Abstract This paper proposes an iterated local search (ILS) based heuristic for the weighted vertex coloring problem (WVCP). Given a graph G ( V , E ) with a weight w ( v ) associated with each vertex v ∈ V , the WVCP asks to find a coloring { V 1 , … , V k } of G that minimizes ∑ i = 1 k max v ∈ V i w ( v ) . This problem has many theoretical and practical applications, such as batch scheduling, buffer minimization, and traffic assignment in telecommunication. Our ILS heuristic relies on two new neighborhood structures for the problem, and its local search component is hybridized with a tabu search strategy. We compare our approach with state-of-the-art heuristics and exact methods for the problem. Experimental results on well-known benchmark instances demonstrate that, first, our heuristic is better than the other heuristics in both solution quality and computational time, and, second, it is a good alternative for large instances that cannot be solved by exact methods.

中文翻译：

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带禁忌搜索的迭代局部搜索解决加权顶点着色问题

摘要 本文针对加权顶点着色问题 (WVCP) 提出了一种基于迭代局部搜索 (ILS) 的启发式算法。给定一个图 G ( V , E ) 的权重 w ( v ) 与每个顶点 v ∈ V 相关联，WVCP 要求找到 G 的着色 { V 1 , … , V k } 使 ∑ i = 1 k max 最小化v ∈ V iw ( v ) 。这个问题有很多理论和实际应用，如电信中的批量调度、缓冲区最小化和流量分配。我们的 ILS 启发式依赖于两个新的邻域结构来解决问题，并且其局部搜索组件与禁忌搜索策略相结合。我们将我们的方法与最先进的启发式方法和解决问题的精确方法进行比较。在众所周知的基准实例上的实验结果表明，首先，