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For over a decade, distributed generations (DGs) have sufficiently convinced the researchers that they are the economic and environment-friendly solution that can be integrated with the centralized generations. The optimal planning of distributed generations requires the appropriate location and sizing and their corresponding control with various power network types to obtain the best of the technical, economical, commercial, and regulatory objectives. Most of these objectives are conflicting in nature and require multi-objective solutions. Therefore, this paper brings a comprehensive literature review and a critical analysis of the state of the art of the optimal multi-objective planning of DG installation in the power network with different objective functions and their constraints. The paper considers the adoption of optimization techniques for distributed generation planning in radial distribution systems from different power system performance viewpoints; it considers the use of different DG types, distribution models, DG variables, and mathematical formulations; and it considers the participation of different countries in the stated DG placement and sizing problem. Moreover, the summary of the literature review and critical analysis of this article helps the researchers and engineers to explore the research gap and to find the future recommendations for the robust optimal planning of the DGs working with various objectives and algorithms. The paper considers the adoption of uncertainties on the load and generation side, the introduction of DGs with energy storage backups, and the testing of DG placement and sizing on large and complex distribution networks. [ABSTRACT FROM AUTHOR]