An adaptative differential evolution with enhanced diversity and restart mechanism

Abstract

Differential Evolution (DE) stands out as an exceptional intelligent evolutionary algorithm, acclaimed for its simplicity in implementation and the ability to optimize without necessitating differentiable conditions. However, a significant pitfall of DE lies in its susceptibility to getting trapped in local minima, leading to algorithmic stagnation and substantial performance impairments. To counteract the shortcoming, the Adaptative Differential Evolution with Diversity Maintenance and Restart Mechanism (ADE-DMRM) is proposed. This approach integrates three primary innovations. Firstly, the algorithm controls the number of generations that individuals stay in the external archive based on the successful evolution rate, thereby optimizing the mutation strategy to effectively maintain population diversity. Secondly, ADE-DMRM proposes a novel restart mechanism in which the current stagnant individuals are identified by combining a stagnation tracker and a diversity assessment indicator and then regenerated using a dimension-learning-based approach. Thirdly, wavelet basis functions and Cauchy distributions are employed for scaling factor implementation across different stages, while the dimension change information of successfully evolved individuals is harnessed to refine the adaptive parameter control scheme. Finally, comprehensive experiments were undertaken on the CEC2013, CEC2014, and CEC2017 test sets, assessing accuracy, convergence speed, the efficacy of each module, and time complexity. The results confirm that ADE-DMRM is an efficient single-objective optimization algorithm that outperforms current advanced variants.