Metaheuristics　are　widely　applied　for　their　ability　to　provide　more　efficient　solutions.　The　RIME　algorithm　is　a　recently　proposed　physical-based　metaheuristic　algorithm　with　certain　advantages.　However,　it　suffers　from　rapid　loss　of　population　diversity　during　optimization　and　is　prone　to　fall　into　local　optima,　leading　to　unbalanced　exploitation　and　exploration.　To　address　the　shortcomings　of　RIME,　this　paper　proposes　a　modified　RIME　with　covariance　learning　and　diversity　enhancement　(MRIME-CD).　The　algorithm　applies　three　strategies　to　improve　the　optimization　capability.　First,　a　covariance　learning　strategy　is　introduced　in　the　soft-rime　search　stage　to　increase　the　population　diversity　and　balance　the　over-exploitation　ability　of　RIME　through　the　bootstrapping　effect　of　dominant　populations.　Second,　in　order　to　moderate　the　tendency　of　RIME　population　to　approach　the　optimal　individual　in　the　early　search　stage,　an　average　bootstrapping　strategy　is　introduced　into　the　hard-rime　puncture　mechanism,　which　guides　the　population　search　through　the　weighted　position　of　the　dominant　populations,　thus　enhancing　the　global　search　ability　of　RIME　in　the　early　stage.　Finally,　a　new　stagnation　indicator　is　proposed,　and　a　stochastic　covariance　learning　strategy　is　used　to　update　the　stagnant　individuals　in　the　population　when　the　algorithm　gets　stagnant,　thus　enhancing　the　ability　to　jump　out　of　the　local　optimal　solution.　The　proposed　MRIME-CD　algorithm　is　subjected　to　a　series　of　validations　on　the　CEC2017　test　set,　the　CEC2022　test　set,　and　the　experimental　results　are　analyzed　using　the　Friedman　test,　the　Wilcoxon　rank　sum　test,　and　the　Kruskal　Wallis　test.　The　results　show　that　MRIME-CD　can　effectively　improve　the　performance　of　basic　RIME　and　has　obvious　superiorities　in　terms　of　solution　accuracy,　convergence　speed　and　stability.　©　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature　2025.