Chemical process optimization problems often have multiple and conflicting objectives, such as capital cost, operating cost, production cost, profit, energy consumptions and environmental impacts. In such cases, Multi-Objective Optimization (MOO) is suitable in finding many Pareto optimal solutions, to understand the quantitative trade-offs among the objectives, and also to obtain the optimal values of decision variables. Gaseous fuel can be converted into heat, power and electricity, using combustion engine, gas turbine (GT) or Solid Oxide Fuel Cell (SOFC). Of these, SOFC with GT has shown higher thermodynamic performance. This hybrid conversion system leads to a better utilization of natural resource, reduced environmental impacts, and more profit. This study optimizes performance of SOFC-GT system for maximization of annual profit and minimization of annualized capital cost, simultaneously. For optimal SOFC-GT designs, the composite curves for maximum amount of possible heat recovery indicate good performance of the hybrid system. Further, first law energy and exergy efficiencies of optimal SOFC-GT designs are significantly better compared to traditional conversion systems. In order to obtain flexible design in the presence of uncertain parameters, robust MOO of SOFC-GT system was also performed. Finally, Pareto solutions obtained via normal and robust MOO approaches are considered for parametric uncertainty analysis with respect to market and operating conditions, and solution obtained via robust MOO found to be less sensitive.