On Continuation Methods for Non-Linear Bi-Objective Optimization: Certified Interval-Based Approach

Benjamin Martin (1) , Alexandre Goldsztejn (1) , Laurent Granvilliers (1) , Christophe Jermann (1)

1 LINA - Laboratoire d'Informatique de Nantes Atlantique

The global optimization of constrained Non-Linear Bi-Objective Optimization problems (MO) aims at covering their Pareto-optimal front which is in general a manifold in R^2. Continuation methods can help in this context as they can follow a continuous component of this front once an initial point on it is provided. They constitute somehow a generalization of the classical scalarizing framework which transforms the bi-objective problem into a parametric mono-objective problem. Recent works have shown that they can play a key role in global algorithms dedicated to bi-objective problems, e.g. population based algorithms, where they allow discovering large portions of locally Pareto optimal vectors, which turns out to strongly support diversification. In this paper, we provide a survey on continuation techniques in global optimization methods for MO, which allow discovering large portions of locally Pareto-optimal solutions. We also propose a rigorous active set management strategy on top of a previously proposed certified continuation method based on interval analysis, and illustrate it on a challenging bi-objective problem.

Domaines: Recherche opérationnelle [math.OC]

Benjamin Martin, Alexandre Goldsztejn, Laurent Granvilliers, Christophe Jermann. On Continuation Methods for Non-Linear Bi-Objective Optimization: Certified Interval-Based Approach. 2013. ⟨hal-00878729⟩