An improved multi-operator differential evolution with two-phase migration strategy for numerical optimization

Over the last decade, the multi-operator differential evolution (MODE) has become one of the most popular research areas in the differential evolution (DE) family. Among these MODEs, an improved multi-operator differential evolution (IMODE) has achieved success as the winner in CEC2020. Despite its good performance, the random information sharing strategy may not efficiently handle the balance between exploration and exploitation for the complex numerical optimization. To address this limitation, we propose a two-phase migration strategy (TMS) to improve the performance of IMODE, called IMODE-TMS. In the first phase, the top-ranked individuals in each sub-population are retained for exploitation, and all the bottom-ranked individuals are assigned to three sub-populations to maintain diversity. Furthermore, the second phase plays a crucial role in eliminating stagnation. When a sub-population is identified as stagnant by the stagnation indicator, the optimal individual will migrate to that sub-population following the uni-directional ring structure. This process is mainly used to increase the off-trap capability on some problems with complex fitness landscapes. IMODE-TMS is tested on the CEC2020, CEC2021 and CEC2022 benchmark functions, and seven well-known complex global trajectory optimization problems (GTOP). The experimental results show that IMODE-TMS significantly outperforms not only IMODE but also other state-of-the-art comparison algorithms.