Due to the increasing population and the expansion of industry in daily life, a significant depletion of fossil fuel resources is observed, accompanied by escalating environmental concerns. In response to these challenges, this study presents an optimized cogeneration system powered by renewable biomass, designed for simultaneous power and cooling generation. The system integrates a biomass gasification unit, a steam Rankine cycle, a helium-driven gas turbine cycle, and an ammonia-water-based two-stage absorption refrigeration cycle with a bleed line. Thermodynamic and exergoeconomic analyses reveal a net power output of 5356 kW, a cooling load of 360.9 kW, and an exergetic efficiency of 29.52 %. Financially, the system shows a net present value of 11.76 $M and a payback period of 6.51 years. A multi-objective optimization utilizing the gray wolf algorithm improves system performance through the employment of three diverse scenarios, which raises power output to 5864 kW, cooling load to 372 kW, and optimize net present to 14.28 $M with a reduced payback period of 5.96 years. The studied system is well-suited for industrial applications, rural electrification, and district energy systems, and offers a sustainable and economically viable energy solution.