As the feature size of semiconductor technology shrinks to 7 nm and beyond, the multiple patterning lithogra-phy (MPL) attracts more attention from the industry. In this paper, we model the layout decomposition of MPL...
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As the feature size of semiconductor technology shrinks to 7 nm and beyond, the multiple patterning lithogra-phy (MPL) attracts more attention from the industry. In this paper, we model the layout decomposition of MPL as a generalized graph coloring problem, which is addressed by a distribution evolutionary algorithm based on a population of probabilistic model (DEA-PPM). DEA-PPM can strike a balance between decomposition quality and running time, being scalable for varied settings of mask number and lithography resolution. Thanks to the robustness of the DEA-PPM, we get an alternative technique for multiple patterning layout decomposition in next-generation technology nodes.
Graph coloring is a challenging combinatorial optimization problem with a wide range of applications. In this paper, a distribution evolutionary algorithm based on a population of probability model (DEA-PPM) is develo...
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Graph coloring is a challenging combinatorial optimization problem with a wide range of applications. In this paper, a distribution evolutionary algorithm based on a population of probability model (DEA-PPM) is developed to address it efficiently. Unlike existing estimation of distributionalgorithms where a probability model is updated by generated solutions, DEA-PPM employs a distribution population based on a novel probability model, and an orthogonal exploration strategy is introduced to search the distribution space with the assistance of an refinement strategy. By sampling the distribution population, efficient search in the solution space is realized based on a tabu search process. Meanwhile, DEA-PPM introduces an iterative vertex removal strategy to improve the efficiency of k-coloring, and an inherited initialization strategy is implemented to address the chromatic number problem well. The cooperative evolution of the distribution population and the solution population leads to a good balance between exploration and exploitation. Numerical results demonstrate that the DEA-PPM of small population size is competitive to the state-of-the-art metaheuristics.
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