Quantifying the Shape of Pareto Fronts During Multi-Objective Trade Space Exploration

[+] Author and Article Information
Mehmet Unal

Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA 16802 USA

Gordon P. Warn

Civil and Environmental Engineering, The Pennsylvania State University, University Park, PA 16802 USA

Timothy W. Simpson

Mechanical & Nuclear Engineering, The Pennsylvania State University, University Park, PA 16802 USA

1Corresponding author.

ASME doi:10.1115/1.4038005 History: Received February 17, 2017; Revised August 30, 2017


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 must identify and negotiate conflicting objectives to select the best designs. Trade space exploration often involves the projection of non-dominated 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 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 problem, 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 decision-makers with the flexibility to form preferences throughout the process without closely investigating all objective pairs. The limitations and future work are also discussed.

Copyright (c) 2017 by ASME
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