The shipping industry has been facing great pressure to become more sustainable, emanating from the increasingly stringent environmental regulations, fuel prices volatility and societal needs. As a result, a variety of technologies have been developed aiming to improve the environmental and economic performance of the modern ship energy systems, however leading to additional challenges for the technology selection during the design process. This study introduces an innovative method that integrates the economic and environmental aspects of sustainability to support decisions on the synthesis of the modem ship energy systems. The method includes a simulation model for predicting the energy systems performance during the ship lifetime. The genetic algorithm NSGA-II, is employed to solve the multi-objective combinatorial optimisation problem of selecting the integrated ship energy systems configuration. The derived results are visualised to reveal the Pareto front and the trade-offs among the objectives. The method is novel in supporting the synthesis of the integrated ship energy systems, as it includes both environmental and economic objectives, as well as evaluates the performance of the systems over an expected operational profile. The developed method is implemented for the case study of an Aframax oil tanker and the derived results analysis indicates that the ship energy systems sustainability can be improved by adopting LNG fuel and dual fuel engines technology, as well as by introducing other emerging technologies like fuel cells and carbon capture, although the latter is associated with a high cost. It is concluded that the inclusion of both environmental and economic objectives highlights the trade-offs between more environmentally friendly or cost efficient configurations, thus supporting the multi-objective decision-making process.