Legalized　routing　is　an　essential　part　of　PCB　automatic　routing.　It　solves　the　problem　of　wiring　conflicts　and　obtains　routing　results　that　comply　with　the　constraints　of　design　rules.　Traditional　legalized　routing　problems　mostly　use　trial　backtracking　methods,　but　with　increasing　design　complexity　and　design　rules,　avoiding　wiring　conflicts　between　networks　has　become　increasingly　challenging.　This　paper　proposes　a　legalized　routing　algorithm　based　on　linear　programming　to　obtain　the　optimal　wiring　trajectory　under　specified　topological　constraints.　First,　the　corresponding　routing　model　was　established　based　on　numerous　routing　rules,　and　a　routing　grid　diagram　was　found　using　obstacles　as　grid　points.　Secondly,　a　global　routing　algorithm　was　used　to　obtain　the　estimated　wiring　path,　and　integer　linear　programming　was　used　to　realize　the　mathematical　modeling　of　the　legalized　routing　problem.　Finally,　a　multi-line　simultaneous　routing　strategy　was　used　to　design　and　implement　a　detailed　routing　algorithm,　optimizing　the　routing　results.　We　use　C++　to　complete　the　coding　work　and　thoroughly　test　the　PCB　use　cases　of　different　sizes.　The　experimental　results　show　that　our　algorithm　still　maintains　a　100%　routing　success　rate,　good　time　performance,　and　excellent　routing　quality　with　large-scale　use　cases　compared　with　the　trial　backtracking　method.