Operating hydrogen plants efficiently is a critical issue, central to any energy conservation exercise in petroleum refining and fertilizer industries. To achieve this goal, "optimal" operating conditions for improved unit performance need to be identified. In this work, an entire industrial hydrogen plant is simulated using rigorous process models for the steam reformer and shift converters. An adaptation of the nondominated sorting genetic algorithm (NSGA) is then employed to perform a multi-objective optimization on the unit performance. Simultaneous maximization of product hydrogen and export steam flow rates is considered as the two objective functions for a fixed feed rate of methane to the existing unit. For the specified plant configuration, Pareto-optimal sets of operating conditions are successfully obtained by NSGA for different process conditions. The results serve as a target for the operator to aim at, in order to achieve cost effective operation of hydrogen plants.