In this paper, energy, exergy, economic analysis and multiobjective optimization of a pressurized water reactor (PWR) nuclear cogeneration plant for hydrogen production through high-temperature steam electrolysis (HTSE) are carried out. HTSE requires energy in the form of both heat and electrical work. A novel parameter, namely the heat/total energy ratio, is defined, and used as a decision variable in optimization. In addition to energy ratio, hydrogen production capacity, reactor thermal power, live steam temperature, reheating mass flow rate ratio, reheating temperature and steam extraction location are considered as the decision variables to simultaneously optimize the thermal efficiency, thermal-to-hydrogen efficiency, utilization factor, exergy efficiency and total revenue of the cogeneration plant. The analysis and optimization focus on the secondary cycle of the PWR and the effects of hydrogen and electricity prices and ambient conditions are also taken into account since these prices have a significant impact on the optimum design. For a hydrogen price of 4 $/kg and an electricity price of 0.1 $/kWh, when equal preference is given to all objective functions, the optimum production capacity is 6.778 kg/s. The energy ratio has an optimum value if the optimization focuses exclusively on the thermal efficiency and total revenue.