A Hybridizing-Enhanced Quantum-Inspired Differential Evolution Algorithm with Multi-Strategy for Complicated Optimization

Abstract Differential Evolution (DE) has been found to be inefficient and inaccurate for high-dimensional complex problems. Quantum-inspired Differential Evolution (QDE) possesses quantum computational properties, enabling effective handling of high-dimensional problems. However, QDE is plagued by issues of excessive mutation and poor convergence. Therefore, a hybrid enhanced Quantum-inspired Differential Evolution algorithm, termed QAHQDE, is proposed. Within QAHQDE, an improved chaotic strategy is designed. Non-repeating distributed quantum positions are generated, enhancing the diversity of initialized individuals. A quantum-adaptive mutation strategy is adopted to address the over-mutation problem inherent in QDE. The mutation degree is adaptively reduced, and convergence performance is thereby improved. A novel hybrid mutation strategy is constructed. Weighted mutation operators are combined with standard differential evolution. Local and global search capabilities are balanced, and convergence accuracy is enhanced. The performance of QAHQDE was evaluated against 38 algorithms using 48 benchmark functions from CEC2005, CEC2010, and CEC2013, across dimensions D=100, 500, 1000, and 3000. Experimental results demonstrate that QAHQDE outperforms QDE by at least three orders of magnitude. Superior convergence performance, higher convergence accuracy, and excellent stability are exhibited by QAHQDE on most functions.