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Optimization of thermodynamic cycles is important for the efficient utilization of energy sources; indeed, it is more crucial for the cycles utilizing low-grade heat sources where the cycle efficiencies are .smaller compared to high temperature power cycles. This paper presents the optimization of a combined poweri cooling cycle, also known as the Goswami cycle, which combines the Rankine and absorption refrigeration cycles. The cycle uses a special binary fluid mixture as the working fluid and produces a power and refrigeration. In this regard, multi-objective genetic algorithms (GAs) are used for Pareto approach optimization of the thermodynamic cycle. The optimization study includes two cases. In the first case, the performance of the cycle is evaluated as it is used as a bottoming cycle and in the second case, as it is used as a top cycle utilizing solar energy or geothermal sources. The important thermodynamic objectives that have been considered in this work are, namely, work output, cooling capacity, effective first law, and exergy efficiencies. Optimization is carried out by varying the selected design variables, such as boiler temperature and pressure, rectifier temperature, and basic solution concentration. The boiler temperature is varied betu'een 70-150°C and 150-250°C for the first and the second cases, respectively.