Efficient VLSI routing algorithm employing novel discrete PSO and multi-stage transformation

Abstract

For routing industrial circuits, the Steiner minimal tree (SMT) model can be applied in different routing problems, such as wirelength optimization, congestion reduction, and delay optimization. In this paper, an efficient VLSI routing algorithm employing novel discrete particle swarm optimization (PSO) and multi-stage transformation is proposed to build two types of SMT, including X-architecture Steiner minimal tree and rectilinear Steiner minimal tree. Firstly, to simultaneously handle two types of SMT problems, an effective encoding strategy is proposed to be more suitable for PSO and thus it can overcome the difficulty of designing different algorithms for different routing architectures. Secondly, a multi-stage transformation strategy is presented to expand the search space of the proposed algorithm and accelerate the convergence speed of the proposed algorithm. Various combinations of multi-stage transformation strategies have been tested to highlight the best combination. Furthermore, the various genetic operators combined with union-find data structure strategy are proposed to construct the novel and effective discrete particle update formula. Experimental simulation results on industrial circuits show that the proposed algorithm can get the best solutions among the existing algorithms.