The purpose of this study is to compare the performance of classical and metaheuristic models in optimizing the stock portfolios of energy-sector companies listed on the Tehran Stock Exchange. Within the classical framework, the mean–variance Markowitz model and its extended versions were employed as the analytical baseline, and the results were compared with the three metaheuristic algorithms: Multi-Objective Particle Swarm Optimization (MOPSO), Non-dominated Sorting Genetic Algorithm II (NSGA-II), and the Strength Pareto Evolutionary Algorithm 2 (SPEA2). Data related to 19 energy-sector companies during the period 2019–2024 (1398–1403) were collected and analyzed using the Python environment to construct the efficient frontier, derive optimal asset weights, and compute performance indicators including the Modified Sharpe Ratio and the Omega Ratio.
The findings revealed that the MOPSO algorithm outperformed the Markowitz model by generating a more convergent efficient frontier and achieving higher risk-adjusted returns; specifically, the Modified Sharpe Ratio reached 0.84, and the Omega Ratio exceeded one significantly, indicating an asymmetric return distribution and a higher probability of achieving positive returns. In contrast, the NSGA-II algorithm exhibited weaker performance and failed to converge effectively to the efficient frontier, while the SPEA2 algorithm demonstrated intermediate and relatively stable results.