This study proposes an optimization methodology to find optimal heat source paths for point-melting in Electron Beam Melting (EBM) Powder Bed Fusion (PBF) processes, aiming to reduce the need for support structures and improve print quality. The building process is simulated using a time-dependent, one-way coupled, non-linear thermo-mechanical model, assuming negligible molten flow, with elastoplastic behavior and temperature-dependent material parameters. The goal of the optimization problem is to find heat source paths that minimize a global temperature measure with a penalty on excessive local temperatures. The numerical methodology is based on solving the non-linear partial differential equations via the Finite Element Method (FEM) and is applied in numerical examples for printing with titanium alloy Ti6Al4V. Metrics related to heat, residual displacement, and residual stresses are considered to assess the performance of different point-melting strategies and to compare optimized and conventional paths. The feasibility of the proposed optimization methodology for practical applications and alternatives towards future methodological advancements are discussed. The study provides a Python-based, MPI-parallelized implementation using open-source libraries and is made available for further research and applications.