Pattern search ranking and selection algorithms for mixed variable simulation-based optimization

Sriver, Todd A.; Chrissis, James W.; Abramson, Mark A.

doi:10.1016/j.ejor.2008.10.020

Cited by 31 publications

(20 citation statements)

References 33 publications

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“…Other methods, although having value for determining an optimum's desirability, fall short by not automating the user's specific needs or by not considering some important measures that affect the optimum's usefulness for the purposes of the experiment. Ranking optima by their mean in some specified region around the optimum location does not take into account other important measures that concern the user [4]. Selecting optima based on a utility determined by their mean and variance does not take into account that, by moving the tolerance region from the optimum point, its utility may be greatly increased [3].…”

Section: Discussionmentioning

confidence: 99%

“…In [3], the utility was determined by the mean and variance where the variance was determined from a finite set of known probability distributions. In [4], the best candidate optimum was chosen based on the mean of the simulator values at some specified distance from the optimum. In [5], the solution (optimum chosen) is based on the expected value and the associated confidence interval.…”

Section: Introductionmentioning

confidence: 99%

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A Robust Algorithm for Optimum Utility

Guenther¹,

Lee²

2017

JAAM

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The black box functions found in computer experiments often have multiple optima. When there are multiple optima, the goal of a computer experiment should be to determine the best optimum for the purposes of the experiment. This brings up the concept of the utility of an optimum: The degree to which the optimum fulfills the purposes of the experiment. The utility of an optima is based on measures of the variability of the surface in the tolerance region (region of interest around the optima) defined by the accuracy with which influential variables can be specified. This tolerance region can be symmetric or asymmetric. For symmetric optima the tolerance region that provides maximum utility is centered at the optimum point. For asymmetric optima, it may be advantageous to displace the center of the tolerance region from the optimum point. For example, a very skewed optimum (minimum in this case) can increase significantly in one direction but only slightly in the opposite direction from the minimum point. For such an optimum the center point of the tolerance region that provides maximum utility for the optimum is displaced from the optimum point along the direction that only slightly increases. The algorithm discussed in this paper locates the center point for the tolerance region to achieve the best utility for any optimum, symmetric or asymmetric. Making use of the surface predictions of the emulator around the minimum point, it employs pattern search to find the best center point for any optimum and for any dimensionality.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Robust Algorithm for Optimum Utility

Guenther¹,

Lee²

2017

JAAM

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“…Staszewski et al (2000) study the problem of optimal sensor placement for impact detection and location in composite materials. Papadimitriou et al (2000) also discuss optimal placement strategies for structural damage identification.…”

Section: Introductionmentioning

confidence: 99%

Optimal sensor placement for enhancing sensitivity to change in stiffness for structural health monitoring

et al. 2007

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This paper focuses on optimal sensor placement for structural health monitoring (SHM), in which the goal is to find an optimal configuration of sensors that will best predict structural damage. The problem is formulated as a bound constrained mixed variable programming (MVP) problem, in which the discrete variables are categorical; i.e., they may only take on values from a pre-defined list. The problem is particularly challenging because the objective function is computationally expensive to evaluate and first-order derivatives may not be available. The problem is solved numerically using the generalized mixed variable pattern search (MVPS) algorithm. Some new theoretical convergence results are proved, and numerical results are presented, which show the potential of our approach.

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“…Kokkolaras, Audet, and Dennis [21] applied the MVPS algorithm to the design of a thermal insulation system and showed a 65% reduction in the objective function value over previous results that optimized only with respect to the continuous variables. MVPS has also been extended to problems with stochastic noise in the objective function [30] and to problems with nonlinear constraints [4,5]. A more general framework for derivative-free mixed variable optimization is described in [24].…”

Section: Mixed Variable Formulationmentioning

confidence: 99%

Quantitative Object Reconstruction Using Abel Transform X-Ray Tomography and Mixed Variable Optimization

Abramson¹,

Asaki²,

Dennis³

et al. 2008

SIAM J. Imaging Sci.

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Abstract. This paper introduces a new approach to the problem of quantitative reconstruction of an object from few radiographic views. A mixed variable programming problem is formulated in which the variables of interest are the number and types of materials and geometric parameters. To demonstrate the technique, we considered the problem of reconstructing cylindrically symmetric objects of multiple layers from a single radiograph. The mixed variable pattern search algorithm for linearly constrained problems was applied by means of the NOMADm MATLAB software package. Numerical results are presented for several test configurations and show that, while there are difficulties yet to be overcome, the method is promising for solving this class of problems.

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Pattern search ranking and selection algorithms for mixed variable simulation-based optimization

Cited by 31 publications

References 33 publications

A Robust Algorithm for Optimum Utility

A Robust Algorithm for Optimum Utility

Optimal sensor placement for enhancing sensitivity to change in stiffness for structural health monitoring

Quantitative Object Reconstruction Using Abel Transform X-Ray Tomography and Mixed Variable Optimization

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