Many real optimization problems have more than one objective function. When the objectives are in conflict, there is a need for specialized strategies, as is the case of the Multi-objective Optimization Evolutionary Algorithms (MOEAs). However, if the functions evaluation is expensive (high computational or economical costs) many proposed MOEAs are impractical. An alternative might be the use of a machine learning model to approximate the fitness function (surrogates) in the optimization algorithm. This work proposes and investigates a framework called ELMOEA/D that aggregates state-of-the-art MOEAs based on decomposition of objectives (MOEA/D) and extreme learning machines as surrogate models. The proposed framework is tested with different MOEA/D variants and show good results in benchmark problems, compared to a literature algorithm that also encompasses MOEA/D but uses surrogate models based on radial basis function networks. The ELMOEA/D framework is also applied to the protein structure prediction problem (PSPP). Despite the fact that the results achieved by the proposed approach were not as encouraging as the ones achieved in the benchmarks (when the algorithms with and without surrogates are compared), many aspects of both algorithm and problem are explored. Finally, the ELMOEA/D framework is applied to an alternative formulation of the PSPP and the results lead to various directions for future works.