Data Driven Multivariate Adaptive Regression Splines Based Simulation Optimization
This paper proposes a data driven based optimization approach which combines augmented Lagrangian method, MARS with effective data processing. In the approach, an expensive simulation run is required if and only if a nearby data point does not exist in the cumulatively growing database. Over time the database matures and is enriched as more and more optimizations have been performed. MARS is a self-adaptive regression process, which fits in with the multidimensional problems, and uses a modified recursive partitioning strategy to simplify high-dimensional problems into smaller yet highly accurate models. Combining the local response surface of MARS and augmented Lagrangian method improve sequential approximation optimization and reduce simulation times by effective data processing, yet maintain a low computational cost. The approach is applied to a six dimensional test function, a ten dimensional engineering problem and a two dimensional global test functions to demonstrate its feasibility and convergence, and yet some limiting properties.
H. P. Mao et al., "Data Driven Multivariate Adaptive Regression Splines Based Simulation Optimization", Applied Mechanics and Materials, Vols. 44-47, pp. 3800-3806, 2011