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An Optimality Theory Based Proximity Measure for Evolutionary Multi-Objective and Many-Objective Optimization

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Evolutionary Multi-Criterion Optimization (EMO 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9019))

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Abstract

Evolutionary multi- and many-objective optimization (EMO) methods attempt to find a set of Pareto-optimal solutions, instead of a single optimal solution. To evaluate these algorithms, performance metrics either require the knowledge of the true Pareto-optimal solutions or, are ad-hoc and heuristic based. In this paper, we suggest a KKT proximity measure (KKTPM) that can provide an estimate of the proximity of a set of trade-off solutions from the true Pareto-optimal solutions. Besides theoretical results, the proposed KKT proximity measure is computed for iteration-wise trade-off solutions obtained from specific EMO algorithms on two, three, five and 10-objective optimization problems. Results amply indicate the usefulness of the proposed KKTPM as a termination criterion for an EMO algorithm.

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Author information

Authors and Affiliations

  1. Computational Optimization and Innovation (COIN) Laboratory, Michigan State University, East Lansing, MI, 48824, USA

    Kalyanmoy Deb & Mohamed Abouhawwash

  2. Department of Humanities and Social Sciences, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    Joydeep Dutta

Authors
  1. Kalyanmoy Deb
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  2. Mohamed Abouhawwash
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  3. Joydeep Dutta
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Corresponding author

Correspondence to Kalyanmoy Deb .

Editor information

Editors and Affiliations

  1. Institute for Polymers and Composites/I3N University of Minho Guimarães Portugal, Guimaraes, Portugal

    António Gaspar-Cunha

  2. Dept. of Electrical and Computer Engg, University of Coimbra, Coimbra, Portugal

    Carlos Henggeler Antunes

  3. CINVESTAV-IPN Depto. de Computacíon, Col. San Pedro Zacatenco, México DF, Mexico

    Carlos Coello Coello

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Deb, K., Abouhawwash, M., Dutta, J. (2015). An Optimality Theory Based Proximity Measure for Evolutionary Multi-Objective and Many-Objective Optimization. In: Gaspar-Cunha, A., Henggeler Antunes, C., Coello, C. (eds) Evolutionary Multi-Criterion Optimization. EMO 2015. Lecture Notes in Computer Science(), vol 9019. Springer, Cham. https://doi.org/10.1007/978-3-319-15892-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-15892-1_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15891-4

  • Online ISBN: 978-3-319-15892-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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