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.
https://hal.inria.fr/hal-01942159
Contributor : Cheikh Touré
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Submitted on : Monday, December 3, 2018 - 12:11:22 AM
Last modification on : Sunday, July 21, 2019 - 1:48:21 AM
Long-term archiving on : Monday, March 4, 2019 - 12:24:05 PM
Cheikh Touré, Anne Auger, Dimo Brockhoff, Nikolaus Hansen. On Bi-Objective convex-quadratic problems. 10th International Conference on Evolutionary Multi-Criterion Optimization, Mar 2019, East Lansing, Michigan, United States. ⟨hal-01942159⟩
