A　large　number　of　evolutionary　algorithms　have　been　introduced　for　multi-objective　optimization　problems　in　the　past　two　decades.　However,　the　compromise　of　convergence　and　diversity　of　the　non-dominated　solutions　is　still　the　main　difficult　problem　faced　by　optimization　algorithms.　To　handle　this　problem,　an　efficient　competitive　mechanism　based　multi-objective　differential　evolution　algorithm　(CMODE)　is　designed　in　this　work.　In　CMODE,　the　rank　based　on　the　non-dominated　sorting　and　crowding　distance　is　first　adopted　to　create　the　leader　set,　which　is　utilized　to　lead　the　evolution　of　the　differential　evolution　(DE)　algorithm.　Then,　a　competitive　mechanism　using　the　shift-based　density　estimation　(SDE)　strategy　is　employed　to　design　a　new　mutation　operation　for　producing　offspring,　where　the　SDE　strategy　is　beneficial　to　balance　convergence　and　diversity.　Meanwhile,　two　variants　of　the　CMODE　using　the　angle　competitive　mechanism　and　the　Euclidean　distance　competitive　mechanism　are　proposed.　The　experimental　results　on　three　test　suites　show　that　the　proposed　CMODE　performs　better　than　six　state-of-the-art　multi-objective　optimization　algorithms　on　most　of　the　twenty　benchmark　functions　in　terms　of　hypervolume　and　inverted　generation　distance.　Furthermore,　the　proposed　CMODE　is　applied　to　the　feature　selection　problem.　The　comparison　results　on　feature　selection　also　demonstrate　the　efficiency　of　our　proposed　CMODE.　©　2022　Elsevier　B.V.