Two-stage distributionally robust optimization for joint system design and maintenance scheduling in high-consequence systems

Abstract

The failures of high-consequence systems can cause serious harm to humans, including loss of human health, life security, finance, and even social chaos. To protect high-consequence systems, both optimal system design and maintenance activities contribute to improving system reliability and social safety. The existing works generally optimize these two problems sequentially and assume that the degradation process of components is precisely known. However, sequential optimization often results in significant losses due to redundancies, and such a presumption usually cannot be guaranteed in practice, due to limited historical data or a lack of expert knowledge, referred to as epistemic uncertainty. To fill this gap, in this article, we consider an integrated optimization of system design and maintenance scheduling for multi-state high-consequence systems in which the component’s degradation is known with limited distributional information. To address this issue, we utilize the framework of distributionally robust optimization to provide a risk-averse decision to decision-makers even under the worst realizations of random parameters, and develop a two-stage integer distributionally robust model with moment-based ambiguity set to determine the system design and maintenance scheduling simultaneously. The proposed model can be converted to a tractable approximation as an integer linear stochastic programming problem. In order to solve large-scale problems, we develop a sample-based adaptive large neighborhood search algorithm to find the optimal system designs. In the numerical experiments, we present a case study on feedwater heating systems in nuclear power plants and demonstrate that an integrated optimization consideration creates significant benefits in profitability. We also present the out-of-sample performance of the distributionally robust design to avoid extreme risk.

Keywords:

• Reliability optimization
• condition-based maintenance
• preventive maintenance
• uncertainty
• stochastic programming
• distributionally robust optimization

Notes

1 It should be noted that this assumption can be extended to multiple types, and thus the decision is to determine the selection of component types and number of redundant components.

Additional information

Funding

This research is supported by the National Natural Science Foundation of China (71731008 and 71971181) and by Research Grant Council of Hong Kong (11203519 and 11200621). It is also funded by Hong Kong Innovation and Technology Commission (InnoHK Project CIMDA) and the International Science and Technology Cooperation Program of Guangdong Province (Project #2022A0505050047).

Notes on contributors

Hanxiao Zhang

Hanxiao Zhang received her PhD degree in Industrial Engineering from Tsinghua University, and her bachelor’s degree of science in mathematics and applied mathematics from Wuhan University. Since 2022, she has been working as a postdoc fellow at Department of Systems Engineering in City University of Hong Kong and Centre for Intelligent Multidimensional Data Analysis. Her research interests lie on the reliability optimization, maintenance problems and robust optimization.

Yan-Fu Li

Yan-Fu Li is currently the Director of the Institute for Quality & Reliability and a full professor at the Department of Industrial Engineering in Tsinghua University, China. From 2011 to 2016, he was a faculty member at CentraleSupélec in Université Paris-Saclay, France. His research areas mainly include system reliability and PHM with the applications onto railway systems, telecom systems, etc. Dr. Li has published more than 120 research papers, including more than 90 peer-reviewed high-quality international journal papers, the representative ones appear on “IEEE Transactions” series and UTD-24 journals. He is elected as the Highly Cited Chinese Researcher 2019-2022 by Elsevier and Top 2% Scientists Worldwide 2022 by Stanford University. He and his students have won multiple national society and international society search awards. He is currently an Associate Editor of IEEE Transactions on Reliability, a senior member of IEEE and IISE.

Min Xie

Min Xie received a PhD degree in quality technology from Linkoping University, Linkoping, Sweden, in 1987. He is currently a Chair Professor in Department of Systems Engineering, City University of Hong Kong, Kowloon, Hong Kong. He has authored or coauthored about 300 peer-reviewed journal papers and eight books on quality and reliability engineering. His research interests include reliability engineering, quality management, software reliability, and applied statistics. Prof. Xie was elected as a member of the European Academy of Sciences and Arts in 2022. He was the recipient of the prestigious Lee Kuan Yew (LKY) Research Fellowship in 1991. He has chaired many international conferences and given keynote speeches. He also serves as an editor and associate editor and on the editorial board of many established international journals.

Chen Zhang

Chen Zhang is currently a PhD student in the Department of Industrial Engineering at Tsinghua University. She received the BE degree in Industrial Engineering from Tsinghua University in 2019. Her current research interests include maintenance optimization, network optimization and stochastic optimization.