In the multi-objective approach to constraint-handling, a constrained problem is transformed into an unconstrained one by defining additional optimization criteria to account for the problem constraints. In this paper, this approach is explored in the context of the hydrophobic-polar model, a simplified yet challenging representation of the protein structure prediction problem. Although focused on such a particular case of study, this research work is intended to contribute to the general understanding of the multi-objective constraint-handling strategy. First, a detailed analysis was conducted to investigate the extent to which this strategy impacts on the characteristics of the fitness landscape. As a result, it was found that an important fraction of the infeasibility translates into neutrality. This neutrality defines potentially shorter paths to move through the landscape, which can also be exploited to escape from local optima. By studying different mechanisms, the second part of this work highlights the relevance of introducing a proper search bias when handling constraints by multi-objective optimization. Finally, the suitability of the multi-objective approach was further evaluated in terms of its ability to effectively guide the search process. This strategy significantly improved the performance of the considered search algorithms when compared with respect to commonly adopted techniques from the literature.