Rime optimization algorithm (RIME) is an emerging metaheuristic algorithm. However, RIME encounters issues such as an imbalance between exploitation and exploration, susceptibility to local optima, and low convergence accuracy when handling problems. To address these drawbacks, this paper introduces a variant of RIME called IRIME. IRIME integrates the soft besiege (SB) and composite mutation strategy and restart strategy (CMS-RS), aiming to balance exploitation and exploration in RIME, enhance population diversity, improve convergence accuracy, and endow RIME with the capability to escape local optima. To comprehensively validate IRIME's performance, IEEE CEC 2017 benchmark tests were conducted, comparing it against 13 conventional algorithms and 11 advanced algorithms, including excellent algorithms in the CEC competition such as JADE. The results indicate that the performance of IRIME is the best. To validate IRIME's practical applicability, the paper proposes a binary version, bIRIME, 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 performs notably well in feature selection, particularly in high-dimensional datasets.