Combined cooling, heating, and power (CCHP) systems present a step in the right direction as regards advancement in energy management, as they offer a sustainable solution to the rise in energy demand caused by economic and population growth. The integration of solar energy largely reduces the excessive consumption of fossil fuels, thus reducing the associated effects of greenhouse gas emissions. Solar-assisted CCHP systems have inherent fuel efficiency advantages, leading to enhanced overall system efficiency compared to separate power generation systems. However, optimization of CCHP systems is fundamental to realizing optimal system design configuration that improves thermodynamic performance metrics. This study proposes using the genetic algorithm multi-objective approach to optimize the performance of a solar-assisted CCHP system. The objective is to develop a mathematical programming model to determine the optimal compression ratio, pinch point temperature, and inlet turbine and combustion chamber temperatures. The optimization aims to maximize net power and exergy efficiency while minimizing CO2 emissions. The research findings are anticipated to provide valuable insights for enhancing CCHP systems and aiding decision-making processes in the energy production sector.