On the use of metamodel-assisted, multi-objective evolutionary algorithms

Abstract

This article is concerned with the optimal use of metamodels in the context of multi-objective evolutionary algorithms which are based on computationally expensive function evaluations. The goal is to capture Pareto fronts of optimal solutions with the minimum computational cost. In each generation during the evolution, the metamodels act as filters that distinguish the most promising individuals, which will solely undergo exact and costly evaluations. By means of the so-called inexact pre-evaluation phase, based on continuously updated local metamodels, most of the non-promising individuals are put aside without aggravating the overall cost. The gain achieved through this technique is amazing in single-objective problems. However, with more than one objective, noticeable performance degradation occurs. This article scrutinizes the role of metamodels in multi-objective evolutionary algorithms and proposes ways to overcome expected weaknesses and improve their performance. Minimization of mathematical functions as well as aerodynamic shape optimization problems are used for demonstration purposes.

Keywords:

• Evolutionary algorithms
• Metamodels
• Multi-objective optimization
• Pareto front
• Radial-basis function networks
• Self-organizing maps

Acknowledgements

This research was sponsored by Dassault Aviation with Prof. J. Périaux, Pôle Scientifique Dassault Aviation/UPMC, as Project Monitor. The first author was supported by an A.S. Onassis Public Benefit Foundation Scholarship.