Financial Portfolio Innovation via the Dhouib-Matrix-3 Metaheuristic

The portfolio optimization problem is a mathematical and financial decision-making method that aims to achieve an optimal trade-off between financial risk and return. This paper presents the first application of the novel metaheuristic Dhouib-Matrix-3 (DM3) to solve the portfolio optimization problem. DM3 is originally designed to address combinatorial problems, and in this study, it is adapted for a continuous optimization setting and applied to the OR-Library instance (the Hang Seng Index consisting of 31 stocks) as well as to the Tunisian Stock Exchange for the year 2024. The problem is formulated using the Markowitz model, in which return is maximized and risk is minimized. The simulation results show that the novel DM3 metaheuristic is capable of generating the efficient frontier (also known as the set of Pareto nondominated solutions). Our empirical findings for the Tunisian Stock Exchange in 2024 indicate that three indices Consumer Services, Distribution, and Basic Materials are the most sensitive, with the Basic Materials index being particularly prominent. For financial risk, the minimum-risk solution is associated with high values for the Consumer Services and Distribution indices and a lower value for the Basic Materials index. In contrast, for financial return, the maximum-return solution is characterized by lower values for the Consumer Services and Distribution indices and a higher value for the Basic Materials index.