The building design process is crucial in efforts to implement energy-efficient practices by adopting Energy Efficiency Measures (EEMs). However, design choices based solely on reducing operational energy use can significantly increase a building's embodied energy and Life Cycle Energy (LCE) use, because there is a trade-off between embodied and operational energy. This article presents a case study in which multi-objective optimization was used to explore the effects of various EEMs on the aforementioned trade-off. Optimal solution(s) for six different building shapes (rectangular, H-, U-, l-, T- and cross-shaped) based on two sets of EEMs were investigated and compared. The first set of EEMs consisted of EEMs that can be implemented or modified during the early design phase, such as the building's shape, orientation, Window to Wall Ratio (WWR), and constituent materials. The second set comprised EEMs that can be implemented later in the design phase (i.e. EEMs relating to the constituent materials). The LCE reductions achieved by finding optimal solutions for EEMs in the first set (ranged from 2175.2 to 3803.8 GJ) were significantly (over 5 times) higher than those achieved for the second set (ranged from 418.6 to 625.6 GJ) for all building shapes. Moreover, LCE use for pre-optimization building designs varied significantly with building shape. However, after optimization, the differences in LCE use between the optimal solutions of different building shapes were modest. This means that designers and construction companies can select building shapes based on customer requirements, but also highlights the importance of using multi-objective optimization during early design process to identify optimal combinations of EEMs that minimize LCE use.