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To solve single and multi-objective optimization problems, evolutionary algorithms have been created. We use the non-dominated sorting genetic algorithm (NSGA-II) to find the Pareto front in a two-objective portfolio query, and its extended variant NSGA-III to find the Pareto front in a three-objective portfolio problem, in this article. Furthermore, in both portfolio problems, we quantify the Karush-Kuhn-Tucker Proximity Measure (KKTPM) for each generation to determine how far we are from the effective front and to provide knowledge about the Pareto optimal solution. In the portfolio problem, looking for the optimal set of stock or assets that maximizes the mean return and minimizes the risk factor. In our numerical results, we used the NSGA-II for the portfolio problem with two objective functions and find the Pareto front. After that, we use Karush-Kuhn-Tucker Proximity Measure and find that the minimum KKT error metric goes to zero with the first few generations, which means at least one solution converges to the efficient front within a few generations. The other portfolio problem consists of three objective functions used NSGA-III to find the Pareto front and we use Karush-Kuhn-Tucker Proximity Measure and find that The minimum KKT error metric goes to zero with the first few generations, which means at least one solution converges to the efficient front within a few generations. Also, the maximum KKTPM metric values don’t show any convergence until the last generation. Finally, NSGA-II is effective only for two objective functions, and NSGA-III is effective only for three objective functions.

On NSGA-II and NSGA-III in Portfolio Management