One of the challenges in the design and development of a latent heat storage unit (LHSU) is to increase the charging and discharging rates which are inherently low because of low thermal conductivity of phase change materials (PCM). Out of various heat transfer enhancement techniques, employing annular fins is very simple, efficient and no fabrication complexity is involved. Fin parameters (fin size and number of fins) significantly influence the enhancement in heat transfer rate. Hence, optimization of fin parameters is necessary for the efficient design of an LHSU. While designing an LHSU along with heat transfer rate, entropy generation should also be considered in order to make it exergetically efficient. Therefore, the present study is aimed at multi-objective optimization of annular fin parameters to minimize the melting time and entropy generation. Fin diameter and the number of fins are taken as the variables. The influence of these two variables on the melting time, average Nusselt number, energy stored, and distribution of entropy is presented. The melting rate is increased, and global entropy generation decreased by increasing the number of fins up to 15. An increase in the fin diameter reduced the melting time while entropy generation got increased. For the multi-objective optimization, the multi-objective optimization based on ratio analysis (MOORA) technique is chosen and the optimized values of fin diameter and number of fins are observed to be 80 mm and 15 respectively. Finally, optimized parameters are represented in non-dimensional form to make them applicable for any size of the LHSU.