Towards more efficient local search for weighted graph coloring problem in massive graphs

The weighted graph coloring problem (WGCP) is a well-known NP-hard combinatorial optimization problem with various practical applications. Due to its theoretical significance and practical relevance, numerous algorithms have been developed to address the WGCP. In the past, both exact and heuristic algorithms have primarily focused on solving classic benchmarks, with relatively few efforts dedicated to tackling the challenges posed by massive WGCP real-world applications. In our work, we propose an effective local search algorithm for the WGCP based on three main ideas. First, we introduce anew variant of configuration checking to escape from local optima. Second, we devise a novel method for selecting vertex movements that guides the search towards more favorable directions. Third, we propose a novel deep optimization strategy to perturb the solution. Extensive experiments demonstrate that our proposed algorithm outperforms several state-of-the-art algorithms on both classic and massive benchmarks. This indicates the effectiveness and superiority of our approach in solving the WGCP.