The algorithm#
The box-subdivision outer approximation is a bi-level method for multimodal nonlinear problems. A Cartesian subdivision of the design space defines a finite set of boxes; a mixed-integer master problem selects a box, and a local nonlinear solver solves the original problem within it. Exploration and local optimization are thus carried out at two distinct levels.
Motivation, bi-level formulation, the two formulations of the sub-problem, convexification, trust region and hierarchies.
Components added to GEMSEO, their common one-hot layout, extensions, and two errors that produce no warning.
Construction of a GEMSEO scenario with either formulation, main settings, and refinement of a box.
Comparison with the enumeration of the boxes and with baselines, effect of the subdivision density and of the convexity settings, extensions, and an application to topology optimization.
Summary of the results, their limitations, and directions for further work.
Test problems, baselines, tuning of the master settings, and detailed results of the extensions.