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Global optimization of non-convex piecewise linear regression splines

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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.

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Acknowledgements

This research was partially supported by National Science Foundation Award CMMI–1434401.

Author information

Authors and Affiliations

  1. American Airlines, 4333 Amon Carter Blvd., HDQ1 MD 5358, Fort Worth, TX, 76155-2664, USA

    Nadia Martinez

  2. Department of Industrial and Manufacturing Systems Engineering, University of Texas at Arlington, Arlington, TX, 76019, USA

    Hadis Anahideh, Jay M. Rosenberger & Victoria C. P. Chen

  3. TMAC, 202 E. Border St., Ste. 323, Arlington, TX, 76010, USA

    Diana Martinez

  4. Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX, 76019, USA

    Bo Ping Wang

Authors
  1. Nadia Martinez
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  2. Hadis Anahideh
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  3. Jay M. Rosenberger
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  4. Diana Martinez
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  5. Victoria C. P. Chen
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  6. Bo Ping Wang
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Corresponding author

Correspondence to Hadis Anahideh.

Appendices

Appendix 1

Table 9 displays the scaled and unscaled solutions found with MARSOPT using both the SLR model and the PL-MARS model for the objective function, while Table 10 reports the objective values and the output variables (left-hand sides of the constraints) for both solutions.

Table 9 Scaled and unscaled solutions obtained from MARSOPT using SLR model and PL-MARS model
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Table 10 Objective value and output values for the constraints
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Appendix 2

The unscaled solutions for Solutions 5, 14, and 15 found using MARSOPT and Solution 4 from Data Set 1 are displayed in Table 11.

Table 11 Unscaled solutions for selected points
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Martinez, N., Anahideh, H., Rosenberger, J.M. et al. Global optimization of non-convex piecewise linear regression splines. J Glob Optim 68, 563–586 (2017). https://doi.org/10.1007/s10898-016-0494-5

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  • DOI: https://doi.org/10.1007/s10898-016-0494-5

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