Quantum differential evolutionary algorithm with quantum-adaptive mutation strategy and population state evaluation framework for high-dimensional problems

Differential Evolution (DE) has been found to be inefficient and inaccurate in addressing high-dimensional complex problems. The Quantum-inspired Differential Evolution algorithm (QDE), endowed with quantum computing characteristics, efficiently manages high-dimensional problems but suffers from excessive mutation and poor convergence performance. Therefore, a new quantum differential evolutionary algorithm with quantum-adaptive mutation strategy and population state evaluation framework, namely PSEQADE is proposed. In PSEQADE, the quantum adaptive mutation strategy is employed to address the issue of excessive mutation in QDE, which adaptively reduces the degree of mutation, taking full advantage of the exceptional performance of quantum computing to enhance convergence accuracy. The quantum adaptive PSE framework is introduced to monitor the unstable mutation trends within the population, evaluate the population's state, and intervene accordingly, thereby significantly improving the convergence performance and stability of the quantum differential evolution algorithm. 20 well-known functions from CEC2017 were selected for comparison with EPSDE, SADE, SHADE, JADE, CODE algorithms in dimensions of 500, 1000 and 3000. Additionally, comparisons were conducted with MLSHADE-SPA, SHADE-ILS, CCPSO2, NFDDE, DBO, and RIME algorithms in the dimension of 3000. Experimental results demonstrate that PSEQADE exhibits excellent convergence performance, high convergence accuracy, and exceptional stability in solving high-dimensional complex problems.