Guiding Solution Based Local Search for Obstacle-Avoiding Rectilinear Steiner Minimal Tree Problem

Tiancheng Zhang, Zhipeng Lü, Junwen Ding

Abstract: The obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) problem plays an important role in the physical design of very large scale integrated circuits. It aims to find a Steiner tree with minimal wire length to connect all the terminal vertices in the routing region. Due to the existence of obstacles on the chip, it is more complex than rectilinear Steiner minimal tree problem which is known to be NP-complete. This article proposes a guiding solution based local search method (GSLS) to solve the OARSMT problem. First, we generate the escape graph for the OARSMT problem. Second, for an initial solution, we combine the U-shaped pattern refinement and the super edge replacement to optimize the solution. Third, we propose a guiding solution based local search to further improve the quality of solutions. Experimental results show that the proposed GSLS algorithm outperforms the state-of-the-art algorithms in terms of both solution quality and computational efficiency. In particular, GSLS improves the best known solution and obtains the optimal solutions for 1 and 19 out of 22 benchmark instances, respectively.