In many materials and product design problems, desirable candidates exhibit properties that fall within an acceptable range rather than achieve a single optimum. Recovering multiple, distinct solutions that satisfy such specifications is also practically valuable, as some candidates may be preferred for reasons of cost, processability, or robustness that are difficult to encode directly in an objective function. Here, we develop a range-aware Bayesian optimization (BO) framework in which the acquisition function directly scores the posterior probability that a candidate satisfies a target range. The framework naturally extends to parallel pursuit of multiple distinct specifications over a shared candidate space. Across benchmark tasks, range-aware acquisition consistently recovers larger and more diverse sets of valid designs than standard BO baselines and recent goal-seeking methods. Its utility is further demonstrated in two practically motivated design case studies involving optimizing reaction conditions for polymer synthesis and sequence-defined oligomer discovery for prescribed optical absorption bands, supported by quantum chemical calculations. These results suggest that range-aware BO can provide a practical and sample-efficient foundation for specification-driven design, particularly when design flexibility and solution diversity are important considerations.

翻译：在许多材料和产品设计问题中，理想的候选设计其属性通常落在可接受的范围内，而非追求单一最优值。同时，恢复满足此类规范的多个不同解也具有实际价值，因为某些候选设计可能因成本、可加工性或鲁棒性等难以直接编码到目标函数中的因素而更受青睐。本文提出了一种范围感知贝叶斯优化框架，其采集函数直接对候选设计满足目标范围的后验概率进行评分。该框架可自然扩展至在共享候选空间中并行追求多个不同规范。在基准测试任务中，与标准贝叶斯优化基线方法和近期目标导向方法相比，范围感知采集函数始终能恢复出更大规模且更多样化的有效设计集合。该方法在两项实际驱动的设计案例研究中进一步展示了其实用性：一是涉及聚合物合成反应条件优化，二是基于量子化学计算，针对规定光吸收带发现序列定义低聚物。这些结果表明，当设计灵活性和解多样性至关重要时，范围感知贝叶斯优化能为规范驱动型设计提供实用且样本高效的基准方法。