Computational Optimization and Applications

, Volume 11, Issue 2, pp 177–194 | Cite as

Optimal Control of Continuous Casting by Nondifferentiable Multiobjective Optimization

  • Kaisa Miettinen
  • Marko M. Mäkelä
  • Timo Männikkö


A new version of an interactive NIMBUS method for nondifferentiable multiobjective optimization is described. It is based on the reference point idea and the classification of the objective functions. The original problem is transformed into a single objective form according to the classification information. NIMBUS has been designed especially to be able to handle complicated real-life problems in a user-friendly way.

The NIMBUS method is used for solving an optimal control problem related to the continuous casting of steel. The main goal is to minimize the defects in the final product. Conflicting objective functions are constructed according to certain metallurgical criteria and some technological constraints. Due to the phase changes during the cooling process there exist discontinuities in the derivative of the temperature distribution. Thus, the problem is nondifferentiable.

Like many real-life problems, the casting model is large and complicated and numerically demanding. NIMBUS provides an efficient way of handling the difficulties and, at the same time, aids the user in finding a satisficing solution. In the end, some numerical experiments are reported and compared with earlier results.

nonsmooth optimization multiple criteria optimization Stefan problems 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Kaisa Miettinen
    • 1
  • Marko M. Mäkelä
    • 1
  • Timo Männikkö
    • 1
  1. 1.Department of MathematicsUniversity of JyväskyläJyväskyläFinland

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