Computing maximum weight independent sets in graphs is an important NP-hard optimization problem. The problem is particularly difficult to solve in large graphs for which data reduction techniques do not work well. To be more precise, state-of-the-art branch-and-reduce algorithms can solve many large-scale graphs if reductions are applicable. Otherwise, their performance quickly degrades due to branching requiring exponential time. In this paper, we develop an advanced memetic algorithm to tackle the problem, which incorporates recent data reduction techniques to compute near-optimal weighted independent sets in huge sparse networks. More precisely, we use a memetic approach to recursively choose vertices that are likely to be in a large-weight independent set. We include these vertices into the solution, and further reduce the graph. We show that identifying and removing vertices likely to be in large-weight independent sets opens up the reduction space and speeds up the computation of large-weight independent sets remarkably. Our experimental evaluation indicates that we are able to outperform state-of-the-art algorithms. For example, our two algorithm configurations compute the best results among all competing algorithms for 205 out of 207 instances. Thus can be seen as a useful tool when large-weight independent sets need to be computed in~practice.

翻译：计算图中的最大权重独立集是一个重要的NP-hard优化问题。当数据约简技术在大规模图中效果不佳时，该问题尤为棘手。具体而言，若适用约简技术，当前最先进的分支-约简算法能够解决许多大规模图；否则，由于分支需要指数时间，其性能会迅速下降。本文开发了一种先进的模因算法来解决该问题，该算法整合了最新的数据约简技术，用于在巨大稀疏网络中计算近最优权重独立集。更精确地说，我们采用模因方法递归地选择可能属于大权重独立集的顶点，将这些顶点纳入解中，并进一步约简图。我们证明，识别并移除可能属于大权重独立集的顶点能够打开约简空间，并显著加速大权重独立集的计算。实验评估表明，我们能够超越当前最先进的算法。例如，我们的两种算法配置在207个实例中的205个上取得最优结果，因此可视为实践中计算大权重独立集的有效工具。