Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

A numerical approach to robust in-line control of roll forming processes

The quality of roll formed products is known to be highly sensitive and dependent on the process parameters and thus the unavoidable variations of these parameters during mass production. To maintain a constant high product quality, a new roll former with an adjustable final roll forming stand is developed at Deakin University enabling the continuous compensation for possible shape defects. In this work, a numerical approach to robust in-line control of the roll forming of a V-section profile is presented, combining the aspects of robust process design and in-line compensation methods. A numerical study is performed to determine the relationship between controllable process settings and uncontrollable variation of incoming material properties with respect to the common product defects longitudinal bow and springback. The computationally expensive non-linear FE simulations used in this study are subsequently replaced by metamod-els based on efficient Single Response Surfaces. Using these metamodels, the optimal setting for the adjustable stand is determined with robust optimization techniques and the effect on product quality analyzed. It is shown that the subsequent adjustment of the final roll stand position leads to a significantly improved product quality by preventing product defects and minimizing the deteriorating effects of scattering variables

Robust optimization based energy dispatch in smart grids considering demand uncertainty

In this study we discuss the application of robust optimization to the problem of economic energy dispatch in smart grids. Robust optimization based MPC strategies for tackling uncertain load demands are developed. Unexpected additive disturbances are modelled by defining an affine dependence between the control inputs and the uncertain load demands. The developed strategies were applied to a hybrid power system connected to an electrical power grid. Furthermore, to demonstrate the superiority of the standard Economic MPC over the MPC tracking, a comparison (e.g average daily cost) between the standard MPC tracking, the standard Economic MPC, and the integration of both in one-layer and two-layer approaches was carried out. The goal of this research is to design a controller based on Economic MPC strategies, that tackles uncertainties, in order to minimise economic costs and guarantee service reliability of the system.Postprint (author's final draft