This study aims to find the optimal switching angles in a cascaded H-bridge multilevel inverter (CHB-MLI) fed by photovoltaic (PV) panels, keeping the output voltage constant regardless of the panel voltage change and eliminating low-order harmonics. For this purpose, Red Deer Algorithm (RDA), a newly developed algorithm, has been applied to solve selective harmonic elimination (SHE) equations. Calculated switching angles are simulated by applying three-phase 7-level CHB-MLI in Matlab/Simulink environment. RDA optimization has been compared in performance to evolutionary algorithms such as particle swarm optimization (PSO), genetic algorithm (GA) and pigeon inspired optimization (PIO). The results show that in the case of unequal DC voltage, RDA can suppress selected harmonics accurately and quickly while controlling the fundamental voltage with a 0.02% error. The proposed RDA optimization can be used for multilevel inverters fed by any number of variable input voltages to eliminate selected harmonics and reduce total harmonic distortion (THD) without complex analytical calculations.