A Multi-objective Optimization Framework for Portfolio Selection

This paper introduces a novel multi-objective optimization framework for the portfolio rebalancing problem, incorporating return, risk, and liquidity as the central financial objectives. Unlike static models, our approach captures market dynamics by allowing periodic reallocation of assets and explicitly modeling transaction costs. To address uncertainty in key financial parameters such as expected returns, volatility, and asset liquidity, we employ interval arithmetic, offering a flexible representation without requiring distributional assumptions. The framework models risk using semi-absolute deviation, which better reflects downside exposure compared to traditional variance. A distinctive feature of the model is the integration of nonlinear transaction costs, ensuring higher realism in trading scenarios. The optimization problem is formulated with interval coefficients and solved under multiple decision-making strategies: pessimistic, optimistic, and mixed (via convex combination). To validate the model, we conduct a case study on a cryptocurrency portfolio consisting of Bitcoin, Ethereum, Solana, and Binance Coin, covering the period January–March 2025. The numerical simulations demonstrate the adaptability of the proposed methodology under different investor attitudes and market conditions. Our findings show that the interval-based, multi-objective framework provides robust, diversified portfolio allocations and valuable strategic insights for decision-makers operating under uncertainty.