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

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.

A Quantum Tunneling and Bio-Phototactic Driven Enhanced Dwarf Mongoose Optimizer for UAV Trajectory Planning and Engineering Problem

With the widespread adoption of unmanned aerial vehicles (UAV), effective path planning has become increasingly important. Although traditional search methods have been extensively applied, metaheuristic algorithms have gained popularity due to their efficiency and problem-specific heuristics. However, challenges such as premature convergence and lack of solution diversity still hinder their performance in complex scenarios. To address these issues, this paper proposes an Enhanced Multi-Strategy Dwarf Mongoose Optimization (EDMO) algorithm, tailored for three-dimensional UAV trajectory planning in dynamic and obstacle-rich environments. EDMO integrates three novel strategies: (1) a Dynamic Quantum Tunneling Optimization Strategy (DQTOS) to enable particles to probabilistically escape local optima; (2) a Bio-phototactic Dynamic Focusing Search Strategy (BDFSS) inspired by microbial phototaxis for adaptive local refinement; and (3) an Orthogonal Lens Opposition-Based Learning (OLOBL) strategy to enhance global exploration through structured dimensional recombination. EDMO is benchmarked on 39 standard test functions from CEC2017 and CEC2020, outperforming 14 advanced algorithms in convergence speed, robustness, and optimization accuracy. Furthermore, real-world validations on UAV three-dimensional path planning and three engineering design tasks confirm its practical applicability and effectiveness in field robotics missions requiring intelligent, adaptive, and time-efficient planning.