This study introduces Gaussian Binary Particle Swarm Optimization (G-BPSO), designed to address binary optimization challenges effectively. G-BPSO employs new transfer functions of the Gaussian type derived from the power functions to enable mapping of real-valued vectors of individual encodings into binary form. This ensures smooth change between steps and improved convergence. To assess the effectiveness of G-BPSO, a host of complex optimization problems such as the un-capacitated facility location problem are investigated. Enhanced efficiency and improvement over existing methods in binary optimization is observed. The MATLAB code of G-BPSO is made open-access through https://github.com/kanak02/GBPSO.