学习符号表达式：混合式公式化，切割和启发式
Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics
摘要：
在本文中，我们考虑的问题，学习回归函数，而不假设其功能的形式。这个问题被称为符号回归。表达式树通常用于表示解函数，该解函数通过将运算符和操作数分配给节点来确定。符号回归问题可以被公式化为非凸混合整数非线性规划（MINLP），其中二进制变量用于分配运算符，并且非线性表达式用于通过非线性运算符（诸如平方、平方根和指数）来传播数据值。我们通过增加新的削减，提高了这个具有挑战性的MINLP的解决方案，扩展了这个配方。我们还提出了一个启发式，迭代地建立一个表达式树，通过解决限制MINLP。我们进行计算实验，并比较我们的方法与混合整数规划为基础的方法和神经网络为基础的方法从文献中。
英文摘要：
In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. The symbolic regression problem can be formulated as a nonconvex mixed-integer nonlinear program (MINLP), where binary variables are used to assign operators and nonlinear expressions are used to propagate data values through nonlinear operators such as square, square root, and exponential. We extend this formulation by adding new cuts that improve the solution of this challenging MINLP. We also propose a heuristic that iteratively builds an expression tree by solving a restricted MINLP. We perform computational experiments and compare our approach with a mixed-integer program-based method and a neural-network-based method from the literature.
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