The emergence of building performance optimization is recognized as a way to achieve sustainable building designs. In this paper, the problem consists in minimizing simultaneously the emissions of greenhouse gases (GHG) related to building energy consumption and those related to building materials. This multi-objective optimization problem involves variables with different hierarchical levels, i.e. variables that can become obsolete depending on the value of the other variables. To solve it, NSGA-II is compared with an algorithm designed specifically to deal with hierarchical variables, namely sNSGA. Evaluation metrics such as convergence, diversity and hypervolume show that both algorithms handle hierarchical variables, but the analysis of the Pareto front confirms that in the present case, NSGA-II is better to identify optimal solutions than sNSGA. All the optimal solutions are made of buildings with wooden envelopes and relied either on heat pumps or on electrical heaters for proving heating.