An improved strategy based on the t-distribution perturbation factor and random differential mutation operator was proposed, in order to address the issue of the RIME(the rime optimization algorithm) algorithm's monolithic search strategy and its limited search and development capabilities in the later stages, resulting in insufficient algorithm stability. Building on the hard-rime puncture mechanism of the RIME algorithm, the t-distribution perturbation factor was introduced to expand the search range within a local scope, aiming to explore superior positions around the optimal location. After the algorithm's iteration was completed, the random differential mutation operator was employed to mutate the newly updated particle positions, yielding better particles. Comparative experiments with similar algorithms on test sets CEC2017 and CEC2022 reveal that the improved RIME algorithm possesses enhanced search capabilities and better stability. Additionally, a Wilcoxon signed-rank test was conducted to verify the significant differences of the algorithm. Using classical test functions, the algorithm's characteristics were analyzed from four dimensions: optimal value iteration curve, average fitness value, first-dimensional variation trend, and population historical positions. Finally, the improved RIME algorithm was applied to optimize PID(proportional integral derivative) parameters in a simulation experiment, validating the algorithm's effectiveness and applicability.