Novel quantum tunneling and fractional calculus-based metaheuristic for robust global data optimization and its applications in engineering design

Background:: Bound-constrained single-objective optimization and constrained engineering design often feature heterogeneous landscapes and barrier-like structures, motivating search procedures that are scale-aware, robust near constraints, and economical in tuning. Contributions:: We introduce Quantum Tunneling and Fractional Calculus-Based Metaheuristic (QTFM), a physics-inspired metaheuristic that is parameter-lean and employs bounded, range-aware operators to reduce sensitivity to tuning and to prevent erratic steps close to constraints. Methodology:: QTFM couples fractional-step dynamics for scale-aware exploitation with a quantum-tunneling jump for barrier crossing, and augments these with a wavefunction-collapse local search that averages a small neighborhood and applies minimal perturbations to accelerate refinement without sacrificing diversity. Results:: On the IEEE Congress on Evolutionary Computation CEC 2022 single-objective bound-constrained suite, QTFM ranked first on ten of twelve functions; it reached the best optimum on F1 and achieved the best mean values on F2–F8 and F10–F11 with stable standard deviations. In three constrained engineering problems, QTFM produced the lowest mean and the best-found solution for the robotic gripper design, and the lowest mean for the planetary gear train and three-bar truss design. Findings:: The proposed fractional–quantum approach delivers fast, accurate, and robust search across heterogeneous landscapes and real-world design problems.