A Penalty Approach for Nonlinear Optimization with Discrete Design Variables

  • Dong K. Shin
  • Z. Gurdal
  • O. H. GriffinJr.
Conference paper
Part of the Lecture Notes in Engineering book series (LNENG, volume 42)


A penalty approach for the solution of nonlinear discrete optimization problems is proposed. In general, the penalty approach is used for converting a constrained op-timization problem into a sequence of unconstrained problems. The objective function for the unconstrained problem at each step of the sequential optimization includes terms that introduce penalty depending on the degree of constraint violation. In addition to the penalty terms for constraint violation, the proposed approach intro-duces penalty terms to reflect the requirement that the design variables take discrete values. A variable magnitude penalty term in the form of a sine function is introduced and implemented with the extended interior penalty method of the optimization package NEWSUMT-A. The performance of the proposed method is investigated by several numer-ical examples.


Response Surface Design Variable Penalty Term Constraint Violation Discrete Optimization 
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Copyright information

© Springer-Verlag Berlin, Heidelberg 1989

Authors and Affiliations

  • Dong K. Shin
    • 1
  • Z. Gurdal
    • 1
  • O. H. GriffinJr.
    • 1
  1. 1.Department of Engineering Science and MechanicsVPI & SUBlacksburgUSA

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