Robust dual-response optimization

ABSTRACT

This article presents a robust optimization reformulation of the dual-response problem developed in response surface methodology. The dual-response approach fits separate models for the mean and the variance and analyzes these two models in a mathematical optimization setting. We use metamodels estimated from experiments with both controllable and environmental inputs. These experiments may be performed with either real or simulated systems; we focus on simulation experiments. For the environmental inputs, classic approaches assume known means, variances, or covariances and sometimes even a known distribution. We, however, develop a method that uses only experimental data, so it does not need a known probability distribution. Moreover, our approach yields a solution that is robust against the ambiguity in the probability distribution. We also propose an adjustable robust optimization method that enables adjusting the values of the controllable factors after observing the values of the environmental factors. We illustrate our novel methods through several numerical examples, which demonstrate their effectiveness.

Keywords:

• Robust optimization
• dual-response optimization
• simulation optimization
• phi-divergence

Additional information

Notes on contributors

İhsan Yanıkoğlu

İhsan Yanıkoğlu is an Assistant Professor of Industrial Engineering at Özyeğin University, İstanbul, Turkey. He obtained his Ph.D. in Econometrics and Operations Research at Tilburg University in 2014. His research focuses on developing robust optimization methodologies and their applications in real-life problems. His research has been published in journals such as INFORMS Journal on Computing and OMEGA.

Dick den Hertog

Dick den Hertog is a Professor of Operations Research at Tilburg University. His research interests cover various fields in linear and nonlinear optimization; e.g., robust optimization and simulation-based optimization. He is also active in applying operations research theory in real-life applications. He obtained his Ph.D. degree in 1992 at Delft University of Technology. From 1992 to 1999 he worked as an OR consultant for CQM in Eindhoven. In 2000 he received the EURO Best Applied Paper Award, together with Peter Stehouwer (CQM). In 2013 he was a member of the team that received the INFORMS Franz Edelman Award. He has been an Associate Editor for Operations Research Letters and Journal of Industrial and Management Optimization and is currently an Associate Editor for both Management Science and Operations Research (area: optimization).

Jack P. C. Kleijnen

Jack P.C. Kleijnen is Emeritus Professor of Simulation and Information Systems at Tilburg University, where he is still an active member of both the Department of Management and the Operations Research Group of the Center for Economic Research (CentER) in the Tilburg School of Economics and Management. His research concerns the statistical design and analysis of experiments with simulation models in many scientific disciplines including management science, operations research, and engineering. He was a consultant for several organizations in the United States and Europe, and served on many international editorial boards and scientific committees. He also spent several years in the United States, at universities and private companies. He has received several awards; e.g., in 2008 he became a Knight in the Order of the Netherlands Lion and in 2005 he received the Lifetime Professional Achievement Award from the INFORMS Simulation Society.