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Global optimization of non-convex piecewise linear regression splines

Author

Listed:
  • Nadia Martinez

    (American Airlines)

  • Hadis Anahideh

    (University of Texas at Arlington)

  • Jay M. Rosenberger

    (University of Texas at Arlington)

  • Diana Martinez

    (TMAC)

  • Victoria C. P. Chen

    (University of Texas at Arlington)

  • Bo Ping Wang

    (University of Texas at Arlington)

Abstract

Multivariate adaptive regression spline (MARS) is a statistical modeling method used to represent a complex system. More recently, a version of MARS was modified to be piecewise linear. This paper presents a mixed integer linear program, called MARSOPT, that optimizes a non-convex piecewise linear MARS model subject to constraints that include both linear regression models and piecewise linear MARS models. MARSOPT is customized for an automotive crash safety system design problem for a major US automaker and solved using branch and bound. The solutions from MARSOPT are compared with those from customized genetic algorithms.

Suggested Citation

  • Nadia Martinez & Hadis Anahideh & Jay M. Rosenberger & Diana Martinez & Victoria C. P. Chen & Bo Ping Wang, 2017. "Global optimization of non-convex piecewise linear regression splines," Journal of Global Optimization, Springer, vol. 68(3), pages 563-586, July.
    • Handle: RePEc:spr:jglopt:v:68:y:2017:i:3:d:10.1007_s10898-016-0494-5
    DOI: 10.1007/s10898-016-0494-5
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    References listed on IDEAS

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    1. Regis, Rommel G. & Shoemaker, Christine A., 2007. "Parallel radial basis function methods for the global optimization of expensive functions," European Journal of Operational Research, Elsevier, vol. 182(2), pages 514-535, October.
    2. Rommel G. Regis & Christine A. Shoemaker, 2007. "A Stochastic Radial Basis Function Method for the Global Optimization of Expensive Functions," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 497-509, November.
    3. Ahmet B. Keha & Ismael R. de Farias & George L. Nemhauser, 2006. "A Branch-and-Cut Algorithm Without Binary Variables for Nonconvex Piecewise Linear Optimization," Operations Research, INFORMS, vol. 54(5), pages 847-858, October.
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    Cited by:

    1. Bjarne Grimstad & Brage R. Knudsen, 2020. "Mathematical programming formulations for piecewise polynomial functions," Journal of Global Optimization, Springer, vol. 77(3), pages 455-486, July.

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