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A trajectory-based method for mixed integer nonlinear programming problems

Author

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  • Terry-Leigh Oliphant

    (School of Computer Science and Applied Mathematics
    University of the Witwatersrand)

  • M. Montaz Ali

    (School of Computer Science and Applied Mathematics
    Faculty of Engineering and Built Environment
    University of the Witwatersrand)

Abstract

A local trajectory-based method for solving mixed integer nonlinear programming problems is proposed. The method is based on the trajectory-based method for continuous optimization problems. The method has three phases, each of which performs continuous minimizations via the solution of systems of differential equations. A number of novel contributions, such as an adaptive step size strategy for numerical integration and a strategy for updating the penalty parameter, are introduced. We have shown that the optimal value obtained by the proposed method is at least as good as the minimizer predicted by a recent definition of a mixed integer local minimizer. Computational results are presented, showing the effectiveness of the method.

Suggested Citation

  • Terry-Leigh Oliphant & M. Montaz Ali, 2018. "A trajectory-based method for mixed integer nonlinear programming problems," Journal of Global Optimization, Springer, vol. 70(3), pages 601-623, March.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:3:d:10.1007_s10898-017-0570-5
    DOI: 10.1007/s10898-017-0570-5
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    References listed on IDEAS

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