Optimization problems in real-world applications across the medical and engineering domains often involve potential risks when evaluating candidate solutions. Safe optimization aims to perform optimization while suppressing unsafe solution evaluations in such situations. For continuous search spaces, there exist safe optimization methods based on evolutionary computation. However, the algorithm development of safe optimization methods for binary search spaces has not been adequately addressed. In this study, we incorporate additional mechanisms for safe optimization into a binary optimization method, the adaptive stochastic natural gradient method (ASNG) with a family of Bernoulli distributions. For safety functions that must be kept non-negative during optimization, the proposed method, safe ASNG, estimates the Lipschitz constants with respect to the Hamming distance by constructing surrogate models of safety functions based on discrete Walsh functions. Then, safe ASNG computes a safe region that consists of safe solutions around the previously evaluated safe solutions. By projecting newly generated solutions to their nearest neighbors within the safe region, safe ASNG suppresses unsafe solution evaluations. Experimental results on benchmark problems on binary domains confirm that, while the comparative methods fail to suppress unsafe solution evaluations, safe ASNG achieves efficient optimization while effectively suppressing unsafe solution evaluations.

翻译：在医疗和工程领域的实际应用中，优化问题通常涉及评估候选方案时的潜在风险。安全优化旨在此类情境下，在抑制不安全解评估的同时执行优化。对于连续搜索空间，已存在基于进化计算的安全优化方法。然而，针对二进制搜索空间的安全优化算法开发尚未得到充分解决。在本研究中，我们将安全优化的额外机制整合到一种二进制优化方法——基于伯努利分布族的自适应随机自然梯度方法（ASNG）中。针对优化过程中必须保持非负的安全函数，所提出的方法——安全ASNG——通过基于离散沃尔什函数构建安全函数的代理模型，来估计关于汉明距离的利普希茨常数。随后，安全ASNG计算由先前评估的安全解周围的安全解组成的的安全区域。通过将新生成的解投影到安全区域内最近的相邻解，安全ASNG抑制了不安全解的评估。在二进制域上的基准问题实验结果表明，虽然对比方法无法抑制不安全解的评估，但安全ASNG在有效抑制不安全解评估的同时，实现了高效的优化。