Flux balance analysis (FBA) provides a framework for the estimation of intracellular fluxes and energy balance analysis (EBA) ensures the thermodynamic feasibility of the computed optimal fluxes. Previously, these techniques have been used to obtain optimal fluxes that maximize a single objective. Because mammalian systems perform various functions, a multi-objective approach is needed when seeking optimal flux distributions in such systems. For example, hepatocytes perform several metabolic functions at various levels depending on environmental conditions; furthermore, there is a potential benefit to enhance some of these functions for applications such as bioartificial liver (BAL) support devices. Herein we developed a multi-objective optimization approach that couples the normalized Normal Constraint (NC) with both FBA and EBA to obtain multi-objective Pareto-optimal solutions. We investigated the Pareto frontiers in gluconeogenic and glycolytic hepatocytes for various combinations of liver-specific objectives (albumin synthesis, glutathione synthesis, NADPH synthesis, ATP generation, and urea secretion). Next, we evaluated the impact of experimental flux measurements on the Pareto frontiers. We found that measurements induce dramatic changes in Pareto frontiers and further constrain the network fluxes. This multi-objective optimality analysis may help explain certain features of the metabolic control of hepatocytes, which is relevant to the response to hepatocytes and liver to various physiological stimuli and disease states.