Dynamic Design Space Partitioning for Optimization of an Integrated Thermal Protection System
Diane C. Villanueva, Rodolphe Le Riche, Gauthier Picard, Raphael T. Haftka · 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference · 2013
In this paper, we explore the use of design space partitioning to tackle optimization problems in which each point is expensive to evaluate and there are multiple local optima. The overarching goal of the method presented in this paper is to locate all local optima rather than just the global one. Locating multiple designs provides insurance against discovering that late in the design process a design is poor due to modeling errors or overlooked objectives or constraints. The proposed strategy to locate multiple candidate designs dynam-ically partitions the search space among several “agents ” that approximate their sub-region landscape using surrogates. Agents coordinate by exchanging points to form an approximation of the objective function or constraints in the sub-region and by modifying the boundaries of their sub-regions. Through a self-organized process of creation and deletion, agents adapt the partition as to exploit potential local optima and explore un-known regions. This idea is demonstrated on a six-dimensional analytical function, and a practical engineering example, the design of an integrated thermal protection system. Nomenclature c = center f = objective function F = objective function values associated with design of experiments in database g = constraint G = constraint values associated with design of experiments in database t = time x = design variables X = design of experiments in database f ̂ = surrogate prediction of f g ̂ = surrogate prediction of g I.