Survey of Modeling and Optimization Strategies for High-Dimensional Design Problems
Songqing Shan, G. Gary Wang · 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2008
The integration of optimization methodologies with computational analyses/simulations has profound impact on the product design. Such integration, however, faces multiple challenges. The most eminent challenges arise from high-dimensional problems, expensive analysis/simulation functions, and unknown function properties (i.e., black-box functions). The merge of these three challenges severely aggravates the difficulty and becomes a major hurdle for design optimization. This paper provides a survey on modeling and optimization strategies for high-dimensional design problems with expensive black-box functions. This survey screens out 191 references including multiple historical reviews on relevant subjects from about 1000 papers in Statistics, Mathematics, Chemistry, Physics, Computer Science, and various engineering disciplines. The survey has been performed in three areas: strategies tackling high-dimensionality of problems, model approximation techniques, and optimization strategies for expensive functions. Major contributions in each area are discussed and presented in an organized manner. The survey also exposes that modeling and optimization strategies for high-dimensional expensive black-box function are scarce and sporadic, partially due to our lack of understanding of high dimensional spaces and the difficulty of the problem itself. Based on the review results, observations and summaries will be given. The authors will offer our perspectives on the challenges and directions for future research.