The current study investigates a cogeneration system based on a gas turbine, integrated with a Rankine cycle and an absorption refrigeration cycle, considering energy and exergy perspectives. The fuel used in the gas turbine’s combustion chamber is obtained through biomass gasification, specifically using wood as the biomass fuel. To enhance the system’s performance, solar energy is utilized to preheat the working fluid in the Rankine cycle, reducing the energy required in the heat recovery steam generator. Additionally, an absorption refrigeration cycle is incorporated to recover waste heat from exhaust gases and improve the plant’s exergy efficiency. A two-objective optimization is conducted to determine the optimal operating conditions of the proposed system, considering exergy efficiency and carbon dioxide emission index as criteria. The case study reveals that the gasifier and combustion chamber contribute the most to system irreversibility, accounting for 46.7% and 22.9% of the total exergy destruction rate, respectively. A parametric study is performed to assess the impact of compression ratio, turbine bleed steam pressure, gas turbine inlet temperature, and solar share (the ratio of energy received by solar collectors to biomass fuel input energy) on system performance. The findings demonstrate that maximum energy and exergy efficiencies of the power generation system are achieved at a pressure ratio of 10. Furthermore, a 1% reduction in the gas turbine’s compression pressure ratio can be compensated by a 9.3% increase in the solar share within the steam Rankine cycle.