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

TL;DR

This work tackles high-dimensional, constraint-rich portfolio optimization by recasting the Sharpe-ratio objective as an unconstrained single-objective problem using adaptive penalties. It introduces Quantum Hybrid Differential Evolution (QHDE), a quantum-inspired enhancement of Differential Evolution featuring good-point-set chaos initialization, a Schrödinger-like population evolution mechanism, and a dynamic elite-pool with Cauchy–Gaussian perturbations. Across CEC benchmark suites and real-world portfolios with 20–80 assets, QHDE delivers faster convergence, higher precision, and improved robustness, outperforming seven state-of-the-art optimizers by up to 73.4%. The approach demonstrates strong global exploration and local exploitation in high-dimensional, constrained financial optimization, with potential extensions to multi-objective and dynamic portfolio tasks.

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 propose a Quantum Hybrid Differential Evolution (QHDE) algorithm, which integrates Quantum-inspired probabilistic behavior into the standard DE framework. QHDE employs a Schrodinger-inspired probabilistic mechanism for population evolution, enabling more flexible and diversified solution updates. To further enhance performance, a good point set-chaos reverse learning strategy is adopted to generate a well-dispersed initial population, and a dynamic elite pool combined with Cauchy-Gaussian hybrid perturbations strengthens global exploration and mitigates premature convergence. Experimental validation on CEC benchmarks and real-world portfolios involving 20 to 80 assets demonstrates that QHDE's performance improves by up to 73.4%. 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 and advancing quantum-inspired evolutionary research in computational finance.

Figures (6)

• Figure 1: Flow chart of QHDE
• Figure 1: Evaluation and comparison of QHDE applied to 40-80 stocks alongside other metaheuristic algorithms.
• Figure 2: Ranking distribution of different algorithms on CEC 2020 (Dim=10).
• Figure 3: Ranking distribution of different algorithms on CEC 2022. (a) Dim = 10, (b) Dim = 20.
• Figure 4: Box plots of QHDE and other algorithms on CEC 2022 functions.