Quantum-inspired differential evolution with Elite Perturbation for high-dimensional portfolio optimization

Abstract High-dimensional portfolio optimization is a challenging computational problem due to its large search space, nonlinear objective structure, and practical constraints on asset allocation. To improve the computational tractability of Sharpe ratio-based portfolio optimization, this paper reformulates the original constrained model as an unconstrained single-objective problem by embedding equality and inequality constraints into the objective function through penalty terms. This reformulation simplifies constraint handling while retaining the financial interpretation of risk-return optimization. To solve the transformed problem, a quantum-inspired variant of Differential Evolution, termed Quantum-Inspired Differential Evolution with Elite Perturbation (QEPDE), is proposed. QEPDE extends the standard Differential Evolution framework through three complementary mechanisms. First, a good point set-chaos reverse learning strategy is introduced to generate a more diverse and well-distributed initial population. Second, a quantum-inspired population evolution strategy is designed to enhance global exploration and improve the flexibility of individual updates. Third, a dynamic elite pool with Cauchy-Gaussian hybrid perturbation is developed to preserve high-quality search information and reduce premature convergence. QEPDE is evaluated on the CEC 2020 and CEC 2022 benchmark suites, as well as four in-sample portfolio optimization instances involving 20, 40, 60, and 100 assets, and is compared with ADE, AVOA, DBO, DE, GWO, QHDBO, and WOA. On the CEC 2020 suite, QEPDE achieves the best results on 8 of the 10 functions at both 10 and 20 dimensions, with Friedman average ranks of 2.21 and 2.24, respectively. On the 20-dimensional CEC 2022 suite, QEPDE achieves the best results on 11 of the 12 functions and obtains the lowest Friedman average rank of 1.17. In the portfolio experiments, QEPDE achieves the highest mean penalized objective value on all four tested in-sample instances and the best or second-best mean Sharpe ratio across the four instances, while maintaining the full-investment constraint measure close to 1. These results indicate that QEPDE is competitive on the tested high-dimensional constrained optimization problems. All comparative performance statements in this abstract refer to the adopted equal-population-size and equal-iteration-count protocol rather than to an equal objective-function-evaluation budget.