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A successful application of the interactive multiobjective optimization method NIMBUS to a design problem in papermaking technology is described. Namely, an optimal shape design problem related to the paper machine headbox is studied. First, the NIMBUS method, the numerical headbox model, and the associated multiobjective optimization problem are described. Then, the results of numerical experiments are presented.

A non-smooth biobjective optimization problem for designing the shape of a slice channel in a paper machine headbox is described. The conflicting goals defining the optimization problem are the ones determining important quality properties of produced paper: 1) basis weight should be even and 2) the wood fibers of paper should mainly be oriented to the machine direction across the width of the whole paper machine. The novelty of the considered approach is that maximum deviations are used instead of least squares when objective functions are formed. For the solution of this problem, a multiobjective genetic algorithm based on nondominated sorting is considered. The numerical results demonstrate the ability to obtain a large set of nondominated designs.

A shape optimization problem for incompressible flows within a stabilized finite element framework is studied. The goal is to develop and test numerical realizations of optimal shape design problems that could be applied to non-trivial industrial problems. The resulting algorithm is applied to the optimization of the geometry of a tapered header in a paper machine headbox. Copyright © 2000 John Wiley & Sons, Ltd.