Abstract: This paper introduces a matrix-based Genetic Algorithm for portfolio optimization under second-order stochastic dominance and cardinality constraints. By reformulating all evolutionary operations—evaluation, selection, and mutation—into matrix algebra, the proposed method achieves substantial computational gains while maintaining accuracy comparable to exact mixed-integer programming solutions. The results demonstrate that the matrix-based implementation reduces computation time by more than an order of magnitude compared to individual-based genetic algorithms, enabling the use of significantly larger populations without prohibitive runtime. The boosted configuration with 10,000 individuals shows stable convergence and consistent attainment of near-optimal portfolios, confirming that matrix-based evaluation provides both efficiency and scalability for large-scale second-order stochastic dominance constrained optimization problems.

Keywords: Genetic Algorithm, Mixed-Integer Programming, Portfolio Optimization, Risk Management, Stochastic Dominance, Vectorization

Pages: 2824-2833