The problem of protein structured prediction (PSP) is one of the most important challenges in molecular biology. Because this problem is very difficult, different simplified models have been proposed to solve it. One of the most studied is the Hydrophobic-Polar model HP this model provides an estimate of the protein energy based on the sum of hydrophobic contacts. However, despite the simplifications made in the HP model, the problem remains complex, belonging to the class of NP-Hard problems. Many techniques have been proposed to solve this problem as genetic algorithms. In many cases the GA techniques have been used successfully, but, however, with GA approaches often do not adequately address the generated solutions, impairing the performance of the search. Furthermore, in some cases would attain the minimum energy for a known conformation, these models do not take care the protein shape, a very important factor to obtain more compact proteins. This work developed a multiobjective genetic algorithm to PSP in HP model evaluating more efficiently, the conformations produced. This model is a combination of assessment based on the collisions numbers, hydrophobic contacts, hydrophobic and hydrophilic core compression, obtaining thus more natural structures with minimum energy. The results demonstrate the efficiency of this algorithm to obtain protein structures indicators providing compact compression of the hydrophobic and hydrophilic core protein.