In　the　present　study,　an　optimization　model　of　double-layered　microchannel　heat　sink　(DL-MCHS)　is　developed　based　on　a　derivative-free　method,　BOBYQA　algorithm,　which　solves　optimization　problems　without　using　derivatives　of　the　objective　function.　Overall,　thermal　resistance　R-T　and　pumping　power　are　adopted　as　multi-objective　functions　to　search　for　optimal　design　variables.　The　effect　of　weight　factors　on　results　of　optimization　is　discussed.　With　the　increase　of　increases.　Moreover,　the　effect　of　design　variables　of　the　bottom　layers　on　flow　and　heat　transfer　performance　is　more　obvious　than　that　of　the　upper　layers.　Finally,　the　Pareto　fronts　of　counter-flow　and　cross-flow　DL-MCHS　are　calculated.　Results　indicate　that　counter-flow　heat　sink　shows　better　thermal　performance　compared　to　cross-flow　heat　sink　under　the　same　pumping　power　consumption.