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Computational study of a branching algorithm for the maximum k-cut problem
Discrete Optimization ( IF 1.1 ) Pub Date : 2021-07-01 , DOI: 10.1016/j.disopt.2021.100656
Vilmar Jefté Rodrigues de Sousa , Miguel F. Anjos , Sébastien Le Digabel

This work considers the graph partitioning problem known as maximum k-cut. It focuses on investigating features of a branch-and-bound method to obtain global solutions. An exhaustive experimental study is carried out for the two main components of a branch-and-bound algorithm: Computing bounds and branching strategies. In particular, we propose the use of a variable neighborhood search metaheuristic to compute good feasible solutions, the k-chotomic strategy to split the problem, and a branching rule based on edge weights to select variables. Moreover, we analyze a linear relaxation strengthened by semidefinite-based constraints, a cutting plane algorithm, and node selection strategies. Computational results show that the resulting method outperforms the state-of-the-art approach and discovers the solution of several instances, especially for problems with k5.



中文翻译:

最大分支算法的计算研究 -切割问题

这项工作考虑了称为最大值的图分区问题 -切。它侧重于研究分支定界方法的特征以获得全局解决方案。对分支定界算法的两个主要组成部分进行了详尽的实验研究:计算边界和分支策略。特别是,我们建议使用可变邻域搜索元启发式来计算良好的可行解,即-chotomic 策略来拆分问题,以及基于边权重的分支规则来选择变量。此外,我们分析了由基于半定的约束、切割平面算法和节点选择策略增强的线性松弛。计算结果表明,所得到的方法优于最先进的方法,并发现了多个实例的解决方案,特别是对于5.

更新日期:2021-07-02
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