In the present study, multi-objective optimization has been conducted to optimize a novel multigeneration system that is based on biomass energy, and uses the cold energy of the liquid natural gas as a heat sink. The designed system is an integration of combined gas-steam cycle, a cascade Rankine cycles, a lithium bromide-water absorption refrigeration cycle, a proton exchange membrane electrolyzer, and a liquid natural gas subsystem. The proposed system aims to produce power, cooling, natural gas, and hydrogen. Following thermodynamic and exergoeconomic analysis, two conflicting objectives, that is, total product cost rate and exergy efficiency, are selected for the optimization process. The genetic algorithm is used to optimize the system and the Pareto front plot is achieved. The obtained results for this system reveal that the final optimization point has an exergy efficiency of 39.023% and a total product cost rate of 1107$/h. This point is a trade-off between thermodynamic and thermoeconomic single-objective optimization cases. In addition, the biomass gasification-gas turbine cycle, organic Rankine cycles, and proton exchange membrane have the highest exergy destruction rates, respectively. Finally, it is shown that the liquid pressure ratio of the natural gas pump and inlet temperature of the steam turbine have the most important effects on the balance between the selected objective parameters.