Evolutionary multi-objective (3 or 4) optimization portfolio using fuzzy logic in Tehran Stock Exchange

The problem of portfolio optimization and stock selection is one of the major areas for financial investors in financial markets. In this paper, some of the challenges of simultaneously multi-objective portfolio optimization are addressed. Four different models are designed: a fuzzy multi-objective programming model has been used to consider the multi-criteria nature of stock selection and the uncertainty associated with the return on assets and a simple model for doing this. The models are designed in such a way that both the nature of the multiplicity of the problem of portfolio selection is considered and the considerations of the investor in the choice of portfolios are involved. After designing the evolutionary 3 and 4 objective models of portfolio optimization, multi-objective evolutionary algorithm NSGA-II was used to solve this models. Concretely, it optimizes return, the downside-risk, skewness and the Kurtosis of a given daily returns, taking into account budget, and investor constraints. Because of the NP-HARD nature of the above models, the NSGA-II proprietary algorithm was coded in the MATLAB, and after solving each model and extracting the Pareto frontier, the best portfolio on the Pareto front was selected based on the maximum Sortino ratio. Finally, the results of the obtained portfolios in both fuzzy and non-phase conditions were compared according to the trainer's ratio, and it was determined that the use of fuzzy logic in quadratic evolutionary algorithms, compared to a situation where fuzzy logic is not used in the design and use of these algorithms., Creates more favorable results.