Global optimization with multivariate adaptive regression splines.
This paper presents a novel procedure for approximating the global optimum in structural design by combining multivariate adaptive regression splines (MARS) with a response surface methodology (RSM). MARS is a flexible regression technique that uses a modified recursive partitioning strategy to simplify high-dimensional problems into smaller yet highly accurate models. Combining MARS and RSM improves the conventional RSM by addressing highly nonlinear high-dimensional problems that can be simplified into lower dimensions, yet maintains a low computational cost and better interpretability when compared to neural networks and generalized additive models. MARS/RSM is also compared to simulated annealing and genetic algorithms in terms of computational efficiency and accuracy. The MARS/RSM procedure is applied to a set of low-dimensional test functions to demonstrate its convergence and limiting properties.
Crino
Scott
S
United States Military Academy at West Point, West Point, NY 10996, USA. scott.crino@us.army.mil
Brown
Donald E
DE
D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D008962:Models, Theoretical; D015999:Multivariate Analysis; D009716:Numerical Analysis, Computer-Assisted; D012044:Regression Analysis