Multi-objective　optimisation　algorithm　based　on　decomposition　(MOEA/D)　is　a　well-known　multi-objective　optimisation　algorithm,　which　was　widely　applied　for　solving　multi-objective　optimisation　problems　(MOPs).　MOEA/D　decomposes　a　multi-objective　problem　into　a　set　of　scalar　single　objective　sub-problems　using　aggregation　function　and　evolutionary　operator.　A　further　improved　version　of　MOEA/D　with　dynamic　resource　allocation　strategy　(MOEA/D-DRA)　has　exhibited　outstanding　performance　on　CEC2009　in　terms　of　the　convergence.　However,　it　is　very　sensitive　to　the　neighbourhood　size.　In　this　paper,　a　new　enchanted　MOEA/D-ANA　strategy　based　on　the　adaptive　neighbourhood　size　adjustment　(MOEA/D-ANA)　was　presented　to　increase　the　diversity,　which　mainly　focuses　on　the　solutions　density　around　sub-problems.　The　experiment　results　demonstrate　that　MOEA/D-ANA　performs　the　best　compared　with　other　five　classical　MOEAs　on　the　CEC2009　test　instances.