<![CDATA[Over decades, numerous methods have been used to optimize objective functions. Where cost and emissions clash. The improved non-dominated sorting genetic algorithm (NSGA-II) employs elitism to discover the optimum value and speed convergence in multi-objective optimization problems. Population variant differential evolution algorithm alters differential evolution (DE). The main distinction between DE and population variant differential evolution algorithm (PVDE) is population replenishment. NSGA-II and PVDE are combined in the suggested hybrid approach. The hybrid technique solves multi-objective optimization problems efficiently by combining two or more methods. The hybrid technique solves multi-objective optimization problems well. This optimization problem pits cost vs pollution. The hybrid approach exposes half the population to the NSGA-II algorithm and half to the PVDE algorithm. In optimization problems with opposing aims, such as minimizing costs and emissions, a hybrid technique is utilized to find the optimal solution. Elitist diversity-preserving strategies avoid optimization issues becoming converging too soon. A 10-generator IEEE 39 bus test system was validated using this method. The hybrid NSGA-II and PVDE methodology achieves global optimal solutions with more durability, simplicity, and optimization performance than existing methods.]]>
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