Search

In this article, a bi-level optimization problem covering upper (design) and lower (operation) levels is defined and a solution procedure for bi-level optimization problems is presented. This is devised as a dynamic multiobjective optimization problem, i.e. the values of the control and state variables change over a predefined time horizon and several competing criteria are optimized simultaneously. Moreover, the interaction between the upper and lower levels is analysed. The benefits of bi-level dynamic multiobjective optimization are illustrated in detail by examining an industrial case in which the design of a paper mill (upper level) and the mill operation (lower level) are optimized at the same time. However, the problem definition and the solution procedure are not limited to any specific application but can be exploited in many different industrial areas.

Dynamic modeling and simulation software can be used to simulate the industrial processes such as papermaking in order to improve the efficiency of the process. A dynamic simulation model can be combined with an optimization method to maximize the advantages which simulation tools can offer. In this paper, we combine dynamic process simulation and optimization to see how it can benefit a papermaking process which was envisaged to consist of a TMP mill, stock preparation, short circulation, a paper machine, and a reel. The aim is to increase the efficiency and minimize the costs involved in papermaking.

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.

In this paper, we study multidisciplinary optimization problems where the objective functions and the vector-valued mathematical models are not necessarily differentiable in a classical sense. Moreover, we assume that the state equation consists of several submodels, that is, unit-process models. This study is based on the nonsmooth analysis introduced by Clarke and the theory of H-differentiable functions by Gowda. It concentrates on two mathematical tools needed in sensitivity analysis of the multidisciplinary optimization problems, namely, the generalized chain rule for vector-valued functions and the implicit subdifferentiation formula. We employ these tools to obtain subgradient information of the problems considered. Finally, we present a numerical example and compare the obtained results with finite differences by means of accuracy and computational efficiency.

Development of tailored software tools based on coupling of Computational Fluid Dynamics (CFD) with optimization is presented in this paper. In papermaking, industrial applications deal with fluid dynamics at the wet-end of a paper machine as well as in the entire papermaking process.