The biomass gasification coupled with a solid oxide fuel cell (SOFC) system is one of the most efficient and environmentally friendly technologies for combined heat and power generations. For the development and improvement of the integrated process systems, the optimization problem has more than one conflicting objective functions to be optimized (i.e., thermodynamic performance, environmental impacts, annual profit, capital and operating costs) simultaneously. Multi-objective optimization (MOO) methods are used to find a set of optimal (or non-dominated) solutions. In this work, MOO of a sorption enhanced steam biomass gasification (SEG) integrated with an SOFC and gas turbine (GT) system, for combined heat and power production from Eucalyptus wood chips as biomass feedstock, is investigated. Firstly, the model of this integrated plant is developed in Aspen Plus that can be divided into five parts: (1) SEG, (2) hot gas cleaning and steam reforming, (3) SOFC, (4) catalytic burning, GT and CO2 compression, and (5) Portland cement production. As the annual profit demonstrates the economic viability of the plant and annualized capital cost (ACC) indicates availability of investments, the MOO of the integrated plant is performed to obtain Pareto-optimal solutions based on the minimization of ACC and maximization of annual profit with five important decision variables. After that, ten selection methods are used to recommend practical solutions for implementing in the integrated plant. In order to explore the effect of decision variables uncertainty on obtained Pareto-optimal solutions, random variations in decision variables are used to quantify deviations in objective functions. The Pareto-optimal solutions are ranked based on the normalized variations for decision variables uncertainty. At the end of this study, robust MOO of the integrated plant is performed, with respect to uncertainties in the market and operating parameters.