Energy　efficiency　is　the　major　concern　in　hierarchical　wireless　sensor　networks(WSNs),　where　the　major　energy　consumption　originates　from　radios　for　communication.　Due　to　notable　energy　expenditure　of　long-range　transmission　for　cluster　members　and　data　aggregation　for　Cluster　Head　(CH),　saving　and　balancing　energy　consumption　is　a　tricky　challenge　in　WSNs.　In　this　paper,　we　design　a　CH　selection　mechanism　with　a　mobile　sink　(MS)　while　proposing　relay　selection　algorithms　with　multi-user　multi-armed　bandit　(UM-MAB)　to　solve　the　problem　of　energy　efficiency.　According　to　the　definition　of　node　density　and　residual　energy,　we　propose　a　conception　referred　to　as　a　Virtual　Head　(VH)　for　MS　to　collect　data　in　terms　of　energy　efficiency.　Moreover,　we　naturally　change　the　relay　selection　problem　into　permutation　problem　through　employing　the　two-hop　transmission　in　cooperative　power　line　communication,　which　deals　with　long-distance　transmission.　As　far　as　the　relay　selection　problem　is　concerned,　we　propose　the　machine　learning　algorithm,　namely　MU-MAB,　to　solve　it　through　the　reward　associated　with　an　increment　for　energy　consumption.　Furthermore,　we　employ　the　stable　matching　theory　based　on　marginal　utility　for　the　allocation　of　the　final　one-to-one　optimal　combinations　to　achieve　energy　efficiency.　In　order　to　evaluate　MU-MAB,　the　regret　is　taken　advantage　to　demonstrate　the　performance　by　using　upper　confidence　bound　(UCB)　index.　In　the　end,　simulation　results　illustrate　the　efficacy　and　effectiveness　of　our　proposed　solutions　for　saving　and　balancing　energy　consumption.