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Global routing is an important link in very large scale integration (VLSI) design. As the best model of global routing, X-architecture Steiner minimal tree (XSMT) has a good performance in wire length optimization. XSMT belongs to non-Manhattan structural model, and its construction process cannot be completed in polynomial time, so the generation of XSMT is an NP hard problem. In this paper, an X-architecture Steiner minimal tree algorithm based on multi-strategy optimization discrete differential evolution (XSMT-MoDDE) is proposed. Firstly, an effective encoding strategy, a fitness function of XSMT, and an initialization strategy of population are proposed to record the structure of XSMT, evaluate the cost of XSMT and obtain better initial particles, respectively. Secondly, elite selection and cloning strategy, multiple mutation strategies, and adaptive learning factor strategy are presented to improve the search process of discrete differential evolution algorithm. Thirdly, an effective refining strategy is proposed to further improve the quality of the final Steiner tree. Finally, the results of the comparative experiments prove that XSMT-MoDDE can get the shortest wire length so far, and achieve a better optimization degree in the larger-scale problem.

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As the timing delay becomes a critical issue of the chip performance, there comes a burning desire for IC design under smart manufacturing to optimize the delay. As the best connection model for multi-terminal nets, the wirelength and the maximum source-to-sink pathlength of the Steiner minimum tree are both the decisive factors of timing delay for routing. In addition, considering that X-routing can get the utmost out of routing resources, this paper proposes a Timing-Driven X-routing Steiner Minimum Tree (TD-XSMT) algorithm based on two-stage competitive particle swarm optimization. The paper utilizes the multi-objective particle swarm optimization algorithm and redesigns its framework, thus improving its performance. First, a two-stage learning strategy is presented, which balances the exploration and exploitation capabilities of the particle by learning edge structures and pseudo-Steiner point choices. Especially in the second stage, a hybrid crossover strategy is designed to guarantee convergence quality. Second, the competition mechanism is adopted to select particle learning objects and enhance diversity. Finally, according to the characteristics of the discrete TD-XSMT problem, the mutation and crossover operators of the genetic algorithm are used to effectively discretize the proposed algorithm. Experimental results reveal that TSCPSO-TD-XSMT can obtain a smooth trade-off between wirelength and maximum source-to-sink pathlength, and achieve distinguished timing delay optimization.

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