Uncrowded Hypervolume Improvement: COMO-CMA-ES and the Sofomore framework

We present a framework to build a multiobjective algorithm from single-objective ones. This framework addresses the \(p \times n\)-dimensional problem of finding p solutions in an n-dimensional search space, maximizing an indicator by dynamic subspace optimization. Each single-objective algorithm op...

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Bibliographic Details
Published in:arXiv.org 2019-04
Main Authors: Touré, Cheikh, Hansen, Nikolaus, Auger, Anne, Brockhoff, Dimo
Format: Article
Language:English
Subjects:
Algorithms
Multiple objective analysis
Optimization
Online Access:Get full text
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Summary:We present a framework to build a multiobjective algorithm from single-objective ones. This framework addresses the \(p \times n\)-dimensional problem of finding p solutions in an n-dimensional search space, maximizing an indicator by dynamic subspace optimization. Each single-objective algorithm optimizes the indicator function given \(p - 1\) fixed solutions. Crucially, dominated solutions minimize their distance to the empirical Pareto front defined by these \(p - 1\) solutions. We instantiate the framework with CMA-ES as single-objective optimizer. The new algorithm, COMO-CMA-ES, is empirically shown to converge linearly on bi-objective convex-quadratic problems and is compared to MO-CMA-ES, NSGA-II and SMS-EMOA.
ISSN:2331-8422
DOI:10.48550/arxiv.1904.08823