## 1 Introduction
This study aims to construct an optimal portfolio composed of efficient stocks from automotive companies while simultaneously managing the systematic risk. To this end, the MSV model is developed by integrating DEA with beta risk metrics. In contrast to traditional portfolio optimization approaches--such as mean variance or mean semivariance models that mainly depend on historical returns and risk measures like variance or semivariance--the proposed methodology assesses assets within a multidimensional analytical framework. DEA incorporates multiple financial indicators, treating risk and financial leverage as inputs and metrics like return on equity, earnings per share, and the inverse price-to-earnings ratio as outputs. This approach provides a more comprehensive perspective on asset performance and financial health, facilitating the identification of assets that have not only generated favorable returns but are also fundamentally robust. When an asset (typically a company's stock) is deemed fundamentally robust, it signifies that the issuing company possesses sound financial characteristics and indicators that suggest long-term stability, profitability, and growth potential. These attributes pertain to the company's operational performance and intrinsic value, rather than solely its stock price in the market. By allowing investors to prioritize criteria aligned with their objectives (e.g., earnings quality, valuation metrics, or capital structure), DEA enhances the portfolio selection process. As a result, the integration of DEA with the MSV model enables the construction of portfolios that excel not only in risk-return performance but also in foundational strength. This methodology transcends traditional optimization techniques by incorporating fundamental and operational factors, ensuring that selected assets operate efficiently and possess long-term growth potential. Portfolio optimization problems highlight the limitations of traditional analytical techniques, which struggle to address non-linear objective functions, multiple constraints, and high-dimensional search spaces. These challenges render conventional approaches computationally inefficient or impractical in real-world scenarios. To overcome these shortcomings, the proposed methodology employs neural networks and multi-objective evolutionary algorithms (NSGA2 and SPEA2). Neural networks excel by learning intricate patterns in financial data, while evolutionary algorithms--inspired by natural selection--systematically explore vast solution spaces to identify near-optimal portfolios. This synergy enables the model to navigate the complexities of portfolio construction, prioritizing risk-return trade-offs and investor-specific criteria with greater adaptability and precision. The remainder of this paper is organized as follows. Section 2 establishes the mathematical foundations of the DEA-\(\beta\)-MSV framework, detailing its components and theoretical principles. Section 3 follows with a comprehensive description of the feedforward neural network, emphasizing its architecture, training methodology, and adaptability to non-linear financial data for solving the optimization model. Section 4 then introduces the NSGA2 and SPEA2 algorithms, explaining their evolutionary mechanisms, parameter configurations, and integration into the multi-objective optimization workflow. Section 5 subsequently analyzes the empirical results derived from applying the proposed hybrid model to automotive sector portfolios, comparing the performance metrics across methodologies to evaluate their effectiveness. Finally, Section 6 synthesizes the key findings, discusses practical implications for portfolio management, and outlines potential directions for future research, reinforcing the study's contributions to adaptive and robust investment strategies.