Impact of response variability on Pareto front optimization

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

doi:10.1002/sam.11279

Cited by 9 publications

(8 citation statements)

References 10 publications

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“…For the chemical process, it is likely that only one input combination will be selected at which to run the process, and this needs to be decided based on the priorities of the experimenters. For this example, Chapman et al describe a structured process to incorporate subjective priorities into the selection process, while taking into account the variability of the responses. Figures , and show how the large differences in the shape and location of the PFs across the simulations will impact the changes in the optimal combination obtained and the uncertainty in the input locations.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

Uncertainty analysis of trade‐offs between multiple responses using hypervolume

Cao

Anderson‐Cook

2017

Quality & Reliability Eng

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“…A discrete representation of a Pareto frontier (a collection of solutions distributed along the Pareto front that provide a finite and manageable alternative solutions to the decision-maker) is, in general, sufficient for selecting a solution for MRO problems. Majority of the literature has focused on how to find the Pareto frontier with its most promising choices without providing more insights on how to proceed from those choices to a final decision [5]. However, it is important to be aware that some Pareto solutions may lead to operation conditions more hazardous, more costly or more difficult to implement and control than others.…”

Section: Reproducibility Of Non-dominated Solutionsmentioning

confidence: 99%

Responses’ Prediction Standard Error Analysis in Pareto Solutions

Costa

Lourenço

2017

MATEC Web Conf.

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A Pareto front provides to the decision-maker a set of optimal solutions from where a unique solution should be selected to solve a multiresponse problem. However, the responses' prediction standard error for each one of the optimal solutions is different, which impacts on the reproducibility of Pareto solutions. This means that the decision-maker has to take into account the responses' prediction standard error in the solution selection process. For this purpose, a metric is presented. A bi-objective problem is used as example and results displayed graphically.

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“…In addition to understanding the shape of the PF, the trade‐offs between responses, and the relationship between the responses and input factors based on the mean model, we also want to understand the uncertainty in the estimated response surfaces, which as a result can lead to different PFs and possibly different solutions chosen as optimal. Chapman et al . found that the set of PF optimal solutions can be influenced by the signal‐to‐noise ratio for the different response variables.…”

Section: Multiple Response Decision Making Using a Pareto Front Approachmentioning

confidence: 99%

“…Chapman et al . describe how to incorporate this uncertainty into the PF decision‐making process, and Chapman et al . examine how the varied amount of variability in the response variables can impact the Pareto optimal solutions.…”

Section: Introductionmentioning

confidence: 99%

“…One of the key elements of the final three stages of DMRCS and PF two‐stage decision‐making processes is to use a structured approach paired with versatile graphical tools to facilitate informed decision making. This requires using efficient graphical summaries to quantify and visualize the PF solutions as well as the contending choices with different possible user priorities. For multiple response optimization, visualization of the responses, the PF, and the contending candidate solutions becomes difficult even for moderate dimensions of both the response variables and input factors.…”

Section: Introductionmentioning

confidence: 99%

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Multiple Response Optimization for Higher Dimensions in Factors and Responses

Chapman

Anderson‐Cook

2016

Quality & Reliability Eng

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When optimizing a product or process with multiple responses, a two-stage Pareto front approach is a useful strategy to evaluate and balance trade-offs between different estimated responses to seek optimum input locations for achieving the best outcomes. After objectively eliminating non-contenders in the first stage by looking for a Pareto front of superior solutions, graphical tools can be used to identify a final solution in the second subjective stage to compare options and match with user priorities. Until now, there have been limitations on the number of response variables and input factors that could effectively be visualized with existing graphical summaries. We present novel graphical tools that can be more easily scaled to higher dimensions, in both the input and response spaces, to facilitate informed decision making when simultaneously optimizing multiple responses. A key aspect of these graphics is that the potential solutions can be flexibly sorted to investigate specific queries, and that multiple aspects of the solutions can be simultaneously considered.Recommendations are made about how to evaluate the impact of the uncertainty associated with the estimated response surfaces on decision making with higher dimensions.

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Impact of response variability on Pareto front optimization

Cited by 9 publications

References 10 publications

Uncertainty analysis of trade‐offs between multiple responses using hypervolume

Uncertainty analysis of trade‐offs between multiple responses using hypervolume

Responses’ Prediction Standard Error Analysis in Pareto Solutions

Multiple Response Optimization for Higher Dimensions in Factors and Responses

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