Energy efficiency of the conventional boil-off gas re-liquefaction process in the LNG-fueled ships, which is based on a single expander cycle, can be improved with structural modifications, such as a dual expander cycle. Herein, a structural optimization framework concept is proposed to systematically screen a wide range of configurational options for dual expander processes, and to evaluate their techno-economic impacts in a holistic manner. Ten possible process configurations are embedded in the framework, with which the strategic use of design options, including splitting and/or mixing of streams, and introduction of extra hot stream in the exchanger, are fully investigated. Furthermore, a cascaded cycle is compared as a possible candidate for improving the energy efficiency of the single expander process. The optimum process design is investigated by optimizing process variables to achieve maximum energy efficiency with aid of GA (Genetic Algorithm). The optimized performance of the dual-expander process is 23% better than the single expander system in terms of energy efficiency. The advantage of the proposed modeling and optimization framework is its adaptability to other liquefaction processes.