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Average Cuboid Volume as a Convergence Indicator and Selection Criterion for Multi-objective Biochemical Optimization

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EVOLVE – A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation VII

Part of the book series: Studies in Computational Intelligence ((SCI,volume 662))

Abstract

The performance of a multi-objective evolutionary algorithm (MOEA) is evaluated with regard to the quality of the populations under two aspects: the distance of the non-dominated set of a population to the true Pareto front (\(PF_{true}\)) and the spread among these solutions. Diverse convergence indicators have been proposed in the past with different requirements: either \(PF_{true}\) or a reference set of Pareto-optimal solutions is required. Furthermore, most of the convergence indicators are restricted to a non-dominated solution set, and therefore, the quality of the entire population is only represented by the non-dominated solutions. This work presents a statistically reasonable convergence indicator that is able to reflect the quality of the entire population. The average cuboid volume (ACV) assigns desirable aspects regarding the classification of entire populations. These preferable features are demonstrated and discussed. Furthermore, ACV is used as selection criterion to determine the solutions of the succeeding generation in a proposed customized NSGA-II for biochemical optimization. Two selection strategies based on the ACV indicator are proposed and empirically compared to a Pareto rank-based selection strategy. These selection strategies depend on two parameters and the adaption of the selection pressure by a variation of these parameters is empirically investigated on a three-dimensional biochemical minimization problem.

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Authors and Affiliations

  1. University of Applied Sciences, FHDW, Hauptstr. 2, 51465, Bergisch Gladbach, Germany

    Susanne Rosenthal & Markus Borschbach

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  1. Susanne Rosenthal
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  2. Markus Borschbach
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Correspondence to Susanne Rosenthal .

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Editors and Affiliations

  1. Leiden Institute of Advanced Com. Sci., Leiden University Leiden Institute of Advanced Com. Sci., CA Leiden, The Netherlands

    Michael Emmerich

  2. Leiden Institute of Advanced Com. Sci., Leiden University Leiden Institute of Advanced Com. Sci., CA Leiden, The Netherlands

    André Deutz

  3. Depto. de Ingeniería Eléctrica, CINVESTAV-IPN Depto. de Ingeniería Eléctrica, México, D.F., Mexico

    Oliver Schütze

  4. University of Bordeaux, Université Bordeaux Victoire , Bordeaux Cedex, France

    Pierrick Legrand

  5. Luxembourg Centre for Systems Biomedicin, University of Luxembourg Luxembourg Centre for Systems Biomedicin, Belval, Luxembourg

    Emilia Tantar

  6. Computer Science & Comm. Research Unit, University of Luxembourg Computer Science & Comm. Research Unit, Luxembourg, Luxembourg

    Alexandru-Adrian Tantar

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Rosenthal, S., Borschbach, M. (2017). Average Cuboid Volume as a Convergence Indicator and Selection Criterion for Multi-objective Biochemical Optimization. In: Emmerich, M., Deutz, A., Schütze, O., Legrand, P., Tantar, E., Tantar, AA. (eds) EVOLVE – A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation VII. Studies in Computational Intelligence, vol 662. Springer, Cham. https://doi.org/10.1007/978-3-319-49325-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-49325-1_9

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  • Online ISBN: 978-3-319-49325-1

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