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Title: Uncertainty analysis of trade-offs between multiple responses using hypervolume

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. In order 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. Our 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. Furthermore, 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.
Authors:
 [1] ;  [2] ;  [3]
  1. Indiana Univ. of Pennsylvania, Indiana, PA (United States). Dept. of Mathematics
  2. Univ. of South Florida, Tampa, FL (United States). Dept. of Mathematics and Statistics
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
LA-UR-17-22570
Journal ID: ISSN 0748-8017
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Quality and Reliability Engineering International
Additional Journal Information:
Journal Name: Quality and Reliability Engineering International; Journal ID: ISSN 0748-8017
Publisher:
Wiley
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Mathematics
OSTI Identifier:
1375877

Cao, Yongtao, Lu, Lu, and Anderson-Cook, Christine M. Uncertainty analysis of trade-offs between multiple responses using hypervolume. United States: N. p., Web. doi:10.1002/qre.2193.
Cao, Yongtao, Lu, Lu, & Anderson-Cook, Christine M. Uncertainty analysis of trade-offs between multiple responses using hypervolume. United States. doi:10.1002/qre.2193.
Cao, Yongtao, Lu, Lu, and Anderson-Cook, Christine M. 2017. "Uncertainty analysis of trade-offs between multiple responses using hypervolume". United States. doi:10.1002/qre.2193. https://www.osti.gov/servlets/purl/1375877.
@article{osti_1375877,
title = {Uncertainty analysis of trade-offs between multiple responses using hypervolume},
author = {Cao, Yongtao and Lu, Lu and Anderson-Cook, Christine M.},
abstractNote = {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. In order 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. Our 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. Furthermore, 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.},
doi = {10.1002/qre.2193},
journal = {Quality and Reliability Engineering International},
number = ,
volume = ,
place = {United States},
year = {2017},
month = {8}
}