Quantum-computing-driven Bat Algorithm: Balancing Exploration-Exploitation with Predictive Mutation and Frequency Adjustment for Optimization

Quantum computing (QC) has recently gained significant traction across various fields, spurring the integration of swarm intelligence algorithms into the quantum realm to boost their search capabilities. The bat algorithm (BA), modeled on bats’ echolocation-based prey-hunting behavior, is a swarm intelligence algorithm, but it often gets stuck in local minima under certain conditions. To solve the problems, this research puts forward a hybrid predictive mutation operation and adaptive frequency adjustment strategy from a QC perspective to optimize the BA for better performance in complex problems. The method evolves the BA system into a highly uncertain complex nonlinear system via the state superposition principle, adds an optimization factor to balance global exploration and local exploitation, builds a rigorous mathematical model based on QC, and conducts a convergence analysis proof. Three parameter-control-mode experiments are designed to explore key parameter impacts. Numerical experiments on classic benchmarks and the three-dimensional trajectory planning for UAVs show that the proposed APMQF-QBA method outperforms comparison algorithms. Overall, the new strategy effectively improves the BA, avoiding local extrema and accelerating convergence, offering a more efficient solution for relevant fields.