@inproceedings{a08c7dc8fb53430098e7620015f7bd01,
title = "On the Pareto Set and Front of Multiobjective Spherical Functions with Convex Constraints",
abstract = "We analyze a fundamental class of multiobjective constrained problems where the objectives are spherical functions and the constraints are convex. As an application from the projection theorem on closed convex sets, we prove that the constrained Pareto set corresponds to the orthogonal projection of the unconstrained Pareto set onto the feasible region. We establish this fundamental geometric property and illustrate its implications using visualizations of Pareto sets and fronts under various constraint configurations. Furthermore, we assess the performance of NSGA-II on these problems, examining its ability to approximate the constrained Pareto set across different dimensions. Our findings highlight the importance of theoretically grounded and understood benchmark problems for assessing algorithmic behavior and contribute to a deeper understanding of constrained multiobjective landscapes.",
keywords = "benchmarking, multiobjective constrained optimization, test functions",
author = "Anne Auger and Dimo Brockhoff and Jordan Cork and Tea Tu{\v s}ar",
note = "Publisher Copyright: {\textcopyright} 2025 Copyright held by the owner/author(s). Publication rights licensed to ACM.; 2025 Genetic and Evolutionary Computation Conference, GECCO 2025 ; Conference date: 14-07-2025 Through 18-07-2025",
year = "2025",
month = jul,
day = "13",
doi = "10.1145/3712256.3726432",
language = "English",
series = "GECCO 2025 - Proceedings of the 2025 Genetic and Evolutionary Computation Conference",
publisher = "Association for Computing Machinery, Inc",
pages = "527--535",
editor = "Gabriela Ochoa",
booktitle = "GECCO 2025 - Proceedings of the 2025 Genetic and Evolutionary Computation Conference",
}