The minimum weight vertex cover problem (MWVCP) is a fundamental combinatorial optimization problem with various real-world applications. The MWVCP seeks a vertex cover of an undirected graph such that the sum of the weights of the selected vertices is as small as possible. In this paper, we present an effective algorithm to solve the MWVCP. First, a master-apprentice evolutionary algorithm based on two individuals is conducted to enhance the diversity of solutions. Second, a hybrid tabu search combined configuration checking and solution-based tabu search is introduced to intensify local search procedure. Harnessing the power of the evolutionary strategy and a novel variant of hybrid tabu search, Master-Apprentice Evolutionary Algorithm with Hybrid Tabu Search, MAE-HTS, is presented. Results of extensive computational experiments using standard benchmark instances and other large-scale instances demonstrate the efficacy of our algorithm in terms of solution quality, running time, and robustness compared to state-of-the-art heuristics from the literature and the commercial MIP solver Gurobi. We also systematically analyze the role of each individual component of the algorithm which when worked in unison produced superior outcomes. In particular, MAE-HTS produced improved solutions for 2 out of 126 public benchmark instances with better running time. In addition, our MAE-HTS outperforms other state-of-the-art algorithms DLSWCC and NuMWVC for 72 large scale MWVCP instances by obtaining the best results for 64 ones, while other two reference algorithms can only obtain 27 best results at most.

中文翻译：

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最小权重顶点覆盖问题的快速鲁棒启发式算法

这 最小重量顶点覆盖问题（MWVCP）是各种实际应用中的基本组合优化问题。MWVCP寻找无向图的顶点覆盖，以使所选顶点的权重之和尽可能小。在本文中，我们提出了一种解决MWVCP的有效算法。首先，进行了基于两个个体的主学徒进化算法，以提高解决方案的多样性。其次，引入了混合禁忌搜索，结合了配置检查和基于解决方案的禁忌搜索，以加强本地搜索过程。利用进化策略的力量和混合禁忌搜索的一种新颖变体，提出了具有混合禁忌搜索的主学徒进化算法MAE-HTS。使用标准基准实例和其他大规模实例进行的大量计算实验的结果证明，与文献和商业MIP求解器中的最新启发式算法相比，我们的算法在解决方案质量，运行时间和鲁棒性方面均有效古罗比 我们还系统地分析了算法中每个单独组成部分的作用，这些组成部分协同工作可产生更好的结果。特别是，MAE-HTS为126个公共基准实例中的2个提供了改进的解决方案，并具有更好的运行时间。此外，对于72个大型MWVCP实例，我们的MAE-HTS优于其他最新算法DLSWCC和NuMWVC，因为它可以获得64个实例的最佳结果，而其他两个参考算法最多只能获得27个最佳结果。