A local optimal processing framework for differential evolution

Differential evolution (DE) algorithms often fall into local optimal, severely limiting the performance. Existing solutions fail to accurately detect stagnation and lead to false positives of stagnation, which makes it difficult to obtain diverse solutions. In response to the above challenges, this paper proposes a local optimal processing framework for DE (LOPFDE). LOPFDE intelligently determines the individual's current search status by sensing the individual's position in the search space. When an individual falls into a stagnant state, LOPFDE uses diversity-controlled candidate solutions or the individual's historical optimal values ​​to replace the stagnant individual to help the search get rid of the local optimal. Overall, LOPFDE provides a powerful framework for stagnant individuals to escape from the local optimum and opens up a new way for identifying stagnant individuals in DE. LOPFDE is integrated into six representative DE variants and compared with the original algorithm on the CEC 2019 test set. The results show that LOPFDE can be integrated into various DE algorithms and significantly improve their convergence speed and solution accuracy.