Resource　usage　prediction　in　cloud　data　centers　is　critically　important.　It　can　improve　providers＇　service　quality　and　avoid　resource　wastage　and　insufficiency.　However,　the　time　series　of　resource　usage　in　cloud　environments　is　characterized　by　multidimensional,　nonlinear,　and　high-volatility　characteristics.　Achieving　high-accuracy　prediction　for　time　series　with　such　characteristics　is　necessary　but　difficult.　Traditional　prediction　methods　based　on　regression　algorithms　and　recurrent　neural　networks　cannot　effectively　extract　nonlinear　features　from　data　sets.　Besides,　many　deep　learning　models　suffer　from　gradient　explosion　or　gradient　vanishing　during　the　training　stage.　Current　commonly　used　prediction　methods　fail　to　uncover　some　vital　information　about　the　frequency　domain　features　in　the　time　series.　To　resolve　these　challenges,　we　design　a　Forecasting　method　based　on　the　Integration　of　a　Savitzky-Golay　(SG)　filter,　a　frequency　enhanced　decomposed　transformer　(FEDformer)　model,　and　a　frequency-enhanced　channel　attention　mechanism　(FECAM),　named　FISFA.　It　adopts　the　SG　filter　to　reduce　noise　and　smooth　sequences　in　the　raw　sequences　of　resources.　Then,　we　develop　a　hybrid　transformer-based　model　integrating　FEDformer　and　the　FECAM,　effectively　capturing　the　frequency　domain　patterns.　Besides,　a　meta-heuristic　optimization　algorithm,　i.e.,　genetic　simulated　annealing-based　particle　swarm　optimizer,　is　proposed　to　optimize　key　hyperparameters　of　FISFA.　Then,　FISFA　predicts　the　future　needs　for　multidimensional　resources　in　highly　fluctuating　traces　in　real-life　cloud　environments.　Experimental　results　demonstrate　that　FISFA　achieves　higher　accuracy　and　performs　more　efficient　prediction　than　several　benchmark　forecasting　methods　with　realistic　data　sets　collected　from　Alibaba　and　Google　cluster　traces.　FISFA　improves　the　prediction　accuracy　on　average　by　32.14%,　25.49%,　and　27.71%　over　vanilla　long　short-term　memory,　transformer,　and　Informer　methods,　respectively.