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.

通过使用图数据挖掘技术，本文提出了利用局部最优网络作为适应度景观的代理，以定性和定量分析探索这些景观中嵌入的潜在拓扑结构信息，从而解决了实际情况中推断相似性的困难。通过在三个经典组合优化问题上进行大规模实证实验，我们获得了支持同类景观之间在邻近维度存在结构相似性的确凿证据，并探究了不同问题类之间的景观关系。