Evolutionary　algorithms　have　shown　their　promise　in　coping　with　many-objective　optimization　problems.　However,　the　strategies　of　balancing　convergence　and　diversity　and　the　effectiveness　of　handling　problems　with　irregular　Pareto　fronts　(PFs)　are　still　far　from　perfect.　To　address　these　issues,　this　paper　proposes　an　adaptive　sorting-based　evolutionary　algorithm　based　on　the　idea　of　decomposition.　First,　we　propose　an　adaptive　sorting-based　environmental　selection　strategy.　Solutions　in　each　subpopulation　(partitioned　by　reference　vectors)　are　sorted　based　on　their　convergence.　Those　with　better　convergence　are　further　sorted　based　on　their　diversity,　then　being　selected　according　to　their　sorting　levels.　Second,　we　provide　an　adaptive　promising　subpopulation　sorting-based　environmental　selection　strategy　for　problems　which　may　have　irregular　PFs.　This　strategy　provides　additional　sorting-based　selection　effort　on　promising　subpopulations　after　the　general　environmental　selection　process.　Third,　we　extend　the　algorithm　to　handle　constraints.　Finally,　we　conduct　an　extensive　experimental　study　on　the　proposed　algorithm　by　comparing　with　start-of-the-state　algorithms.　Results　demonstrate　the　superiority　of　the　proposed　algorithm.