# Approximating Pareto sets with Stochastic Search Algorithms

1 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
LIFL - Laboratoire d'Informatique Fondamentale de Lille, Inria Lille - Nord Europe
Abstract : Recent studies show the growing interest in the design of suitable archiving strategies for their use with evolutionary multi-objective optimization algorithms. So far, nearly all works deal with Pareto {\em front} approximations, that is, with archiving strategies which provide a certain approximation quality in the limit which is measured in the image space of the underlying model. However, there are as well cases where it is of great importance for the decision maker to have the knowledge about the entire Pareto {\em set}. Investigations in this field are scarce, and so far no theoretical investigation has been done. We propose and investigate a novel archiving strategy for the approximation of a superset of the Pareto set, which includes the set of all $\epsilon$-efficient points of a given multi-objective optimization problem defined in continuous space. For this, we propose the set of interest, investigate its topology and state a convergence result for a generic stochastic search algorithm toward this set of interest. Finally, we present some numerical results indicating the practicability of the novel approach.
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https://hal.inria.fr/inria-00157741
Contributor : Oliver Schuetze <>
Submitted on : Wednesday, June 27, 2007 - 12:50:38 AM
Last modification on : Thursday, May 28, 2020 - 9:22:09 AM
Long-term archiving on: : Thursday, April 8, 2010 - 6:28:21 PM

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• HAL Id : inria-00157741, version 1

### Citation

Oliver Schuetze, Carlos A. Coello Coello, El-Ghazali Talbi. Approximating Pareto sets with Stochastic Search Algorithms. 2007. ⟨inria-00157741v1⟩

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