Quantifying the Shape of Pareto Fronts During Multi-Objective Trade Space ExplorationSource: Journal of Mechanical Design:;2018:;volume( 140 ):;issue: 002::page 21402DOI: 10.1115/1.4038005Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Recent advances in simulation and computation capabilities have enabled designers to model increasingly complex engineering problems, taking into account many dimensions, or objectives, in the problem formulation. Increasing the dimensionality often results in a large trade space, where decision-makers (DM) must identify and negotiate conflicting objectives to select the best designs. Trade space exploration often involves the projection of nondominated solutions, that is, the Pareto front, onto two-objective trade spaces to help identify and negotiate tradeoffs between conflicting objectives. However, as the number of objectives increases, an exhaustive exploration of all of the two-dimensional (2D) Pareto fronts can be inefficient due to a combinatorial increase in objective pairs. Recently, an index was introduced to quantify the shape of a Pareto front without having to visualize the solution set. In this paper, a formal derivation of the Pareto Shape Index is presented and used to support multi-objective trade space exploration. Two approaches for trade space exploration are presented and their advantages are discussed, specifically: (1) using the Pareto shape index for weighting objectives and (2) using the Pareto shape index to rank objective pairs for visualization. By applying the two approaches to two multi-objective problems, the efficiency of using the Pareto shape index for weighting objectives to identify solutions is demonstrated. We also show that using the index to rank objective pairs provides DM with the flexibility to form preferences throughout the process without closely investigating all objective pairs. The limitations and future work are also discussed.
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contributor author | Unal, Mehmet | |
contributor author | Warn, Gordon P. | |
contributor author | Simpson, Timothy W. | |
date accessioned | 2019-02-28T11:03:54Z | |
date available | 2019-02-28T11:03:54Z | |
date copyright | 12/13/2017 12:00:00 AM | |
date issued | 2018 | |
identifier issn | 1050-0472 | |
identifier other | md_140_02_021402.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4252275 | |
description abstract | Recent advances in simulation and computation capabilities have enabled designers to model increasingly complex engineering problems, taking into account many dimensions, or objectives, in the problem formulation. Increasing the dimensionality often results in a large trade space, where decision-makers (DM) must identify and negotiate conflicting objectives to select the best designs. Trade space exploration often involves the projection of nondominated solutions, that is, the Pareto front, onto two-objective trade spaces to help identify and negotiate tradeoffs between conflicting objectives. However, as the number of objectives increases, an exhaustive exploration of all of the two-dimensional (2D) Pareto fronts can be inefficient due to a combinatorial increase in objective pairs. Recently, an index was introduced to quantify the shape of a Pareto front without having to visualize the solution set. In this paper, a formal derivation of the Pareto Shape Index is presented and used to support multi-objective trade space exploration. Two approaches for trade space exploration are presented and their advantages are discussed, specifically: (1) using the Pareto shape index for weighting objectives and (2) using the Pareto shape index to rank objective pairs for visualization. By applying the two approaches to two multi-objective problems, the efficiency of using the Pareto shape index for weighting objectives to identify solutions is demonstrated. We also show that using the index to rank objective pairs provides DM with the flexibility to form preferences throughout the process without closely investigating all objective pairs. The limitations and future work are also discussed. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Quantifying the Shape of Pareto Fronts During Multi-Objective Trade Space Exploration | |
type | Journal Paper | |
journal volume | 140 | |
journal issue | 2 | |
journal title | Journal of Mechanical Design | |
identifier doi | 10.1115/1.4038005 | |
journal fristpage | 21402 | |
journal lastpage | 021402-13 | |
tree | Journal of Mechanical Design:;2018:;volume( 140 ):;issue: 002 | |
contenttype | Fulltext |