Energy　saving　is　a　great　challenge　for　clean　transportation.　In　this　paper,　we　study　the　Energy　Minimization　Traveling　Salesman　Problem　(EMTSP),　which　is　a　generation　of　the　classical　Traveling　Salesman　Problem　(TSP),　and　an　important　theoretical　basis　and　a　special　case　of　the　Energy　Minimization　Vehicle　Routing　Problem　(　EMVRP).　The　objective　of　the　studied　problem　is　to　minimize　the　sum　of　the　product　of　load　(including　curb　weight　of　the　vehicle)　and　traveled　distances.　An　approximation　algorithm　based　on　the　Christofides＇s　Heuristic　is　proposed　and　its　worst-case　ratio　bound　is　proven.　A　branch　and　bound　(B&B)　algorithm　integrated　with　a　fast　1-tree　based　lower　bound　is　developed　to　obtain　optimal　solutions.　The　results　of　computational　experiments　show　the　efficiency　and　the　effectiveness　of　the　B&B　algorithm,　as　well　as　the　heuristic　methods.　(C)　2019　Elsevier　Ltd.　All　rights　reserved.