Random Pareto front surfaces
Ben Tu, Nikolas Kantas, Robert M. Lee, Behrang Shafei

TL;DR
This paper introduces a novel polar coordinate parameterization of Pareto front surfaces, enabling rigorous statistical analysis, uncertainty quantification, and improved visualization in multi-objective optimization tasks.
Contribution
It proposes a scalar length function representation of Pareto fronts, facilitating stochastic modeling and practical decision-making in multi-objective optimization.
Findings
Derived Pareto front surface statistics such as expectation, covariance, and quantiles.
Developed visualization techniques for uncertainty quantification.
Applied methodology to real-world air pollution data case study.
Abstract
The goal of multi-objective optimisation is to identify the Pareto front surface which is the set obtained by connecting the best trade-off points. Typically this surface is computed by evaluating the objectives at different points and then interpolating between the subset of the best evaluated trade-off points. In this work, we propose to parameterise the Pareto front surface using polar coordinates. More precisely, we show that any Pareto front surface can be equivalently represented using a scalar-valued length function which returns the projected length along any positive radial direction. We then use this representation in order to rigorously develop the theory and applications of stochastic Pareto front surfaces. In particular, we derive many Pareto front surface statistics of interest such as the expectation, covariance and quantiles. We then discuss how these can be used in…
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · 3D Shape Modeling and Analysis · Computational Geometry and Mesh Generation
MethodsSparse Evolutionary Training · Focus
