Optimal Control of Continuous Casting by Nondifferentiable Multiobjective Optimization

  • Authors:

  • Kaisa Miettinen;Marko M. Mäkelä;Timo Männikkö

  • Affiliations:

  • Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland. E-mail: Email: miettine@math.jyu.fi;Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland. E-mail: Email: makela@math.jyu.fi;Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland. E-mail: Email: mannikko@math.jyu.fi

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 1998

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Abstract

A new version of an interactive NIMBUS method for nondifferentiablemultiobjective optimization is described. It is based on the referencepoint idea and the classification of the objective functions. The originalproblem is transformed into a single objective form according to theclassification information. NIMBUS has been designed especially to be able to handle complicated real-life problems in a user-friendlyway.The NIMBUS method is used for solving an optimal control problemrelated to the continuous casting of steel. The main goal is to minimize thedefects in the final product. Conflicting objective functions areconstructed according to certain metallurgical criteria and some technologicalconstraints. Due to the phase changes during the cooling process thereexist discontinuities in the derivative of the temperaturedistribution. Thus, the problem is nondifferentiable.Like many real-life problems, the casting model is large and complicatedand numerically demanding. NIMBUS provides an efficient way of handlingthe difficulties and, at the same time, aids the user in finding asatisficing solution. In the end, some numerical experiments are reportedand compared with earlier results.