Demonstrator (ALFRED) core design, which is modeled using the multigroup diffusion module of the Fast REactor NEutronics/Thermal-hydraulICs (FRENETIC) multiphysics code. The results suggest that the energy grid can be profitably optimized using a representation with two chromosomes. The optimal solutions yielded by the GA are justified on a physical basis by looking at some relevant figures of merit.