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Conference Papers Year : 2019

On Bi-Objective convex-quadratic problems

Anne Auger
  • Function : Author
  • PersonId : 751513
  • IdHAL : anne-auger
Dimo Brockhoff
Nikolaus Hansen


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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Dates and versions

hal-01942159 , version 1 (03-12-2018)





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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