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Simulation-based optimization for industrial process lines is discussed in this paper. Our approach combines multidisciplinary modeling, modern sensitivity analysis methodology as well as multiobjective optimization by means of object-oriented software design principles. As a result, a simulation and optimization approach that can be extended and modified due to users’ needs can be developed. Our approach is illustrated by a real-world example from papermaking industry.

Multiobjective optimization methodology for the development of the papermaking process is considered. The aim is to find efficient and reliable solution procedures for the process line model consisting of sequential unit-process models; some of them based on physics, whereas others on experimental data. By the consequence of modeling procedures, nonphysical states or inherited from modeling data in statistical case, the unit-process models may suffer from undesired unreliability. To control the uncertainty resulting from the unit-process models, a new multiobjective optimization approach is introduced where both the papermaking targets as well as the uncertainty related unit-process models are simultaneously taken into account. We illustrate the solution process by numerical examples related to the quality of the produced paper.

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.

This volume contains major lectures given at ENUMATH 99, the 3rd European Conference on Numerical Mathematics and Advanced Applications. The ENUMATH conferences were established in 1995 to provide a forum for discussing topics in numerical mathematics. They convene leading experts and young scientists, with special emphasis on contributions from Europe. Results and trends are discussed in the analysis of numerical algorithms, as well as their application to challenging scientific and industrial problems. The topics of ENUMATH 99 included finite element methods, "a posteriori" error control and adaptive mesh design, non-matching grids, least-squares methods for partial differential equations, boundary element methods and optimization in partial differential equations. Apart from theoretical aspects, a major part of the conference was devoted to numerical methods in interdisciplinary applications such as problems in computational fluid, electrodynamics, and telecommunications software, as well as visualization.