This article presents an initial solution based selective harmonic elimination(SHE) method for multilevel inverter(MLI) that aims to solve SHE problem with high accuracy while significantly reducing the number of iterations. Initial SHE solution is defined as a set of initial switching angles that has less accuracy as compared to the final SHE solution. To find initial SHE solution, tunicate swarm algorithm(TSA), grey wolf optimization(GWO) and whale optimization(WO) are used to solve five-dimensional SHE problem. A comparative analysis demonstrates that TSA achieved the desired initial SHE solution within lesser iterations as compared to GWO and WO for a wide range of modulation indices. The initial switching angles found using TSA are further optimized using Newton-Raphson(NR) method being the proposed TSANR method, which exploits the SHE search space with quadratic rate of convergence to find final SHE solution. The proposed TSANR method significantly minimizes the computational time and further improves the accuracy of the SHE solution as compared to the state-of-the-art SHE methods. Detailed simulations, experimental and harmonic analysis under dynamic change in modulation index are presented to show the efficacy of the proposed SHE method in terms of control over fundamental and detrimental harmonics.