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Multivariate adaptive regression splines (MARS) is a flexible statisticalmodeling method that has been popular for data mining applications. MARS hasalso been employed to approxmiate unknown relationships in optimzation forcomplex systems, including surrogate optimization, dynamic programming, andtwo-stage stochastic programming. Given the increasing desire to optimize realworld systems, this paper presents an approach to globally optimize a MARSmodel that allows up to two-way interaction terms that are products oftruncated linear univariate functions (TITL-MARS). Specifally, such a MARSmodel consists of linear and quadratic structure. This structure is exploitedto formulate a mixed integer quadratic programming problem (TITL-MARS-OPT). Toappreciate the contribution of TITL-MARS-OPT, one must recognize that popularheurstic optimization approaches, such as evolutionary algorithms, do notguarantee global optimality and can be computationally slow. The use of MARSmaintains the flexibility of modeling within TITL-MARS-OPT while also takingadvantage of the linear modeling structure of MARS to enable global optimality.Computational results compare TITL-MARS-OPT with a genetic algorithm for twotypes of cases. First, a wind farm power distribution case study is describedand then other TITL-MARS forms are tested. The results show the superiority ofTITL-MARS-OPT over the genetic algorithm in both accuracy and computationaltime.

Global optimization using mixed integer quadratic programming on  non-convex two-way interaction truncated linear multivariate adaptive  regression splines