Steiner　minimal　tree　is　the　best　model　of　routing　stage　in　modern　very　large-scale　integration　(VLSI)　chips,　and　is　often　used　for　pre-routing,　wirelength　optimization,　and　congestion　estimation.　Therefore,　it　is　of　great　significance　to　construct　a　high-performance　Steiner　minimal　tree　algorithm.　However,　with　the　emergence　of　obstacles　such　as　IP　blocks　and　the　continuous　improvement　of　circuit　density,　obstacles　have　become　a　factor　that　cannot　be　ignored　in　the　Steiner　minimal　tree　construction　problem.　Considering　that　in　modern　multi-layer　routing,　obstacles　often　only　occupy　the　device　layer　and　the　lower　metal　layer.　Therefore,　the　routing　on　the　top　of　the　obstacles　is　possible,　and　it　can　make　full　use　of　routing　resources　and　further　optimize　the　wirelength.　Since　the　Steiner　minimal　tree　construction　problem　is　an　NP-hard　problem,　the　particle　swarm　optimization　algorithm　has　a　good　application　prospect　in　solving　NP-hard　problems.　Therefore,　on　the　basis　of　the　particle　swarm　optimization　algorithm,　further　considering　the　model　of　slew　constraints　that　can　effectively　prevent　signal　distortion,　and　the　X-architecture　with　better　wirelength　optimization,　this　paper　is　the　first　work　to　propose　an　X-architecture　Steiner　minimal　tree　algorithm　with　slew　constraints　based　on　hybrid　discrete　particle　swarm　optimization.　Firstly,　in　order　to　avoid　frequent　slew　calculation　and　judgment　between　routing　and　obstacles,　an　efficient　preprocessing　strategy　is　proposed.　In　this　preprocessing　strategy,　the　information　between　all　possible　routing　of　any　two　pins　and　all　obstacles　is　calculated　in　advance,　and　a　suitable　lookup　table　is　generated　based　on　this　information　for　subsequent　queries.　Secondly,　in　order　to　effectively　solve　the　discrete　problem　of　Steiner　minimal　tree　construction,　an　effective　discrete　update　operation　formula　of　particle　swarm　optimization　algorithm　is　redesigned,　which　is　based　on　the　mutation　operator　and　the　crossover　operator.　For　discrete　particle　swarm　optimization,　a　pin-pair　coding　method　that　is　more　suitable　for　this　discrete　particle　swarm　optimization　and　a　targeted　penalty　mechanism　that　can　effectively　consider　slew　constraints　are　proposed.　In　addition,　so　as　to　speed　up　the　search　efficiency　of　the　particle　swarm　optimization　algorithm,　the　Prim　method　is　used　to　construct　a　minimum　spanning　tree　under　a　given　pin　set,　and　initialize　the　population.　Thirdly,　in　order　to　further　optimize　wirelength　of　the　routing　tree,　an　effective　local　optimal　refining　strategy　is　proposed.　In　this　step,　the　Steiner　tree　is　divided　into　multiple　subtrees　with　roots　as　pins　and　a　depth　of　2.　By　traversing　all　possible　routing　structures　in　the　subtree,　the　routing　structure　with　the　highest　degree　of　routing　resource　sharing　is　selected　to　replace　the　original　routing　structure.　Thereby　the　goal　of　optimizing　the　wirelength　is　achieved.　Finally,　in　order　to　make　the　Steiner　minimal　tree　fully　satisfy　the　slew　constraints,　a　hybrid　correction　strategy　is　proposed.　In　this　part,　by　estimating　the　cost　of　adjusting　the　routing,　this　paper　selects　the　overall　adjustment　strategy　or　the　adjustment　strategy　along　the　barrier　to　correct　the　routing　that　violates　the　slew　constraints.　Experiments　show　that　the　proposed　algorithm　can　achieve　the　best　routing　result　and　fully　satisfy　the　slew　constraints.　©　2021,　Science　Press.　All　right　reserved.