Optimization problems involving mixed variables, i.e., variables of numerical and categorical nature, can be challenging to solve, especially in the presence of complex constraints. Moreover, when the objective function is the result of a simulation or experiment, it may be expensive to evaluate. In this paper, we propose a novel surrogate-based global optimization algorithm, called PWAS, based on constructing a piecewise affine surrogate of the objective function over feasible samples. We introduce two types of exploration functions to efficiently search the feasible domain via mixed integer linear programming (MILP) solvers. We also provide a preference-based version of the algorithm, called PWASp, which can be used when only pairwise comparisons between samples can be acquired while the objective function remains unquantified. PWAS and PWASp are tested on mixed-variable benchmark problems with and without constraints. The results show that, within a small number of acquisitions, PWAS and PWASp can often achieve better or comparable results than other existing methods.

翻译：涉及混合变量（即数值型与类别型变量）的优化问题，在存在复杂约束时求解尤为困难。当目标函数来自仿真或实验时，其评估可能代价高昂。本文提出一种新型基于代理的全局优化算法PWAS，该算法通过构建目标函数在可行样本上的分段线性代理进行优化。我们引入两种探索函数，利用混合整数线性规划（MILP）求解器高效搜索可行域。同时，我们提供该算法的偏好版本PWASp，适用于仅能获取样本间成对比较而目标函数无法量化的场景。PWAS与PWASp在有无约束的混合变量基准问题上进行测试。结果表明，在少量采样次数内，PWAS与PWASp通常能取得优于或媲美现有方法的结果。