multi-objective evolutionary optimization algorithm

Selecting the optimal stock portfolio is one of the most important issues in the field of financial research, which tries to choose the optimal combination of assets in order to create maximum utility for the investor, Given that the return on securities in the real world is often vague and inaccurate, one of the most important investment challenges is uncertainty about the future. In this paper the problem of selecting and optimizing securities portfolios with different modeling goals has been solved and compared. The designed models have considered both the nature of the portfolio selection issue and the considerations considered by the shareholder in the portfolio selection. The uncertainty quality of the future return of a given portfolio is estimated using fuzzy LR numbers, while its return torques are measured using possibility theory. The most important purpose of this paper is to solve the problem and compare portfolio selection models with simultaneous optimization of two, three, and four objectives. For this purpose, the NSGA-II genetic algorithm is used and the mutation and intersection operators are designed specifically to generate possible solutions to the cardinality constraint of the problem. Finally, the efficiency and performance of the models in case of using fuzzy logic and not using it have been compared and it has been determined that the use of fuzzy logic and possibility theory leads to the formation of portfolios with higher performance and higher efficiency.