Global optimization on non-convex two-way interaction truncated linear multivariate adaptive regression splines using mixed integer quadratic programming - Ju, Xinglong; Rosenberger, Jay M.; Chen, Victoria C.P.; Liu, Feng (Information sciences, 2022)
•A novel method, TITL-MARS-OPT, for global optimization on non-convex two-way interaction truncated linear multivariate adaptive regression splines is proposed.•The results show the superiority of TITL-MARS-OPT over the genetic algorithm and the gradient descent method on TITL-MARS models.•The Python code is made open-source on GitHub to help other researchers. Multivariate adaptive regression splines (MARS) has been adopted as a popular surrogate function to model the unknown relationships between input and output variables in complex systems. Searching optimal solutions on the complicated surrogate response surface of MARS serves as important tasks in various applications. In this paper, we present an efficient and effective approach to find a global optimal value of MARS models that incorporate two-way interaction terms which are products of truncated linear univariate functions (TITL-MARS). Specifically, with a MARS model consisting of linear and quadratic structures, we can reformulate the optimization problem on TITL-MARS into a mixed integer quadratic programming problem (TITL-MARS-OPT), which can be further solved in a more principled way. To illustrate the effectiveness of our proposed approach TITL-MARS-OPT, we come up with a genetic algorithm and a gradient descent algorithm to solve the original version of TITL-MARS, and we compared the performance of the proposed approach with the benchmark algorithms. Numerical experiments are conducted on a spectrum of examples with different levels of complexity, including 6 existing models and a real world application in the wind farm optimization. Our proposed approach can find a global optimal successfully and efficiently while the comparison algorithms fail to find a global optimal solution. In the end, Python code for TITL-MARS and TITL-MARS-OPT is made available on GitHub ( https://github.com/JuXinglong/TITL-MARS-OPT).