Protein Structure Prediction (PSP) problem is to determine the three-dimensional structure of a protein only from its primary structure. Misfolding of a protein causes human diseases. Thus, the knowledge of the structure and functionality of proteins, combined with the prediction of their structure is a complex problem and a challenge for the area of computational biology. The metaheuristic optimization algorithms are naturally applicable to support in solving NP-hard problems.These algorithms are bio-inspired, since they were designed based on procedures found in nature, such as the successful evolutionary behavior of natural systems. In this paper, we present a survey on methods to approach the \textit{ab initio} protein structure prediction based on evolutionary computing algorithms, considering both single and multi-objective optimization. An overview of the works is presented, with some details about which characteristics of the problem are considered, as well as specific points of the algorithms used. A comparison between the approaches is presented and some directions of the research field are pointed out.