Utility functions as optimization criteria for separations by high-performance liquid chromatography

Weyland, J. Willem; Bruins, C.H.P.; Debets, H.J.G.; Bajema, B.L.; Doornbos, D.A.

doi:10.1016/s0003-2670(00)85491-4

Cited by 25 publications

(4 citation statements)

References 11 publications

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“…Furthermore, this approach to optimization of analytical methods should be applicable to any technique for which advance prediction can be carried out. A similar approach has been used in a recent study of response functions for the optimization of chromatographic analyses (26).…”

Section: Resultsmentioning

confidence: 99%

Simplex optimization by advance prediction for single-element instrumental neutron activation analysis

Burgess¹,

Hayumbu²

1984

Anal. Chem.

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Section: Resultsmentioning

confidence: 99%

Simplex optimization by advance prediction for single-element instrumental neutron activation analysis

Burgess¹,

Hayumbu²

1984

Anal. Chem.

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“…Using either overlaid contour plots or sets of PO predictions, we can compare the options and select a suitable compromise. The selection of the optimal compromise is automated by preference techniques, such as utility functions (Weyland, Bruins, Debets, Bajema, and Doornbos 1983), desirability functions (Harrington 1965;Derringer and Suich 1980), and a distance measure (Khuri and Conlon 1981), which create a single response from the multiple responses using weights and specifications. Utility functions are weighted arithmetic means of unbounded functions of the responses, whereas desirability is a geometric mean of functions bounded by [0, 1].…”

Section: Multiple-response Optimization Literaturementioning

confidence: 99%

Steepest Ascent for Multiple-Response Applications

Mee

Xiao²

2008

Technometrics

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The path of steepest ascent proposed by Box and Wilson consists of points that maximize the predicted response for a fitted first-order model among all points with the same standard error of prediction. When there are multiple responses or additional constraints (on, e.g., cost or throughput), the standard steepest ascent is of limited use, because it often optimizes one response to the detriment of others. We answer three pertinent questions: (1) For multiple-response applications, what search directions are inferior and can be excluded from consideration?; (2) What graphical tools can assist in our understanding the tradeoffs and choosing a compromise direction for exploration?; and (3) Do compromise directions exist that ensure improvement in all responses? We prove that only search directions that are convex combinations of the paths of steepest ascent/descent need be considered. We also construct confidence bounds for improvement of each response relative to its performance at the center of the design. Whereas the literature often deals with multiple response optimization in the later stages of response surface exploration, our article addresses how to proceed after a successful initial screening experiment.

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“…[42][43][44][45][46] Until now, MCDM optimization methods have received little attention in enantiomeric separations. A number of MCDM procedures are useful for bicriteria optimizations, e.g., the threshold [48][49][50][51] and the pareto-optimality approach. 38 A pareto-optimal point is a point where no experiment yields better results on one criterion without having a worse on another.…”

Section: Calculations and Softwarementioning

confidence: 99%

Optimization of the chiral separation of some 2‐arylpropionic acids on an avidin column by modeling a combined response

et al. 2001

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The enantiomeric separation of some nonsteroidal antiinflammatory drugs was investigated on an avidin column. An experimental design approach (central composite design) was used to evaluate the effects of three method parameters (pH, concentration of organic modifier, and buffer concentration) on the analysis time and the resolution, as well as to model these responses. This revealed that the organic modifier concentration and sometimes the pH are significant parameters to control because of their influence on both analysis time and resolution. Furthermore, the central composite design results were combined in a multicriteria decision-making approach in order to obtain a set of optimal experimental conditions leading to the most desirable compromise between resolution and analysis time.

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Utility functions as optimization criteria for separations by high-performance liquid chromatography

Cited by 25 publications

References 11 publications

Simplex optimization by advance prediction for single-element instrumental neutron activation analysis

Simplex optimization by advance prediction for single-element instrumental neutron activation analysis

Steepest Ascent for Multiple-Response Applications

Optimization of the chiral separation of some 2‐arylpropionic acids on an avidin column by modeling a combined response

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