The Minimum Gap Graph Partitioning Problem (MGGPP) consists in partitioning a vertex-weighted undirected graph into a given number of connected subgraphs with the minimum difference between the largest and the smallest weight in each subgraph. We propose a two-level Tabu Search algorithm and an Adaptive Large Neighborhood Search algorithm to solve the MGGPP in reasonable time on instances with up to about 23 000 vertices. The quality of the heuristic solutions is assessed comparing them with the solutions of a polynomially solvable combinatorial relaxation.

中文翻译：

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最小间隙图划分问题的元启发式

的最小间隙图形划分问题（MGGPP）由在分区的顶点加权无向图与在每个子图的最大和最小的重量之间的最小差值连接子图的给定数目。我们提出了两级禁忌搜索算法和自适应大邻域搜索算法，以在合理的时间内对大约23000个顶点的实例求解MGGPP 。评估启发式解决方案的质量，并将其与多项式可解组合松弛的解决方案进行比较。