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Graph Matching with Distance-Preserving Crossover

Graph models are fundamental to any kind of application on structured real-world problems. Any comparison between graphs by a graph distance measure requires the solution of the inexact graph matching problem, which constitutes a hard combinatorial optimization problem. An inexact matching problem includes in its formulation robustness to any type of perturbation, such as, for instance, noise, inherently present in real-world environments. In this paper, we introduce the concept of distance-preserving crossover operators for genetic algorithms for this task. For large graphs, our algorithm outperforms any state-of-the-art approximate algorithm—in particular, genetic algorithms with alternative crossover operators, which are to the best of our knowledge currently limited to no more than 50 nodes. We use a two-level local search heuristic to further enhance the results, pushing the limits to up to 300 nodes: a first local search step is directly integrated into the crossover operator; another one is applied independently during offspring generation.