A passive method with phase change material (PCM) is an appropriate technique in electronic cooling. But, due to its poor thermal conductivity, many enhancers are employed to reduce the thermal resistance offered by the PCM. A partial filling strategy to reduce the cost and weight of foams with fins is used in this study. A hybrid heat sink with a combination of fins placed at the sidewalls of the enclosure and foams filled at certain heights such as 10, 20, and 30 mm is considered in this present work. A two-dimensional numerical model with n-eicosane as PCM is developed in ANSYS Fluent 19. A multi-objective optimization is carried out using a reliable multi criteria decision making approach. Different weightage is distributed to the objective functions in this method depending on the choice of the user. The pore size and density vary for various filling heights, and 60 cases are investigated for both charging and discharging cycles. The pore size of 0.8-0.95 and pore density of 5-25 pores per inch with a broad range is considered. From the discussions, guidelines for selecting a preferable pore size and pore density can be determined based on the filling height and applied weightage.