A Quantum-Driven Evolutionary Framework for Solving High-Dimensional Sharpe Ratio Portfolio Optimization

TL;DR

This paper introduces a quantum-inspired evolutionary algorithm that effectively solves high-dimensional portfolio optimization problems by enhancing exploration, diversity, and convergence speed, validated on benchmark and real-world data.

Contribution

It develops a novel Quantum Hybrid Differential Evolution algorithm with quantum tunneling and chaos strategies, improving optimization performance over existing methods.

Findings

QHDE improves solution quality by up to 96.6%

It achieves faster convergence and higher robustness

Demonstrates effectiveness on portfolios with 20 to 80 assets

Abstract

High-dimensional portfolio optimization faces significant computational challenges under complex constraints, with traditional optimization methods struggling to balance convergence speed and global exploration capability. To address this, firstly, we introduce an enhanced Sharpe ratio-based model that incorporates all constraints into the objective function using adaptive penalty terms, transforming the original constrained problem into an unconstrained single-objective formulation. This approach preserves financial interpretability while simplifying algorithmic implementation. To efficiently solve the resulting high-dimensional optimization problem, we develop a Quantum Hybrid Differential Evolution (QHDE) algorithm, which introduces a dynamic quantum tunneling mechanism that enables individuals to probabilistically escape local optima, dramatically enhancing global exploration and solution flexibility. To further improve performance, a good point set-chaos reverse learning strategy generates a well-dispersed initial population, providing a robust and diverse starting point. Meanwhile, a dynamic elite pool combined with Cauchy-Gaussian hybrid perturbations maintains population diversity and mitigates premature convergence, ensuring stable and high-quality solutions. Experimental validation on CEC benchmarks and real-world portfolios involving 20 to 80 assets demonstrates that QHDE's performance improves by up to 96.6%. It attains faster convergence, higher solution precision, and greater robustness than seven state-of-the-art counterparts, thereby confirming its suitability for complex, high-dimensional portfolio optimization.