Elina Madetoja

Visualizing multi-dimensional pareto-optimal fronts with a 3D virtual reality system

In multiobjective optimization, there are several targets that are in conflict, and thus they all cannot reach their optimum simultaneously. Hence, the solutions of the problem form a set of compromised trade-off solutions (a Pareto-optimal front or Pareto-optimal solutions) from which the best solution for the particular problem can be chosen. However, finding that best compromise solution is not an easy task for the human mind. Pareto-optimal fronts are often visualized for this purpose because in this way a comparison between solutions according to their location on the Pareto-optimal front becomes somewhat easier. Visualizing a Pareto-optimal front is straightforward when there are only two targets (or objective functions), but visualizing a front for more than two objective functions becomes a difficult task. In this paper, we introduce a new and innovative method of using three-dimensional virtual reality (VR) facilities to present multi-dimensional Pareto-optimal fronts. Rotation, zooming and other navigation possibilities of VR facilities make easy to compare different trade-off solutions, and fewer solutions need to be explored in order to understand the interrelationships among conflicting objective functions. In addition, it can be used to highlight and characterize interesting features of specific Pareto-optimal solutions, such as whether a particular solution is close to a constraint boundary or whether a solution lies on a relatively steep trade-off region. Based on these additional visual aids for analyzing trade-off solutions, a preferred compromise solution may be easier to choose than by other means.

Issues related to the computer realization of a multidisciplinary and multiobjective optimization system

Issues and novel ideas to be considered when developing computer realizations of complex multidisciplinary and multiobjective optimization systems are introduced. The aim is to discuss computer realizations that make possible both computationally efficient multidisciplinary analysis and multiobjective optimization of real world problems. We introduce software tools that make typically very time-consuming simulation processes more effective and, thus, enable even interactive multiobjective optimization with a real decision maker. In this paper, we first define a multidisciplinary and multiobjective optimization system and after that present an implementation overview of such problems including basic components participating in the solution process. Furthermore, interfaces and data flows between the components are described. A couple of important features related to the implementation are discussed in detail, for example, the usage of automatic differentiation. Finally, the ideas presented are illustrated with an industrial multiobjective optimization problem, when we describe numerical experiments related to quality properties in paper making.

A decision support system for paper making based on simulation and optimization

In this paper a model-driven decision support system related to paper making is introduced. The intention is to emphasize the necessity of coupling different modeling techniques, multiobjective optimization, and software engineering in order to make the end user application realistic, practical and usable. Firstly the paper making process and selected aspects concerning its mathematical modeling, numerical simulation, and multiobjective optimization are introduced, then the related computerized system, called a virtual paper making line, is described. In addition, the associated decision support system, which provides a suitable level of automation to improve the quality of decision making and support the user’s expertise is discussed. Finally, an example presents different ways of using such a software tool.

CFD-based Optimization for a Complete Industrial Process: Papermaking

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.