Approximation of Computationally Expensive and Noisy Functions for Constrained Nonlinear Optimization

1987 ◽  
Vol 109 (4) ◽  
pp. 528-532 ◽  
Author(s):  
J. W. Free ◽  
A. R. Parkinson ◽  
G. R. Bryce ◽  
R. J. Balling
Keyword(s):  
Nonlinear Programming ◽  
Approximation Method ◽  
Function Approximation ◽  
Experimental Designs ◽  
Test Problems ◽  
Constrained Nonlinear Optimization ◽  
Noisy Functions ◽  
Computationally Expensive ◽  
And Function ◽  
Programming Algorithms

The use of statistical experimental designs is explored as a method of approximating computationally expensive and noisy functions. The advantages of experimental designs and function approximation for use in optimization are discussed. Several test problems are reported showing the approximation method to be competitive with the most efficient optimization algorithms when no noise is present. When noise is introduced, the approximation method is more efficient and solves more problems than conventional nonlinear programming algorithms.

Cluster Analysis for the Cognitive Selection of Nonlinear Programming Algorithms

1990 ◽  
Author(s):  
Jin-xian Ma ◽  
Shi-huai Xie ◽  
Yong Chen
Keyword(s):  
Cluster Analysis ◽  
Nonlinear Programming ◽  
Expert System ◽  
Mechanical Design ◽  
Test Problems ◽  
Comparative Performance ◽  
Nonlinear Programming Algorithms ◽  
Cognitive Selection ◽  
Programming Algorithms ◽  
Selection Of

Abstract In recent years, cluster analysis has played an increasingly important role in statistical pattern recognition. Hoeltzel and Chieng have shown an example on cognitive selection of nonlinear programming algorithms in a mechanical design expert system. In this paper, an improved dynamic clustering of 3000 samples came from a comparative performance evaluation of six typical nonlinear programming softwares with randomly generated test problems has been made. Explanations resulting from the cluster analysis have been used to build rules to form the knowledge base of an optimization expert system.

scholarly journals Identification of mechanical parameters of fiber-reinforced composites by frequency response function approximation method

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041987803 ◽  
Author(s):  
Hui Li ◽  
PengCheng Xue ◽  
Wanchong Rong ◽  
XiaoPeng Li ◽  
BangChun Wen
Keyword(s):  
Frequency Response ◽  
Thin Plate ◽  
Response Function ◽  
Approximation Method ◽  
Function Approximation ◽  
Frequency Response Function ◽  
Fiber Reinforced Composites ◽  
Mechanical Parameters ◽  
Reinforced Composites ◽  
Fiber Reinforced

This article proposes frequency response function approximation method to identify mechanical parameters of fiber-reinforced composites. First, a fiber-reinforced composite thin plate is taken as a research object, and its natural characteristic and vibration response under pulse excitation are solved based on the Ritz method and mode superposition method, so that the theoretical calculation of frequency response function of such composite plates can be realized. Then, the identification principle based on frequency response function approximation method is illustrated and its correctness is validated by comparing with other published literature in the verification example, and the specific identification procedure is also proposed. Finally, frequency response function approximation method is applied in a study case, where the elastic moduli, Poisson’s ratios, and loss factors of the TC300 carbon/epoxy composite thin plate are identified, and the influences of boundary conditions, approximation points, total number of modes, and calculation step size on the identification accuracy and efficiency are discussed. It has been proved that the proposed method can identify mechanical parameters of fiber composite materials with high precision and efficiency.

Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints

2019 ◽  
Vol 31 (4) ◽  
pp. 689-702 ◽  
Author(s):  
Juliane Müller ◽  
Marcus Day
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Black Box ◽  
Direct Search ◽  
Test Problems ◽  
Large Set ◽  
Mesh Adaptive Direct Search ◽  
Surrogate Optimization ◽  
Computationally Expensive ◽  
Hidden Constraints

We introduce the algorithm SHEBO (surrogate optimization of problems with hidden constraints and expensive black-box objectives), an efficient optimization algorithm that employs surrogate models to solve computationally expensive black-box simulation optimization problems that have hidden constraints. Hidden constraints are encountered when the objective function evaluation does not return a value for a parameter vector. These constraints are often encountered in optimization problems in which the objective function is computed by a black-box simulation code. SHEBO uses a combination of local and global search strategies together with an evaluability prediction function and a dynamically adjusted evaluability threshold to iteratively select new sample points. We compare the performance of our algorithm with that of the mesh-based algorithms mesh adaptive direct search (MADS, NOMAD [nonlinear optimization by mesh adaptive direct search] implementation) and implicit filtering and SNOBFIT (stable noisy optimization by branch and fit), which assigns artificial function values to points that violate the hidden constraints. Our numerical experiments for a large set of test problems with 2–30 dimensions and a 31-dimensional real-world application problem arising in combustion simulation show that SHEBO is an efficient solver that outperforms the other methods for many test problems.

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