A PSO-based timing-driven Octilinear Steiner tree algorithm for VLSI routing considering bend reduction

Abstract

Constructing a timing-driven Steiner tree is very important in VLSI performance-driven routing stage. Meanwhile, non-Manhattan architecture is supported by several manufacturing technologies and now well appreciated in the chip manufacturing circle. However, limited progress has been reported on the non-Manhattan performance-driven routing problem. In this paper, an efficient algorithm, namely, TOST_BR_MOPSO, is presented to construct the minimumcost spanning tree with a minimum radius for performancedriven routing in Octilinear architecture (one type of the non-Manhattan architecture) based on multi-objective particle swarm optimization (MOPSO) and Elmore delay model. Edge transformation is employed in our algorithm to make the particles have the ability to achieve the optimal solution while Union-Find partition is used to prevent the generation of invalid solution. For the purpose of reducing the number of bends which is one of the key factors of chip manuCommunicated by V. Loia. facturability, we also present an edge-vertex encoding strategy combined with edge transformation. To our best knowledge, no approach has been proposed to optimize the number of bends in the process of constructing the non-Manhattan timing-driven Steiner tree. Moreover, the theorem of Markov chain is used to prove the global convergence of our proposed algorithm. Experimental results indicate that the proposed MOPSO is worthy of being studied in the field of multiobjective optimization problems, and our algorithm has a better tradeoff between the wire length and radius of the routing tree and has achieved a better delay value. Meanwhile, combining edge transformation with the encoding strategy, the proposed algorithm can significantly reduce nearly 20 % in the number of bends.

A Survey of Swarm Intelligence Techniques in VLSI Routing Problems

“…Liu et al [55], [56], Huang et al [56], [57], and Liu et al [58]- [61] have done a lot of research work on the construction of Octagonal Steiner Minimum Tree (OSMT) based on the following interconnected structure, and have achieved excellent results.…”

“…Like the problems of RST, we also study related problems of OST such as Obstacle-Avoiding Octagonal Steiner Minimum Tree (OAOSMT). References [56]- [58] consider the construction of OST with key issues such as obstacles, delay and number of bends, also based on this encoding method and particle update strategies, while using Union-Find Sets (UFS) to prevent the generation of invalid solutions. Reference [60] constructs OSMT based on self-adapting PSO with an effective Hybrid Transformation Strategy (HTS) to enlarge the search space.…”

“…In recent years, more and more researches [55]- [58], [60], [61], [70], [84], [85] have been conducted on X-architecture SMT construction. However, most of the SI algorithms are used to solve the RSMT problem.…”

An Improved Swarm Intelligence Algorithm for Multi-Item Joint Ordering Strategy of Cruise Ship Supply

“…e larger the value of inertia weight, the stronger the global optimization ability; when it is small, the algorithm is local optimization. Compared with PSO, GA, FOA, and other swarm intelligence algorithms, WFWA has better convergence, global optimization, and search ability [28][29][30][31][32][33][34][35]. erefore, WFWA is a good choice to solve the ordering optimization problem of cruise ship supply to the integrated purchase, delivery, and inventory in the supply chain environment.…”

ODMA: a novel swarm-evolutionary metaheuristic optimizer inspired by open source development model and communities

“…Imperialist competitive algorithm (ICA) (Atashpaz- Gargari and Lucas 2007) is inspired by imperialist competition countries for finding a global optima and solving the problems by simulating the imperialist and colonies behavior. These metaheuristic algorithms have been used in wide range of optimization problems such as pattern recognition (Zuo and Xiao 2014); (Eberhart and Shi 2001); (Zhiqiang et al 2013) machine learning (Goldberg 1989), market modeling (Bajpai and Singh 2007), decision making (Deb et al 2002), industrial planning and construction (Gen and Syarif 2005;Liu et al 2014) and (Mahil and Raja 2014;Ganesan et al 2013;Jiménez et al 2014;Gómez et al 2013).…”