arXiv:2506.14619cs.LG2025-06中稿 · publication at Aut…被引 5

针对高维难寻可行解的优化问题,提出自适应信任域方法加速找到好解。

Feasibility-Driven Trust Region Bayesian Optimization

  • 基于目标与约束模型信息动态调整搜索区域,智能聚焦可行域。
  • 在2到60维、不同约束强度下,显著减少寻找首个可行解所需评估次数。
  • 适合复杂工程仿真、实验设计等受限资源场景,尤其适合高维非规则约束问题。

贝叶斯优化在评估预算紧张的实际优化任务中表现优异,适用于昂贵模拟或实验场景。然而,许多此类任务存在难以解析表达且定义于高维空间中的昂贵约束,可行区域通常稀疏、不规则且难以定位。此时,大量优化预算可能被耗用于寻找首个可行解,严重影响现有方法效率。本文提出可行性驱动的信任域贝叶斯优化(FuRBO)算法,通过结合目标与约束代理模型信息,迭代定义信任区域以选择下一候选解。其自适应策略允许信任域在迭代间大幅移动与缩放,使优化器快速重聚焦,持续加速可行解及高质量解的发现。我们在完整的BBOB-约束COCO基准套件及其他物理启发式基准上进行了广泛测试,对比了多种先进基线方法,在约束严重程度各异、维度从2至60的条件下验证了其有效性。

原文摘要 · Abstract (English)

Bayesian optimization is a powerful tool for solving real-world optimization tasks under tight evaluation budgets, making it well-suited for applications involving costly simulations or experiments. However, many of these tasks are also characterized by the presence of expensive constraints whose analytical formulation is unknown and often defined in high-dimensional spaces where feasible regions are small, irregular, and difficult to identify. In such cases, a substantial portion of the optimization budget may be spent just trying to locate the first feasible solution, limiting the effectiveness of existing methods. In this work, we present a Feasibility-Driven Trust Region Bayesian Optimization (FuRBO) algorithm. FuRBO iteratively defines a trust region from which the next candidate solution is selected, using information from both the objective and constraint surrogate models. Our adaptive strategy allows the trust region to shift and resize significantly between iterations, enabling the optimizer to rapidly refocus its search and consistently accelerate the discovery of feasible and good-quality solutions. We empirically demonstrate the effectiveness of FuRBO through extensive testing on the full BBOB-constrained COCO benchmark suite and other physics-inspired benchmarks, comparing it against state-of-the-art baselines for constrained black-box optimization across varying levels of constraint severity and problem dimensionalities ranging from 2 to 60.

贝叶斯优化约束优化高维搜索

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