Quantifying the shape of a pareto front in support of many-objective trade space exploration

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Complex design optimization problems typically include many conflicting objectives, and the resulting trade space is comprised of numerous design solutions. To efficiently explore a many-objective trade space, form preferences, and select a final design, one must identify and negotiate tradeoffs between multiple, often conflicting, objectives. Identifying conflicting objective pairs allows decision-makers to concentrate on these objectives when selecting preferred designs from the non-dominated solution set, i.e., the Pareto front. Techniques exist to identify and visualize tradeoffs between these conflicting objectives to support trade space exploration; however, these techniques donotquantify, or differentiate, the shape of the Pareto front, which might be useful information for a decisionmaker. More specifically, designers could gain insight from the degree of diminishing returns among solutions on the Pareto front, which can be used to understand the extent of the tradeoffs in the problem. Therefore, the shape of the Pareto front could be used to prioritize exploration of conflicting objective pairs. In this paper, we introduce a novel index that quantifies the shape of the Pareto front to provide information about the degree of diminishing returns. The aim of the index is to help designers gain insight into the underlying tradeoffs in a many-objective optimization problem and support trade space exploration by prioritizing the negotiation of conflicting objectives. The proposed Pareto Shape Index is based on analytical geometry and derived from the coordinates of the Pareto solutions in the n objective trade space. The utility of the Pareto Shape Index in differentiating diminishing returns between conflicting objectives is demonstrated by application to an eight-objective benchmark optimization problem.

Original languageEnglish (US)
Title of host publication42nd Design Automation Conference
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791850114
DOIs
StatePublished - Jan 1 2016
EventASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016 - Charlotte, United States
Duration: Aug 21 2016Aug 24 2016

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume2B-2016

Other

OtherASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016
CountryUnited States
CityCharlotte
Period8/21/168/24/16

Fingerprint

Pareto Front
Diminishing
Trade-offs
Optimization Problem
Pareto
Pareto Solutions
Nondominated Solutions
Space Form
Differentiate
Solution Set
Quantify
Trade
Benchmark
Geometry
Design

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

Cite this

Unal, M., Warn, G. P., & Simpson, T. W. (2016). Quantifying the shape of a pareto front in support of many-objective trade space exploration. In 42nd Design Automation Conference (Proceedings of the ASME Design Engineering Technical Conference; Vol. 2B-2016). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC2016-59716
Unal, Mehmet ; Warn, Gordon P. ; Simpson, Timothy W. / Quantifying the shape of a pareto front in support of many-objective trade space exploration. 42nd Design Automation Conference. American Society of Mechanical Engineers (ASME), 2016. (Proceedings of the ASME Design Engineering Technical Conference).
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abstract = "Complex design optimization problems typically include many conflicting objectives, and the resulting trade space is comprised of numerous design solutions. To efficiently explore a many-objective trade space, form preferences, and select a final design, one must identify and negotiate tradeoffs between multiple, often conflicting, objectives. Identifying conflicting objective pairs allows decision-makers to concentrate on these objectives when selecting preferred designs from the non-dominated solution set, i.e., the Pareto front. Techniques exist to identify and visualize tradeoffs between these conflicting objectives to support trade space exploration; however, these techniques donotquantify, or differentiate, the shape of the Pareto front, which might be useful information for a decisionmaker. More specifically, designers could gain insight from the degree of diminishing returns among solutions on the Pareto front, which can be used to understand the extent of the tradeoffs in the problem. Therefore, the shape of the Pareto front could be used to prioritize exploration of conflicting objective pairs. In this paper, we introduce a novel index that quantifies the shape of the Pareto front to provide information about the degree of diminishing returns. The aim of the index is to help designers gain insight into the underlying tradeoffs in a many-objective optimization problem and support trade space exploration by prioritizing the negotiation of conflicting objectives. The proposed Pareto Shape Index is based on analytical geometry and derived from the coordinates of the Pareto solutions in the n objective trade space. The utility of the Pareto Shape Index in differentiating diminishing returns between conflicting objectives is demonstrated by application to an eight-objective benchmark optimization problem.",
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Unal, M, Warn, GP & Simpson, TW 2016, Quantifying the shape of a pareto front in support of many-objective trade space exploration. in 42nd Design Automation Conference. Proceedings of the ASME Design Engineering Technical Conference, vol. 2B-2016, American Society of Mechanical Engineers (ASME), ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016, Charlotte, United States, 8/21/16. https://doi.org/10.1115/DETC2016-59716

Quantifying the shape of a pareto front in support of many-objective trade space exploration. / Unal, Mehmet; Warn, Gordon P.; Simpson, Timothy W.

42nd Design Automation Conference. American Society of Mechanical Engineers (ASME), 2016. (Proceedings of the ASME Design Engineering Technical Conference; Vol. 2B-2016).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Unal M, Warn GP, Simpson TW. Quantifying the shape of a pareto front in support of many-objective trade space exploration. In 42nd Design Automation Conference. American Society of Mechanical Engineers (ASME). 2016. (Proceedings of the ASME Design Engineering Technical Conference). https://doi.org/10.1115/DETC2016-59716