The　Steiner　minimal　tree　(SMT)　problem　is　an　NP-hard　problem,　which　is　the　best　connection　model　for　a　multi-terminal　net　in　global　routing　problem.　This　paper　presents　a　unified　algorithm　for　octagonal　and　rectilinear　SMT　construction　based　on　hybrid　transformation　strategy　(HTS)　and　self-adapting　particle　swarm　optimization.　Firstly,　an　effective　HTS　is　proposed　to　enlarge　the　search　space　and　improve　the　convergence　speed.　Secondly,　the　proposed　HTS　in　the　evolutionary　process　may　produce　an　ineffective　solution,　and　consequently　the　crossover　and　mutation　operators　of　genetic　algorithm　(GA)　based　on　union-find　sets　is　proposed.　Thirdly,　a　self-adapting　strategy　that　can　adjust　the　acceleration　coefficients　is　proposed　to　further　improve　the　convergence　and　the　quality　of　the　proposed　algorithm.　Finally,　the　hybrid　transformation　can　be　applied　to　GA　and　the　proposed　algorithm　can　be　applied　to　rectilinear　architecture.　To　our　best　knowledge,　the　proposed　algorithm　is　the　first　unified　algorithm　to　solve　the　SMT　construction　under　both　octagonal　and　rectilinear　architecture.　The　experimental　results　show　that　the　proposed　algorithm　can　efficiently　provide　a　better　solution　for　SMT　problem　both　in　octagonal　and　rectilinear　architectures　than　others.　Moreover,　the　algorithm　can　obtain　several　topologies　of　SMT,　which　is　beneficial　for　optimizing　congestion　in　VLSI　global　routing　stage.　©　2019,　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.