A population state evaluation-based improvement framework for differential evolution

Differential evolution (DE) is one of the most efficient evolutionary algorithms for solving numerical optimization problems; however, it still suffers from premature convergence and stagnation. To address these problems, we propose a population state evaluation (PSE)-based improvement framework that can be freely embedded into various existing DE variants and population-based metaheuristic algorithms. The PSE framework comprises two population state evaluation mechanisms: one for tracking the optimization state of the population during evolution and the other for evaluating the distribution state of individuals in the population to identify the specific problem (premature convergence or stagnation) encountered by the corresponding algorithm. In addition, we design two intervention operations (dispersion and aggregation) to address premature convergence and stagnation. To verify the effectiveness of the PSE framework, we conduct comparison experiments using nine algorithms (including two basic DE algorithms, six state-of-the-art DE variants, and one non-DE algorithm) to optimize four real-world problems and 59 test functions from the IEEE CEC 2014 and IEEE CEC 2017 testbeds. The experimental results show that the PSE framework can significantly improve the optimization performance of the existing algorithms.