Optimal Location and Sizing of Distributed Generation Units Using NSAGA-III with Heuristic Sampling and Restricted Mating

The integration of Distributed Generation (DG) units in distribution systems is a well-known approach to minimize power losses and improve voltage stability. This research proposes an improved Non-Dominated Sorting Genetic Algorithm (NSGA)-III framework incorporating Heuristic Sampling (HS) for initialization and Restricted Mating (RM) to enhance diversity preservation. The method is benchmarked against the classical NSGA-II, NSGA-III, CMOPSO, and CTAEA methods on the standard IEEE 33-bus and 69-bus test systems. Simulation results demonstrate that the proposed NSGA3-seeded method produces smoother and better-converged Pareto fronts with more uniform solution distribution. Quantitative evaluations using Hypervolume (HV), Generational Distance (GD), and Spacing-to-Extent (StE) indicators confirm consistent improvements in convergence and diversity. Furthermore, the Friedman statistical test confirms that the performance differences among algorithms are statistically significant (p < 0.05), and that the proposed NSGA3-seeded consistently attains the best overall ranking across all indicators. The findings confirm the robustness and effectiveness of the proposed approach for practical DG siting and sizing problems.