Local Optima Networks (LONs) represent the global structure of search spaces as graphs, but their construction requires iterative execution of a search algorithm to find local optima and approximate transitions between Basins of Attraction (BoAs). In continuous optimization, this high computational cost prevents systematic investigation of the relationship between LON features and evolutionary algorithm performance. To address this issue, we propose an alternative definition of BoAs for Max-Set of Gaussians (MSG) landscapes with explicitly tunable multimodality. This bypasses search-based BoA identification, enabling low-cost LON construction. Moreover, we leverage Novelty Search (NS) to explore the parameter space of the MSG landscape generator, producing instances with diverse graph topologies. Our experiments show that the proposed BoAs closely align with gradient-based BoAs, and that NS successfully generates instances with varied search difficulty and connectivity patterns among optima. Finally, over the instances generated by NS, we predict the success rate of two well-established evolutionary algorithms from LON features. While our LON construction is specific to MSG landscapes, the proposed framework provides a dataset that serves as a foundation for landscape-aware optimization.

翻译：局部最优网络将搜索空间的全局结构表示为图，但其构建需迭代执行搜索算法以寻找局部最优解并近似计算吸引域间的转移关系。在连续优化中，这种高昂的计算成本阻碍了对局部最优网络特征与进化算法性能之间关系的系统性研究。为解决该问题，我们针对具有可显式调节多模态性的高斯混合体景观提出了吸引域的替代定义，从而绕过基于搜索的吸引域识别，实现低成本局部最优网络构建。进一步地，我们利用新颖度搜索探索高斯混合体景观生成器的参数空间，生成具有多样图拓扑结构的实例。实验表明，所提吸引域与基于梯度的吸引域高度吻合，且新颖度搜索能成功生成具有不同搜索难度和最优解连通模式的实例。最终，基于新颖度搜索生成的实例，我们从局部最优网络特征预测了两种经典进化算法的成功率。尽管我们的局部最优网络构建方法专用于高斯混合体景观，但所提框架提供了可作为景观感知优化基础的数据集。