A hybrid machine learning and miqp approach for multi-objective portfolio optimization

Abstract

The hybrid approach between machine learning and mixed-integer quadratic programming (MIQP) is proposed in this study to optimize a multi-objective portfolio that trades off between return rate and downside risk. This research is inspired by traditional approaches such as Markowitz variance and fuzzy-clustering, which rely on historical data and statistical methods that may not fully capture time-dependent non-linear patterns of asset return. The fuzzy logic approach may not provide precise return rate and downside risk results since it handles uncertainty by providing results in a range, which is hard to compare with other approaches and benchmark with a market index, which is crucial to measure performance before real-world decision-making. Therefore, this study provides an approach that is more actionable for decision-making by using machine learning to capture non-linear relationships in data to provide a prediction under uncertainty and using mixed-integer quadratic programming to construct the best single-period portfolio scenario that maximizes return rate while minimizing portfolio downside risk and capturing co-movement between assets. This study focuses on the US mutual fund market by integrating data-driven forecasting and mathematical optimization to improve prediction and allocation efficiency. This framework is separated into two main stages. In the first stage, an Artificial Neural Network (ANN) is used to predict the monthly return rate for each mutual fund by training with historical data and evaluating by splitting 70% for training, 15% for validation, and 15% for testing. After hyper-parameter tuning, ANN is the most suitable model for this continuous numerical dataset when compared with ensemble approaches. It achieved strong performance at the aggregate portfolio level, but at fund-level it was unable to capture volatility, and the prediction moved toward global mean bias. To address this, ANN forecast results were combined with historical average return using weighted blending, where optimal weights were obtained from mixed integer nonlinear programming to minimize mean bias error at the individual level. The final predicted return came from a combination of a machine learning forecast, 36 months average return from 2021 to 2023, and 12 months average return from 2023. In the second stage, the final predicted return was input into the MIQP model to maximize overall return and minimize downside risk measured by the semi-covariance matrix that captures co-movement during negative periods. This allows the model to account for joint downside behaviour and recognize the value of diversification instead of allocating all capital to the best asset. The optimization is conducted in a single-period framework to find the best portfolio scenario in 2024 and compared with the market index benchmark in the same mutual fund universe. The predictive performance of ANN was also compared with a clustering-based approach to validate whether machine learning is a better alternative. The result shows that the fine-tuned ANN predicted aggregate return better than clustering with greater adaptability. Ensemble methods, including voting ANN with Random Forest and stacking ANN–Random Forest–linear regression, were also tested but did not outperform standalone ANN due to similarity in error structure and low signal diversity. Finally, the portfolio allocated by MIQP generated return and downside risk that outperform VTSAX, representing the US Total Market index, in terms of Sharpe ratio, and achieved diversification across multiple funds instead of selecting a single fund. This shows that a hybrid approach between machine learning and MIQP can produce better portfolio performance and provide actionable and comparable results for real investment decision-making.