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Iterated local search with tabu search for the weighted vertex coloring problem. (English) Zbl 1458.90619

Summary: 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 \(v\in V\), the WVCP asks to find a coloring \(\{V_1,\dots,V_k\}\) of \(G\) that minimizes \(\sum_{i=1}^k\max_{v\in V_i}w(v)\). 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.

MSC:

90C35 Programming involving graphs or networks
05C15 Coloring of graphs and hypergraphs
05C85 Graph algorithms (graph-theoretic aspects)
90C59 Approximation methods and heuristics in mathematical programming
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