Legalization　holds　significant　importance　in　VLSI　physical　design,　as　it　significantly　influences　the　manufacturability　and　reliability　of　circuits.　Recently,　advanced　foundry　nodes　introduced　complex　constraints　in　standard-cell　legalization,　which　makes　legalization　even　harder.　In　this　paper,　we　develop　a　legalization　framework　with　design　rule　constraints　enhanced　by　Monte-Carlo-Based　cell　priority　optimization.　We　first　handle　abnormal　density　distribution　to　reduce　the　subsequent　legalization＇s　hardness.　Then,　we　propose　an　interval-assisted　sequential　legalization　algorithm　considering　multiple　design　rule　constraints　with　a　Monte-Carlo-Based　cell　priority　decision　technique.　Besides,　based　on　the　characteristics　and　complexity　of　different　design　rule　constraints,　we　present　a　refinement　phase　to　handle　the　remaining　design　rule　constraints　with　corresponding　detectors.　Compared　with　a　leading　commercial　tool,　experiments　on　industrial　benchmarks　show　that　our　legalization　framework　achieves　11%　smaller　average　displacement,　15%　smaller　maximum　displacement,　1.63×　speedup,　and　13%　fewer　remaining　design　rule　violations　on　average.　©　2025　IEEE.