We describe the optimization algorithm implemented in the open-source derivative-free solver RBFOpt. The algorithm is based on the radial basis function method of Gutmann and the metric stochastic response surface method of Regis and Shoemaker. We propose several modifications aimed at generalizing and improving these two algorithms: (i) the use of an extended space to represent categorical variables in unary encoding; (ii) a refinement phase to locally improve a candidate solution; (iii) interpolation models without the unisolvence condition, to both help deal with categorical variables, and initiate the optimization before a uniquely determined model is possible; (iv) a master-worker framework to allow asynchronous objective function evaluations in parallel. Numerical experiments show the effectiveness of these ideas.

中文翻译：

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关于混合变量问题的全局优化方法的实现

我们描述了在开源无导数求解器 RBFOpt 中实现的优化算法。该算法基于 Gutmann 的径向基函数方法和 Regis 和 Shoemaker 的度量随机响应面方法。我们提出了一些旨在概括和改进这两种算法的修改：（i）使用扩展空间来表示一元编码中的分类变量；(ii) 局部改进候选解决方案的细化阶段；(iii) 没有单解条件的插值模型，以帮助处理分类变量，并在唯一确定的模型成为可能之前启动优化；(iv) 允许并行异步目标函数评估的主从框架。数值实验证明了这些想法的有效性。