Journal of Global Optimization

, Volume 68, Issue 3, pp 563–586 | Cite as

Global optimization of non-convex piecewise linear regression splines

  • Nadia Martinez
  • Hadis Anahideh
  • Jay M. Rosenberger
  • Diana Martinez
  • Victoria C. P. Chen
  • Bo Ping Wang


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.


Global optimization Branch and bound Surrogate methods Multivariate adaptive regression splines Crashworthiness Genetic algorithms 



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


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.American AirlinesFort WorthUSA
  2. 2.Department of Industrial and Manufacturing Systems EngineeringUniversity of Texas at ArlingtonArlingtonUSA
  3. 3.TMACArlingtonUSA
  4. 4.Department of Mechanical and Aerospace EngineeringUniversity of Texas at ArlingtonArlingtonUSA

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