Incorporating response variability and estimation uncertainty into Pareto front optimization

Chapman, Jessica L.; Lu, Lu; Anderson‐Cook, Christine M.

doi:10.1016/j.cie.2014.07.028

Cited by 34 publications

(56 citation statements)

References 13 publications

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“…As previously mentioned, Lee et al and Lee et al suggested posterior approaches for both DRO and MRO. Recently, Chapman et al also proposed a posterior approach to MRO, calling it the “Pareto front approach.”…”

Section: Literature Reviewmentioning

confidence: 99%

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A desirability function method for optimizing mean and variability of multiple responses using a posterior preference articulation approach

Lee

Jeong

Kim

2018

Quality & Reliability Eng

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A desirability function approach has been widely used in multi‐response optimization due to its simplicity. Most of the existing desirability function‐based methods assume that the variability of the response variables is stable; thus, they focus mainly on the optimization of the mean of multiple responses. However, this stable variability assumption often does not apply in practical situations; thus, the quality of the product or process can be severely degraded due to the high variability of multiple responses. In this regard, we propose a new desirability function method to simultaneously optimize both the mean and variability of multiple responses. In particular, the proposed method uses a posterior preference articulation approach, which has an advantage in investigating tradeoffs between the mean and variability of multiple responses. It is expected that process engineers can use this method to better understand the tradeoffs, thereby obtaining a satisfactory compromise solution.

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Section: Literature Reviewmentioning

confidence: 99%

“…Pareto front approach proposed by Chapman et al and the proposed method are similar in that both of them generate a set of Pareto optimal solutions (or nondominated solutions) and then select a solution. In this section, the 2 methods are compared and guidelines for using the methods are presented.…”

Section: Comparison With Pareto Front Approachmentioning

confidence: 99%

A desirability function method for optimizing mean and variability of multiple responses using a posterior preference articulation approach

Lee

Jeong

Kim

2018

Quality & Reliability Eng

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“…The proposed method regard the estimates of model parameters as fixed values. Naively treating them as fixed can lead to overconfidence in the conclusions and potentially sub-optimal solutions which do not perform well in practice (Chapman, Lu, and Anderson-Cook 2014a). Parameter uncertainty due to estimation error has been neglected in the proposed method, which could increase the variability of predicted responses.…”

Section: Discussionmentioning

confidence: 92%

A solution selection approach to multiresponse surface optimization based on a clustering method

Lee

2016

Quality Engineering

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In Multi-Response Surface Optimization (MRSO), responses are often in conflict. To obtain a satisfactory compromise, the preference information of a Decision Maker (DM) on the tradeoffs among the responses should be considered. One of the promising alternatives is a posterior preference articulation approach. It first generates nondominated solutions and then makes the DM select the best one from the nondominated solutions. In this article, a solution selection approach is presented. It takes the posterior approach and employs a clustering method to aid the selection process of the DM. The DM can obtain the satisfactory compromise solution easily by the proposed method.

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“…Since responses from most experiments cannot be simultaneously optimized, finding an appropriate balance between the performance of the responses is generally required when optimizing a product or process. A good initial step in identifying promising input combinations is to construct a Pareto front (PF) that shows the range of possible nondominated choices of response values. The Pareto set (PS) is the corresponding collection of solutions, here, the combination of input factor values that objectively provide the best trade‐off among responses.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty analysis of trade‐offs between multiple responses using hypervolume

Cao

Anderson‐Cook

2017

Quality & Reliability Eng

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When multiple responses are considered in process optimization, the degree to which they can be simultaneously optimized depends on the optimization objectives and the amount of trade‐offs between the responses. The normalized hypervolume of the Pareto front is a useful summary to quantify the amount of trade‐offs required to balance performance across the multiple responses. To quantify the impact of uncertainty of the estimated response surfaces and add realism to what future data to expect, 2 versions of the scaled normalized hypervolume of the Pareto front are presented. To demonstrate the variation of the hypervolume distributions, we explore a case study for a chemical process involving 3 responses, each with a different type of optimization goal. Results show that the global normalized hypervolume characterizes the proximity to the ideal results possible, while the instance‐specific summary considers the richness of the front and the severity of trade‐offs between alternatives. The 2 scaling schemes complement each other and highlight different features of the Pareto front and hence are useful to quantify what solutions are possible for simultaneous optimization of multiple responses.

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Incorporating response variability and estimation uncertainty into Pareto front optimization

Cited by 34 publications

References 13 publications

A desirability function method for optimizing mean and variability of multiple responses using a posterior preference articulation approach

A desirability function method for optimizing mean and variability of multiple responses using a posterior preference articulation approach

A solution selection approach to multiresponse surface optimization based on a clustering method

Uncertainty analysis of trade‐offs between multiple responses using hypervolume

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