Power　capping　is　an　important　solution　to　keep　the　system　within　a　fixed　power　constraint.　However,　for　the　over-provisioned　and　power-constrained　systems,　especially　the　future　exascale　supercomputers,　powercap　needs　to　be　reasonably　allocated　according　to　the　workloads　of　compute　nodes　to　achieve　trade-offs　among　performance,　energy　and　powercap.　Thus　it　is　necessary　to　model　performance　and　energy　and　to　predict　the　optimal　powercap　allocation　strategies.　Existing　power　allocation　approaches　have　insufficient　granularity　within　nodes.　Modeling　approaches　usually　model　performance　and　energy　separately,　ignoring　the　correlation　between　objectives,　and　do　not　expose　the　Pareto-optimal　powercap　configurations.　Therefore,　this　article　combines　the　powercap　with　uncore　frequency　scaling　and　proposes　an　approach　to　predict　the　Pareto-optimal　powercap　configurations　on　the　power-constrained　system　for　input　MPI　and　OpenMP　parallel　applications.　Our　approach　first　uses　the　elaborately　designed　micro-benchmarks　and　a　small　number　of　existing　benchmarks　to　build　the　training　set,　and　then　applies　a　multi-objective　machine　learning　algorithm　which　combines　the　stacked　single-target　method　with　extreme　gradient　boosting　to　build　multi-objective　models　of　performance　and　energy.　The　models　can　be　used　to　predict　the　optimal　processor　and　memory　powercap　settings,　helping　compute　nodes　perform　fine-grained　powercap　allocation.　When　the　optimal　powercap　configuration　is　determined,　the　uncore　frequency　scaling　is　used　to　further　optimize　the　energy　consumption.　Compared　with　the　reference　powercap　configuration,　the　predicted　optimal　configurations　predicted　by　our　method　can　achieve　an　average　powercap　reduction　of　31.35　percent,　an　average　energy　reduction　of　12.32　percent,　and　average　performance　degradation　of　only　2.43　percent.　©　1990-2012　IEEE.