Optimization of the operating conditions for the proton exchange membrane fuel cell (PEMFC) is a challenging part as these are multi-input problems, however optimization is essential to achieve maximum stack efficiency, cost and weight reduction, and fuel utilization. In this article, an analytical model of the fuel cell is obtained by considering the Butler-Volmer and Nernst equations. Effect of operating pressure, temperature on the cell output voltage (Ecell), stack power (Pst), and stack efficiency (ηst) is analyzed to understand the behavior of the fuel cell at various operating conditions. It has been observed that the Pst increases with the increase in current density (i) whereas the ηst reduces with the increase in i. Hence, it is required to optimize the Pst and ηst so that maximum power can be extracted from the fuel cell stack without compromising in its efficiency and performance. For the multi-objective optimization study, eight input parameters are considered: operating pressure (P), operating temperature (T), transfer coefficient (α), internal resistance (Ri), catalyst specific area (ac), catalyst loading (Lc), current density (i) and amount of reaction fuel, i.e., H2 (ṁH2reacted). Multi-objective genetic algorithm solver embedded with MATLAB is used for the optimization of the objective functions (Pst and ηst). The PEMFC provides Ecell = 0.67 V, Pst = 51 kW, and ηst = 57% while operating at the optimum operating conditions. The results indicate that the optimization of input parameters can lead to the better performance of the PEMFC as compared to the base operating condition (25°C and 1 atm). The study can guide the engineers to select the appropriate operating conditions for a fuel cell to get better performance.