Route　optimization　is　a　key　core　technology　to　optimize　network　traffic　distribution,　achieve　network　load　balancing,　and　improve　network　performance.　Traditional　distributed　networks　widely　run　shortest-path　based　routing　protocols,　and　the　path　of　traffic　is　determined　by　the　link　weights　of　the　distributed　network,　so　routing　optimization　methods　are　usually　optimized　around　the　link　weights　of　the　network.　Heuristics-based　link　weight　optimization　methods　are　widely　used.　However,　heuristic　methods　rely　on　manually　set　rules,　which　are　poorly　generalized　and　cannot　adapt　well　to　dynamically　changing　traffic　demands.　Compared　to　heuristics,　deep　reinforcement　learning　(DRL)　has　the　advantage　of　extracting　more　accurate　feature　representations　in　addition　to　its　ability　to　handle　high-dimensional　state　and　action　spaces.　We　propose　a　network　link　weight　optimization　method　based　on　anti-symmetric　deep　graph　networks　(A-DGN)　and　reinforcement　learning　using　a　novel　GNN　framework　anti-symmetric　deep　graph　networks,　where　link　weights　are　adjusted　to　reduce　the　network　link　utilization　with　the　optimization　objective　of　minimizing　the　maximum　link　utilization　in　the　network.　Experimental　results　show　that　the　proposed　method　achieves　significant　performance　improvements　in　the　link　weight　optimization　problem　in　four　real-world　network　topology　scenarios.　©　2024　IEEE.