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Interval-based ranking in noisy evolutionary multi-objective optimization

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  • Hossein Karshenas
  • Concha Bielza
  • Pedro Larrañaga

Abstract

As one of the most competitive approaches to multi-objective optimization, evolutionary algorithms have been shown to obtain very good results for many real-world multi-objective problems. One of the issues that can affect the performance of these algorithms is the uncertainty in the quality of the solutions which is usually represented with the noise in the objective values. Therefore, handling noisy objectives in evolutionary multi-objective optimization algorithms becomes very important and is gaining more attention in recent years. In this paper we present $$\alpha $$ α -degree Pareto dominance relation for ordering the solutions in multi-objective optimization when the values of the objective functions are given as intervals. Based on this dominance relation, we propose an adaptation of the non-dominated sorting algorithm for ranking the solutions. This ranking method is then used in a standard multi-objective evolutionary algorithm and a recently proposed novel multi-objective estimation of distribution algorithm based on joint variable-objective probabilistic modeling, and applied to a set of multi-objective problems with different levels of independent noise. The experimental results show that the use of the proposed method for solution ranking allows to approximate Pareto sets which are considerably better than those obtained when using the dominance probability-based ranking method, which is one of the main methods for noise handling in multi-objective optimization. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Hossein Karshenas & Concha Bielza & Pedro Larrañaga, 2015. "Interval-based ranking in noisy evolutionary multi-objective optimization," Computational Optimization and Applications, Springer, vol. 61(2), pages 517-555, June.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:2:p:517-555
    DOI: 10.1007/s10589-014-9717-1
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    References listed on IDEAS

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    1. Syberfeldt, Anna & Ng, Amos & John, Robert I. & Moore, Philip, 2010. "Evolutionary optimisation of noisy multi-objective problems using confidence-based dynamic resampling," European Journal of Operational Research, Elsevier, vol. 204(3), pages 533-544, August.
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    Cited by:

    1. Ivan Contreras & Remei Calm & Miguel A. Sainz & Pau Herrero & Josep Vehi, 2021. "Combining Grammatical Evolution with Modal Interval Analysis: An Application to Solve Problems with Uncertainty," Mathematics, MDPI, vol. 9(6), pages 1-20, March.

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