Abstract The maximum balanced biclique problem (MBBP) is to find the largest complete bipartite subgraph induced by two equal-sized subsets of vertices in a bipartite graph. MBBP is an NP-hard problem with a number of relevant applications. In this work, we propose a general swap-based multiple neighborhood adaptive search (SBMNAS) for MBBP. This algorithm combines a general k-SWAP operator which is used in local searches for MBBP for the first time, an adaptive rule for neighborhood exploration and a frequency-based perturbation strategy to ensure a global diversification. SBMNAS is evaluated on 60 random dense instances and 25 real-life large sparse instances from the popular Koblenz Network Collection (KONECT). Computational results show that our proposed algorithm attains all but one best-known solutions, and finds improved best-known results for 19 instances (new lower bounds).

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最大平衡双角问题的基于通用交换的多邻域自适应搜索

摘要 最大平衡双方问题(MBBP)是在二部图中找到由两个相等大小的顶点子集诱导的最大完全二部子图。MBBP 是一个具有许多相关应用程序的 NP 难问题。在这项工作中，我们为 MBBP 提出了一种基于交换的通用多邻域自适应搜索（SBMNAS）。该算法结合了首次用于局部搜索 MBBP 的通用 k-SWAP 算子、邻域探索的自适应规则和基于频率的扰动策略，以确保全局多样化。SBMNAS 在来自流行的科布伦茨网络集合 (KONECT) 的 60 个随机密集实例和 25 个现实生活中的大型稀疏实例上进行评估。计算结果表明，我们提出的算法获得了除一个最著名的解决方案之外的所有解决方案，