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Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (2): 423-435.doi: 10.23919/JSEE.2024.000064

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  • 收稿日期:2022-08-16 出版日期:2025-04-18 发布日期:2025-05-20

Multi-objective optimization framework in the modeling of belief rule-based systems with interpretability-accuracy trade-off

Yaqian YOU(), Jianbin SUN(), Yuejin TAN(), Jiang JIANG()   

  • Received:2022-08-16 Online:2025-04-18 Published:2025-05-20
  • Contact: Jianbin SUN E-mail:youyaqian13@nudt.edu.cn;sunjianbin@nudt.edu.cn;yjtan@nudt.edu.cn;jiangjiangnudt@nudt.edu.cn
  • About author:
    YOU Yaqian was born in 1994. She received her B.E. degree in management engineering, M.E. and Ph. D degrees in management science and engineering from National University of Defense Technology, China, in 2017, 2019 and 2023, respectively. She is currently a lecturer at College of Information and Communication, National University of Defense Technology. Her research interests include the decision analysis under uncertainty and evidential reasoning. E-mail: youyaqian13@nudt.edu.cn

    SUN Jianbin was born in 1989. He received his B.E. degree in management engineering, M.E. and Ph.D. degrees in management science and engineering from National University of Defense Technology, Changsha, Hunan, China, in 2012, 2014 and 2018, respectively. He is currently an associate professor of management science and engineering at National University of Defense Technology. He was a visiting scholar with the Lab for Information Retrieval and Knowledge Management, School of Information Technology, York University, Toronto, ON, Canada. His research interests include system of-systems engineering management, and decision analysis under uncertainty. E-mail: sunjianbin@nudt.edu.cn

    TAN Yuejin was born in 1958. He received his B.S. degree from the Department of Mathematics, Hunan Normal University, M.S. degree from the Department of Systems Engineering and Mathematics, National University of Defense Technology, China, in 1981 and 1985, respectively. He is currently a professor of management science and engineering at National University of Defense Technology. He was a visiting scholar at Complex Systems Management Centre, Cranfield University from 1993 to 1994. His research interests include modeling and evaluation technologies of system of systems and complex systems engineering management. E-mail: yjtan@nudt.edu.cn

    JIANG Jiang was born in 1981. He received his B.E. degree in systems engineering, M.E. and Ph.D. degrees in management science and engineering from National University of Defense Technology, Changsha, Hunan, China, in 2004, 2006, and 2011, respectively. He is currently an associate professor of management science and engineering at National University of Defense Technology. He was a visiting scholar at the Harvard University, Boston, MA, USA from 2018 to 2019. His research interests include evidential reasoning, uncertainty decision-making, and risk analysis. E-mail: jiangjiangnudt@nudt.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (71901212) and the Science and Technology Innovation Program of Hunan Province (2020RC4046).

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Abstract:

The belief rule-based (BRB) system has been popular in complexity system modeling due to its good interpretability. However, the current mainstream optimization methods of the BRB systems only focus on modeling accuracy but ignore the interpretability. The single-objective optimization strategy has been applied in the interpretability-accuracy trade-off by integrating accuracy and interpretability into an optimization objective. But the integration has a greater impact on optimization results with strong subjectivity. Thus, a multi-objective optimization framework in the modeling of BRB systems with interpretability-accuracy trade-off is proposed in this paper. Firstly, complexity and accuracy are taken as two independent optimization goals, and uniformity as a constraint to give the mathematical description. Secondly, a classical multi-objective optimization algorithm, nondominated sorting genetic algorithm II (NSGA-II), is utilized as an optimization tool to give a set of BRB systems with different accuracy and complexity. Finally, a pipeline leakage detection case is studied to verify the feasibility and effectiveness of the developed multi-objective optimization. The comparison illustrates that the proposed multi-objective optimization framework can effectively avoid the subjectivity of single-objective optimization, and has capability of joint optimizing the structure and parameters of BRB systems with interpretability-accuracy trade-off.

Key words: belief rule-based (BRB) systems, interpretability, multi-objective optimization, nondominated sorting genetic algorithm II (NSGA-II), pipeline leakage detection

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