Using multilevel inverter in numerous applications is commonplace. Inverters supplied from equal dc source are almost rare. Although variation in dc source affects inverter switching characteristics. Solving a nonlinear transcendental equation set describing harmonic elimination with non-equal dc sources reaches the limitation of contemporary computer algebra software tools as marked in literatures. This paper presents an optimal solution for harmonic reduction namely weight improved particle swarm optimization (WIPSO ), where a set of mathematical equation describing the general output waveform for the computation of total harmonic distortion (THD) is used as the objective function and is employed to compute the optimal solution set of switching angles without knowing proper initial guess. Theoretical analysis is validated through simulations for 5, 7, 9 and 11 level cascaded multilevel inverters performed on MATLAB software. Results show a decrease in THD as level of inverter increases reflecting to approach towards a sinusoidal output voltage waveform thereby eliminating harmonics.