Optimization by moving ridge functions: derivative-free optimization for computationally intensive functions. Issue 4 (3rd April 2022)

• Record Type: Journal Article
• Authors: Gross, James C.; Parks, Geoffrey T.
• Is Part Of: Engineering optimization. Volume 54:Issue 4(2022)
• Page Start: 553
• Page End: 575
• Publication Date: 2022-04-03
• Subjects: Derivative-free optimization -- nonlinear optimization -- trust region methods -- dimension reduction -- ridge functions; Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2021.1886286
• Languages: English
• ISSNs: 0305-215X

Abstract

Abstract : A novel derivative-free algorithm, called optimization by moving ridge functions (OMoRF), for unconstrained and bound-constrained optimization is presented. This algorithm couples trust region methodologies with output-based dimension reduction to accelerate convergence of model-based optimization strategies. The dimension-reducing subspace is updated as the trust region moves through the function domain, allowing OMoRF to be applied to functions with no known global low-dimensional structure. Furthermore, its low computational requirement allows it to make rapid progress when optimizing high-dimensional functions. Its performance is examined on a set of test problems of moderate to high dimension and a high-dimensional design optimization problem. The results show that OMoRF compares favourably with other common derivative-free optimization methods, even for functions in which no underlying global low-dimensional structure is known.