On Bi-Objective convex-quadratic problems

Cheikh Touré (1, 2) , Anne Auger (2) , Dimo Brockhoff (2) , Nikolaus Hansen (2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 RANDOPT - Randomized Optimisation

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.

Mots clés: Convex Pareto front; Bi-objective optimization; Convex-quadratic problems.; Pareto set

Domaines: Informatique [cs]; Réseau de neurones [cs.NE]; Mathématiques [math]; Optimisation et contrôle [math.OC]

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⟩