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Noisy Multiobjective Optimization on a Budget of 250 Evaluations

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Part of the book series:Lecture Notes in Computer Science ((LNTCS,volume 5467))

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Abstract

We consider methods for noisy multiobjective optimization, specifically methods for approximating a true underlying Pareto front when function evaluations are corrupted by Gaussian measurement noise on the objective function values. We focus on the scenario of a limited budget of function evaluations (100 and 250), where previously it was found that an iterative optimization method — ParEGO — based on surrogate modeling of the multiobjective fitness landscape was very effective in the non-noisy case. Our investigation here measures how ParEGO degrades with increasing noise levels. Meanwhile we introduce a new method that we propose for limited-budget and noisy scenarios: TOMO, deriving from the single-objective PB1 algorithm, which iteratively seeks the basins of optima using nonparametric statistical testing over previously visited points. We find ParEGO tends to outperform TOMO, and both (but especially ParEGO), are quite robust to noise. TOMO is comparable and perhaps edges ParEGO in the case of budgets of 100 evaluations with low noise. Both usually beat our suite of five baseline comparisons.

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Manchester, UK

    Joshua Knowles

  2. School of Mathematics and Computer Science, Heriot-Watt University, UK

    David Corne & Alan Reynolds

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  1. Joshua Knowles

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  2. David Corne

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  3. Alan Reynolds

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Editor information

Editors and Affiliations

  1. Department of Engineering Science, The University of Auckland, 70 Symonds Street, Room 415, 1001, Auckland, New Zealand

    Matthias Ehrgott

  2. Faculty of Science and Technolgoy, Department of Electronic Engineering and Informatics, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

    Carlos M. Fonseca

  3. Laboratoire d’ Informatique de Nantes -LINA, UMR CNRS 6241, Université de Nantes, 2, Rue de la Houssinière, BP 92208, 44322, Nantes Cedex 03, France

    Xavier Gandibleux

  4. LERIA, Faculty of Sciences, Université d’Angers, 2 Boulevard Lavoisier, 49045, Angers Cedex 01, France

    Jin-Kao Hao

  5. Université de Bretagne-sud - UEB CNRS, UMR 3192 - Lab-STICC, Centre de Recherche,, BP 92116, 56321, Lorient Cedex, France

    Marc Sevaux

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© 2009 Springer-Verlag Berlin Heidelberg

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Knowles, J., Corne, D., Reynolds, A. (2009). Noisy Multiobjective Optimization on a Budget of 250 Evaluations. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, JK., Sevaux, M. (eds) Evolutionary Multi-Criterion Optimization. EMO 2009. Lecture Notes in Computer Science, vol 5467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01020-0_8

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