Local Pareto approximation for multi-objective optimization

Sergei Utyuzhnikov, Jeremy Maginot, Marin Guenov

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

The design process of complex systems often resorts to solving an optimization problem, which involves different disciplines and where all design criteria have to be optimized simultaneously. Mathematically, this problem can be reduced to a vector optimization problem. The solution of this problem is not unique and is represented by a Pareto surface in the objective function space. Once a Pareto solution is obtained, it may be very useful for the decision-maker to be able to perform a quick local approximation in the vicinity of this Pareto solution for sensitivity analysis. In this article, new linear and quadratic local approximations of the Pareto surface are derived and compared to existing formulas. The case of non-differentiable Pareto points (solutions) in the objective space is also analysed. The concept of a local quick Pareto analyser based on local sensitivity analysis is proposed. This Pareto analysis provides a quantitative insight into the relation between variations of the different objective functions under constraints. A few examples are considered to illustrate the concept and its advantages.

Original languageEnglish
Pages (from-to)821-847
Number of pages27
JournalEngineering Optimization
Volume40
Issue number9
DOIs
Publication statusPublished - Sep 2008
Externally publishedYes

Keywords

  • Approximation
  • Decision-making
  • Multi-objective optimization
  • Pareto surface
  • Sensitivity analysis

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