Solving noncovex Disjunctive Programming (DP) problems for representing symbolic regression trees to build explicit surrogate models from limited data information is challenging. This paper presents an effective global optimization approach to deal with these DPs. Piecewise McCormick envelope-based strategy is used to relax the nonconvex bilinear terms and nonconvex inequality constraints of the DP. A large-scale convex mixed integer nonlinear programing (MINLP) is then generated via the convex hull. A tailored linearization strategy further relaxes tightly all nonlinear terms in the convex MINLP to generate a mixed integer linear programming which is finally solved to global optimality by Generalized Benders Decomposition-based algorithm. Through testing three numerical simulations and Cetane number prediction, when compared to the monolithic approach of the state-of-the-art global optimization solvers such as BARON, the proposed approach is shown to reduce the solution time by up to two orders of magnitude and construct more accurate explicit surrogate models.

解决用于表示符号回归树以从有限的数据信息中建立显式替代模型的非凸析取编程（DP）问题具有挑战性。本文提出了一种有效的全局优化方法来处理这些DP。基于分段麦考密克包络的策略用于放宽DP的非凸双线性项和非凸不等式约束。然后，通过凸包生成大规模凸混合整数非线性编程（MINLP）。量身定制的线性化策略进一步严格地放松了凸MINLP中的所有非线性项，以生成混合整数线性规划，该规划最终通过基于广义Benders分解的算法求解为全局最优。通过测试三个数值模拟和十六烷值预测，