Abstract Efficient energy utilization from renewable energy sources can resolve multidimensional problems of environmental pollution, energy security and reduction in conventional fossil fuel reserves. In this circumstance, biomass-based energy systems can play an important role. In this study, modeling and analysis of an advanced integrated co-generation system comprising of a biomass gasifier, a solid oxide fuel cell module and a heat recovery steam generator have been carried out for generating power and process heat. The proposed system has been evaluated through exergetic and economic methods. Furthermore, response surface methodology has been applied for the multi-objective optimization of the system. Current density, pressure ratio of the secondary air compressor and saturation pressure of steam at the heat recovery steam generator are considered as the inputs for predicting the optimum performance parameters i.e., exergy efficiency, levelized cost of energy and levelized cost of exergy. Regression models, generated from the analysis of variance tool, are found to have a very high degree of accuracy for the exergy efficiency, levelized cost of energy and levelized cost of exergy. The optimal levels of the current density, pressure ratio and saturation pressure of steam are found to be 5101.01 A/m2, 4 and 12 bar, respectively. At this optimum condition, exergy efficiency, levelized cost of energy and levelized cost of exergy of the cogeneration system are 46.58%, 0.0454 $/kWh and 0.0657$/kWh, respectively. Composite desirability is found to be on the higher side (around 0.90), which indicate that the setting seems to attain favorable results for all the responses as a whole.