Towards the Inferrence of Structural Similarity of Combinatorial
  Landscapes
Mingyu Huang Ke Li
One of the most common problem-solving heuristics is by analogy. For a given
problem, a solver can be viewed as a strategic walk on its fitness landscape.
Thus if a solver works for one problem instance, we expect it will also be
effective for other instances whose fitness landscapes essentially share
structural similarities with each other. However, due to the black-box nature
of combinatorial optimization, it is far from trivial to infer such similarity
in real-world scenarios. To bridge this gap, by using local optima network as a
proxy of fitness landscapes, this paper proposed to leverage graph data mining
techniques to conduct qualitative and quantitative analyses to explore the
latent topological structural information embedded in those landscapes. By
conducting large-scale empirical experiments on three classic combinatorial
optimization problems, we gain concrete evidence to support the existence of
structural similarity between landscapes of the same classes within neighboring
dimensions. We also interrogated the relationship between landscapes of
different problem classes.