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Related Experiment Videos

Global optimization with multivariate adaptive regression splines.

Scott Crino1, Donald E Brown

  • 1United States Military Academy at West Point, West Point, NY 10996, USA. scott.crino@us.army.mil

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|April 10, 2007
PubMed
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This study introduces a new method combining multivariate adaptive regression splines (MARS) and response surface methodology (RSM) for efficient structural design optimization. The novel MARS/RSM approach effectively handles complex, high-dimensional problems with reduced computational cost and improved accuracy.

Area of Science:

  • Structural Engineering
  • Computational Mechanics
  • Optimization Methods

Background:

  • Traditional response surface methodology (RSM) struggles with highly nonlinear, high-dimensional problems.
  • Existing methods like neural networks and generalized additive models can be computationally expensive and less interpretable.
  • Simulated annealing and genetic algorithms offer alternative optimization strategies but may differ in efficiency and accuracy.

Purpose of the Study:

  • To present a novel procedure for approximating the global optimum in structural design.
  • To combine the strengths of multivariate adaptive regression splines (MARS) and response surface methodology (RSM).
  • To address limitations of conventional RSM in handling complex, high-dimensional, and nonlinear problems.

Main Methods:

Related Experiment Videos

  • Utilizing multivariate adaptive regression splines (MARS) for its flexible regression and recursive partitioning capabilities.
  • Integrating MARS with response surface methodology (RSM) to create a hybrid MARS/RSM procedure.
  • Comparing the MARS/RSM approach against simulated annealing and genetic algorithms regarding computational efficiency and accuracy.

Main Results:

  • The MARS/RSM procedure demonstrates effectiveness in simplifying high-dimensional problems into accurate, lower-dimensional models.
  • The combined method offers improved interpretability and lower computational cost compared to neural networks and generalized additive models.
  • Application to low-dimensional test functions validates the convergence and limiting properties of the MARS/RSM procedure.

Conclusions:

  • The MARS/RSM procedure provides a computationally efficient and accurate method for approximating global optima in structural design.
  • This novel approach enhances conventional RSM by effectively managing high dimensionality and nonlinearity.
  • The MARS/RSM technique offers a competitive alternative to existing optimization algorithms for complex engineering problems.