A local optima network (LON) encodes local optima connectivity in the fitness landscape of a combinatorial optimisation problem. Recently, LONs have been studied for their fractal dimension. Fractal dimension is a complexity index where a non-integer dimension can be assigned to a pattern. This paper investigates the fractal nature of LONs and how that nature relates to metaheuristic performance on the underlying problem. We use visual analysis, correlation analysis, and machine learning techniques to demonstrate that relationships exist and that fractal features of LONs can contribute to explaining and predicting algorithm performance. The results show that the extent of multifractality and high fractal dimensions in the LON can contribute in this way when placed in regression models with other predictors. Features are also individually correlated with search performance, and visual analysis of LONs shows insight into this relationship.

一个局部最优网络（LON）编码的组合优化问题的适应度景观局部最优连接。最近，已经研究了LON的分形维数。分形维数是复杂度指标，其中可以将非整数维分配给模式。本文研究了LON的分形性质，以及该性质与潜在问题的元启发式性能之间的关系。我们使用视觉分析，相关性分析和机器学习技术来证明存在关系，并且LON的分形特征可以有助于解释和预测算法性能。结果表明，将LON的多重分形程度和高分形维数与其他预测变量一起放入回归模型时，可以通过这种方式做出贡献。功能也分别与搜索性能相关，并且LON的可视化分析显示了对这种关系的了解。