Efficient Robust Optimization of Metal Forming Processes using a Sequential Metamodel Based Strategy

The coupling of Finite Element (FE) simulations to mathematical optimization techniques has contributed significantly to product improvements and cost reductions in the metal forming industries. The next challenge is to bridge the gap between deterministic optimization techniques and the industrial need for robustness. This paper introduces a new and generally applicable structured methodology for modeling and solving robust optimization problems. Stochastic design variables or noise variables are taken into account explicitly in the optimization procedure. The metamodel-based strategy is combined with a sequential improvement algorithm to efficiently increase the accuracy of the objective function prediction. This is only done at regions of interest containing the optimal robust design. Application of the methodology to an industrial V-bending process resulted in valuable process insights and an improved robust process design. Moreover, a significant improvement of the robustness (> 2s ) was obtained by minimizing the deteriorating effects of several noise variables. The robust optimization results demonstrate the general applicability of the robust optimization strategy and underline the importance of including uncertainty and robustness explicitly in the numerical optimization procedure

Data-Driven Robust Optimization

The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee. \edit{We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queuing confirm that our data-driven sets significantly outperform traditional robust optimization techniques whenever data is available.Comment: 38 pages, 15 page appendix, 7 figures. This version updated as of Oct. 201

Relative Robust Portfolio Optimization

Considering mean-variance portfolio problems with uncertain model parameters, we contrast the classical absolute robust optimization approach with the relative robust approach based on a maximum regret function. Although the latter problems are NP-hard in general, we show that tractable inner and outer approximations exist in several cases that are of central interest in asset management

A Powerful Optimization Tool for Analog Integrated Circuits Design

This paper presents a new optimization tool for analog circuit design. Proposed tool is based on the robust version of the differential evolution optimization method. Corners of technology, temperature, voltage and current supplies are taken into account during the optimization. That ensures robust resulting circuits. Those circuits usually do not need any schematic change and are ready for the layout.. The newly developed tool is implemented directly to the Cadence design environment to achieve very short setup time of the optimization task. The design automation procedure was enhanced by optimization watchdog feature. It was created to control optimization progress and moreover to reduce the search space to produce better design in shorter time. The optimization algorithm presented in this paper was successfully tested on several design examples

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