A novel combined-cycle system is proposed for the cogeneration ofelectricityand cooling, in which a dual-loop organic Rankine cycle (ORC)engine is used for waste-heat recovery from a solidoxide fuel cellsystem equipped witha gas turbine(SOFC-GT). Electricity is generated by the SOFC, its associated gas turbine, the two ORC turbines and a liquefied natural gas (LNG)turbine; the LNGsupply tothe fuel cell is also used as the heat sink to the ORC enginesandas a cooling medium for domestic applications. The performance of the system with 20 different combinationsof ORC working fluids isinvestigated by multi-objective optimisationof its capitalcostrateand exergy efficiency, using an integrationof a genetic algorithm and a neural network. The combination of R601(top cycle) and Ethane(bottom cycle)isproposed for the dual-loop ORC system, due to the satisfaction of the optimisationgoals, i.e., an optimal trade-off between efficiency and cost.With theseworking fluids, the overall system achieves an exergy efficiency of51.6%, a total electrical powergeneration of1040kW, with the ORC waste-heat recovery system supplying 20.7% of thispower,and a cooling capacityof 567kW. In addition, an economic analysisof theproposed SOFC-GT-ORCsystemshowsthat the cost of production of an electrical unit amounts to$33.2perMWh, which is 12.9%and 73.9%lowerthan the levelized cost of electricityofseparateSOFC-GT and SOFC systems,respectively. Exergy flow diagrams are usedto determine the flow rate of the exergy andthe value of exergy destructionin each component. In the waste heat recovery system,exergy destruction mainly occurs within theheat exchangers, the highestof which isin the LNG cooling unit followedby the LNG vaporiser and the evaporator ofthe bottom-cycleORCsystem, highlightingthe importance of these components’designin maximising the performance of the overall system.