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Efficient Constrained Optimization by the \(\varepsilon \) Constrained Differential Evolution with Rough Approximation

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Evolutionary Constrained Optimization

Part of the book series: Infosys Science Foundation Series ((ISFSASE))

Abstract

It has been proposed to utilize a rough approximation model, which is an approximation model with low accuracy and without learning process, to reduce the number of function evaluations in unconstrained optimization. Although the approximation errors between true function values and the approximation values estimated by the rough approximation model are not small, the rough model can estimate the order relation of two points with fair accuracy. The estimated comparison, which omits the function evaluations when the result of the comparison can be judged by the approximation values, proposed to use this nature of the rough model. In this chapter, a constrained optimization method is proposed by combining the \(\varepsilon \) constrained method and the estimated comparison, where rough approximation is used not only for an objective function but also for constraint violation. The proposed method is an efficient constrained optimization algorithm that can find near-optimal solutions in a small number of function evaluations. The advantage of the method is shown by solving well-known nonlinear constrained problems.

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Acknowledgments

This research is supported in part by Grant-in-Aid for Scientific Research (C) (No. 24500177, 26350443) of Japan society for the promotion of science and Hiroshima City University Grant for Special Academic Research (General Studies).

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Authors and Affiliations

  1. Hiroshima City University, 3-4-1 Ozuka-higashi, Asaminami-ku, Hiroshima, 731-3194, Japan

    Tetsuyuki Takahama

  2. Hiroshima Shudo University, 1-1-1 Ozuka-higashi, Asaminami-ku, Hiroshima, 731-3195, Japan

    Setsuko Sakai

Authors
  1. Tetsuyuki Takahama
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  2. Setsuko Sakai
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Correspondence to Tetsuyuki Takahama .

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Editors and Affiliations

  1. Dept of Electrical Engineering, Korea Advanced Institute of Sci &Tech, Daejeon, Korea, Republic of (South Korea)

    Rituparna Datta

  2. Electrical and Computer Engineering, Michigan State University, East Lansing, Michigan, USA

    Kalyanmoy Deb

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Takahama, T., Sakai, S. (2015). Efficient Constrained Optimization by the \(\varepsilon \) Constrained Differential Evolution with Rough Approximation. In: Datta, R., Deb, K. (eds) Evolutionary Constrained Optimization. Infosys Science Foundation Series(). Springer, New Delhi. https://doi.org/10.1007/978-81-322-2184-5_6

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  • DOI: https://doi.org/10.1007/978-81-322-2184-5_6

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-2183-8

  • Online ISBN: 978-81-322-2184-5

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