Summary: Rime optimization algorithm (RIME) encounters issues such as an imbalance between exploitation and exploration, susceptibility to local optima, and low convergence accuracy when handling problems. This paper introduces a variant of RIME called IRIME to address these drawbacks. IRIME integrates the soft besiege (SB) and composite mutation strategy (CMS) and restart strategy (RS). To comprehensively validate IRIME’s performance, IEEE CEC 2017 benchmark tests were conducted, comparing it against many advanced algorithms. The results indicate that the performance of IRIME is the best. In addition, applying IRIME in four engineering problems reflects the performance of IRIME in solving practical problems. Finally, the paper proposes a binary version, bIRIME, that can be applied to feature selection problems. bIRIMR performs well on 12 low-dimensional datasets and 24 high-dimensional datasets. It outperforms other advanced algorithms in terms of the number of feature subsets and classification accuracy. In conclusion, bIRIME has great potential in feature selection.