Software engineering predictive modeling involves construction of models, with the help of software metrics, for estimating quality attributes. Recently, the use of search-based techniques have gained importance as they help the developers and project-managers in the identification of optimal solutions for developing effective prediction models. In this paper, we perform a systematic review of 78 primary studies from January 1992 to December 2015 which analyze the predictive capability of search-based techniques for ascertaining four predominant software quality attributes, i.e., effort, defect proneness, maintainability and change proneness. The review analyses the effective use and application of search-based techniques by evaluating appropriate specifications of fitness functions, parameter settings, validation methods, accounting for their stochastic natures and the evaluation of developmental models with the use of well-known statistical tests. Furthermore, we compare the effectiveness of different models, developed using the various search-based techniques amongst themselves, and also with the prevalent machine learning techniques used in literature. Although there are very few studies which use search-based techniques for predicting maintainability and change proneness, we found that the results of the application of search-based techniques for effort estimation and defect prediction are encouraging. Hence, this comprehensive study and the associated results will provide guidelines to practitioners and researchers and will enable them to make proper choices for applying the search-based techniques to their specific situations.