This research investigates the application of multiple solver engines to enhance the optimization of nonlinear programming models, focusing on Evolutionary Strategies. These strategies mitigate the limitations of other optimization techniques, offering a robust approach to complex problems. Quadratic programming is especially beneficial as it allows for more flexible modeling compared to linear programming, accounting for correlations between asset pairs. This paper explores various algorithms for solving quadratic optimization issues, particularly in the financial sector using the mean-variance Markowitz model. The quadratic framework integrates risk factors through a quadratic term in the objective function.

Nonlinear optimization poses significant challenges, with the absence of universal solutions underscoring the importance of understanding the problem at hand to select appropriate methods and parameters. A key difficulty is the tendency of many algorithms to get trapped in local optima, leading to suboptimal results. Evolutionary Strategies, employing iterative trial and error and randomization, help address this by improving the likelihood of finding global optima, although they typically work slower than deterministic solvers. This research highlights Particle Swarm Optimization as an effective solver.

Data from 15 major international stock market indices, covering Europe, Asia, and North America from January 2020 to December 2024, are used to construct a buy-and-hold portfolio over a five-year horizon. Portfolio performance is evaluated using metrics, such as Portfolio Return (mean), Risk (standard deviation), Sharpe Ratio, Treynor Ratio, Sortino Ratio, Omega Ratio, Systematic Risk (Beta, Jensen's Alpha), Portfolio Drawdown (Calmar Ratio), Value at Risk (VaR), Expected Shortfall (ES), and distribution characteristics like Skewness and Kurtosis, to provide a comprehensive analysis of performance.