基于双聚类编辑的制造单元生成方法研究
On Solving Manufacturing Cell Formation via Bicluster Editing
摘要：
本文研究了双聚类图编辑问题（BGEP）以及如何将其应用于解决制造单元形成问题（MCFP）。我们开发了一个精确的方法，由分支和切割的方法结合一个特殊的分离算法的基础上动态规划的BGEP。我们还描述了一个新的预处理程序的BGEP来自输入图中的顶点距离的理论结果。对随机生成的不同难度的实例进行的计算实验表明，我们的分离算法加快了收敛速度，我们的预处理过程是有效的低密度的实例。这项工作的其他贡献是揭示BGEP和MCFP之间的相似之处。我们证明了BGEP和MCFP具有相同的解空间。这一事实导致建议的两个新的精确的方法MCFP的基础上的数学公式的BGEP。这两种方法都使用分组功效测量作为目标函数。据作者所知，这些是第一个确切的方法，采用这样的措施，以最佳地解决MCFP的实例。第一种方法包括迭代地运行几个调用的参数化版本的BGEP，第二个是一个新的分数线性模型的MCFP的线性化。在文献中发现的MCFP的实例上进行的计算实验表明，我们的MCFP的精确方法能够证明几个以前未知的最优。
英文摘要：
This work investigates the Bicluster Graph Editing Problem (BGEP) and how it can be applied to solve the Manufacturing Cell Formation Problem (MCFP). We develop an exact method for the BGEP that consists of a Branch-and-Cut approach combined with a special separation algorithm based on dynamic programming. We also describe a new preprocessing procedure for the BGEP derived from theoretical results on vertex distances in the input graph. Computational experiments performed on randomly generated instances with various levels of difficulty show that our separation algorithm accelerates the convergence speed, and our preprocessing procedure is effective for low density instances. Other contribution of this work is to reveal the similarities between the BGEP and the MCFP. We show that the BGEP and the MCFP have the same solution space. This fact leads to the proposal of two new exact approaches for the MCFP based on mathematical formulations for the BGEP. Both approaches use the grouping efficacy measure as the objective function. Up to the authors' knowledge, these are the first exact methods that employ such a measure to optimally solve instances of the MCFP. The first approach consists of iteratively running several calls to a parameterized version of the BGEP, and the second is a linearization of a new fractional-linear model for the MCFP. Computational experiments performed on instances of the MCFP found in the literature show that our exact methods for the MCFP are able to prove several previously unknown optima.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
