用轮廓图图像+CNN选最优优化器，比单个最好算法还强。
Beyond Numerical Features: CNN-Driven Algorithm Selection via Contour Plots for Continuous Black-Box Optimization
- 把优化问题的探测结果转成轮廓图，输入CNN预测各算法表现。
- 在BBOB 2009上超越单个最佳算法，媲美传统特征方法。
- 无需手工设计特征，适合想自动化选优化器的研究者。
本文提出一种基于表示的新方法用于实例级算法选择，应用于连续黑箱优化场景，旨在从固定算法组合中自动选出最有望成功的求解器。以往研究主要依赖数值描述符，如探索性景观分析（ELA）特征或深度学习嵌入（Deep-ELA）。本文探索了一种互补表示：对探测景观生成的轮廓图。采用卷积神经网络（CNN）回归器，将多个实例特异性的轮廓视图（堆叠或每视图编码后聚合）作为输入，预测各求解器性能，从而依据预测最优值进行选择。在标准的BBOB 2009单目标评估协议下，所构建的选择器显著优于单个最佳求解器（SBS），并可与基于特征的基线方法相媲美。后续在DeepELA设置下的双目标评估进一步表明，使用滑动窗口生成的轮廓图视图时，该图像驱动原理仍具竞争力。整体结果表明，简单视觉模型即可利用探测景观中的空间结构实现算法选择，无需人工设计的ELA特征。
原文摘要 · Abstract (English)
The present paper introduces a new representation-driven approach to per-instance algorithm selection, applied to black-box optimization, for automatically choosing the most promising solver from a fixed portfolio. Prior work in continuous optimization largely relies on numerical descriptors, including Exploratory Landscape Analysis features and learned embeddings such as Deep-ELA. This work studies a complementary representation: contour-map visualizations of probed landscapes. A CNN regressor takes multiple instance-specific contour views (stacked or encoded per view and aggregated) and predicts per-solver performance, enabling selection by the predicted best value. On the standard BBOB 2009 single-objective protocol, the resulting selectors significantly outperform the single best solver (SBS) and are competitive with feature-based baselines. A subsequent bi-objective evaluation under the DeepELA setting further indicates that the same image-based principle can be competitive when using windowed contour views. Overall, the results suggest that simple vision models can exploit spatial structure in probed landscapes for algorithm selection without handcrafted ELA features.
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