A Multi-Objective Approach to Portfolio Optimization Problem Using the Analytic Hierarchy Process (AHP) and Genetic Algorithm

This study analyzes the portfolio optimization model, by considering the financial management and investment science in order to evaluate risks and return in regard with restrictions such as buyers’ assets for purchasing per share. Accordingly, a novel model is designed as linear programming in order to optimize the investment portfolio, considering the expected rate of return, the minimum risk, and the buyer’s assets. After the introduction of the model as linear programming and expressing the related limitations, different types of investments which an investor can consider in order to form an investment portfolio were studied. Finally, an approach is proposed to solve the model by using the genetic algorithm, and is implemented and analyzed in regard with a real example. According to the results of this study, the new model reduced downside risk in comparison with previously proposed models, in a manner that its stair descent continues as the number of shares under study increases.