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On Bi-Objective convex-quadratic problems

Cheikh Touré 1, 2 Anne Auger 2 Dimo Brockhoff 2 Nikolaus Hansen 2
2 RANDOPT - Randomized Optimisation
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : In this paper we analyze theoretical properties of bi-objective convex-quadratic problems. We give a complete description of their Pareto set and prove the convexity of their Pareto front. We show that the Pareto set is a line segment when both Hessian matrices are proportional. We then propose a novel set of convex-quadratic test problems, describe their theoretical properties and the algorithm abilities required by those test problems. This includes in particular testing the sensitivity with respect to separability, ill-conditioned problems, rotational invariance, and whether the Pareto set is aligned with the coordinate axis.
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Submitted on : Monday, December 3, 2018 - 12:11:22 AM
Last modification on : Friday, February 4, 2022 - 3:34:41 AM
Long-term archiving on: : Monday, March 4, 2019 - 12:24:05 PM


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Distributed under a Creative Commons Attribution 4.0 International License


  • HAL Id : hal-01942159, version 1
  • ARXIV : 1812.00289


Cheikh Touré, Anne Auger, Dimo Brockhoff, Nikolaus Hansen. On Bi-Objective convex-quadratic problems. EMO 2019 - 10th International Conference on Evolutionary Multi-Criterion Optimization, Mar 2019, East Lansing, Michigan, United States. ⟨hal-01942159⟩



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