Polynomial interpolation or regression models are an important tool in Derivative-free Optimization, acting as surrogates of the real function. In this work, we propose the use of these models in the multiobjective framework of directional direct search, namely the one of Direct Multisearch. Previously evaluated points are used to build quadratic polynomial models, which are minimized in an attempt of generating nondominated points of the true function, defining a search step for the algorithm. Numerical results state the competitiveness of the proposed approach.

中文翻译：

---

多项式模型在多目标定向直接搜索中的应用

多项式插值或回归模型是无导数优化中的重要工具，可作为实函数的替代。在这项工作中，我们建议在定向直接搜索的多目标框架（即直接多重搜索之一）中使用这些模型。先前评估的点用于构建二次多项式模型，将其最小化以尝试生成真函数的非支配点，从而定义算法的搜索步骤。数值结果表明了该方法的竞争力。