Multi-Objective Portfolio Allocation Optimized via Evolutionary Engineering: Balancing Return, Risk, and Liquidity under Nonlinear Market Constraints

Abstract

Portfolio allocation in real-world financial markets requires balancing multiple conflicting objectives under complex and nonlinear constraints, including liquidity effects, transaction costs, and market impact, which are often inadequately addressed by traditional mean–variance frameworks. This study formulates portfolio weight selection as a multi-objective optimization problem that simultaneously maximizes expected return, minimizes risk measured by variance and Conditional Value-at-Risk (CVaR), and reduces liquidity-related costs arising from transaction costs and market impact. To solve the resulting non-convex and high-dimensional problem, several evolutionary multi-objective optimization algorithms, including NSGA-II, MOEA/D, MOPSO, and differential evolution–based variants, are employed to approximate the Pareto-optimal solution set. Nonlinear financial mathematical models are used to characterize transaction costs and price impact, while regulatory and budget constraints are directly incorporated into the optimization framework. Experimental results show that evolutionary approaches generate diverse and well-distributed Pareto frontiers, clearly revealing the trade-offs among return, risk, and liquidity. Compared with traditional single-objective and scalarized methods, the proposed framework offers greater flexibility and practical relevance, demonstrating the effectiveness of evolutionary multi-objective optimization as a robust decision-support tool for portfolio allocation in liquidity-sensitive and nonlinear market environments.