(621a) Decomposition in Derivative-Free Optimization
In this work, we propose a novel decomposition framework for DFO algorithms. Our framework significantly extends the scope of current DFO solvers to larger-scale problems. We address several key questions, including how to select variables for each subproblem, and how to determine sub-problem dimension and sub-problem function evaluation limits. A practical implementation is developed and exemplified with the global model-based solver Stable Noisy Optimization by Branch and Fit (SNOBFIT). To investigate the performance of the decomposition framework both in terms of quality of solution and efficiency, we conducted extensive computational studies on a collection of over 300 test problems with varying dimensions and complexity. Significant improvements in the quality of solutions obtained under a 2500 function evaluation limit are observed for a large fraction of the test problems. The decomposition framework wins against non-decomposition when the problem has more than 30 variables. It also achieves over 90% wins when the problem has more than 75 variables regardless of problem convexity and smoothness.