In　order　to　obtain　the　optimal　structure　size　of　a　microchannel　heat　sink　(MCHS)　with　arc-shaped　grooves　and　ribs　according　to　the　actual　demand,　multiple　parameters　that　influence　the　performance　of　the　microchannel　are　analyzed　by　combining　the　multi-objective　evolutionary　algorithm　(MOEA)　with　computational　fluid　dynamics　(CFD).　The　design　variables　include　the　relative　groove　height,　relative　rib　height　and　relative　rib　width,　and　the　two　objective　functions　are　to　minimize　the　total　thermal　resistance　and　pumping　power　in　constant　volume　flow　rate.　The　influences　of　the　design　variables　on　the　two　objective　functions　are　analyzed　by　CFD　firstly.　The　results　show　that　each　design　variable　has　a　different　impact　on　the　two　functions.　The　competitive　relationship　between　the　two　objective　functions　is　depicted　in　plots　of　the　Pareto　front　obtained　by　MOEA.　Pareto　sensitivity　analysis　is　carried　out　to　find　that　the　relative　rib　height　has　the　most　significant　impact　on　the　two　objective　functions.