IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v322y2025i2p599-614.html
   My bibliography  Save this article

Bi-objective ranking and selection using stochastic kriging

Author

Listed:
  • Rojas Gonzalez, Sebastian
  • Branke, Juergen
  • Van Nieuwenhuyse, Inneke

Abstract

We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto-optimal solutions among a finite set of candidates for which the objective function values have to be estimated from noisy evaluations. When identifying these solutions, the noise perturbing the observed performance may lead to two types of errors: solutions that are truly Pareto-optimal may appear to be dominated, and solutions that are truly dominated may appear to be Pareto-optimal. We propose a novel Bayesian bi-objective ranking and selection method that sequentially allocates extra samples to competitive solutions, in view of reducing the misclassification errors when identifying the solutions with the best expected performance. The approach uses stochastic kriging to build reliable predictive distributions of the objectives, and exploits this information to decide how to resample. The experiments are designed to evaluate the algorithm on several artificial and practical test problems. The proposed approach is observed to consistently outperform its competitors (a well-known state-of-the-art algorithm and the standard equal allocation method), which may also benefit from the use of stochastic kriging information.

Suggested Citation

  • Rojas Gonzalez, Sebastian & Branke, Juergen & Van Nieuwenhuyse, Inneke, 2025. "Bi-objective ranking and selection using stochastic kriging," European Journal of Operational Research, Elsevier, vol. 322(2), pages 599-614.
    • Handle: RePEc:eee:ejores:v:322:y:2025:i:2:p:599-614
    DOI: 10.1016/j.ejor.2024.11.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724008592
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2024.11.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jalali, Hamed & Van Nieuwenhuyse, Inneke & Picheny, Victor, 2017. "Comparison of Kriging-based algorithms for simulation optimization with heterogeneous noise," European Journal of Operational Research, Elsevier, vol. 261(1), pages 279-301.
    2. Angun, Ebru & Kleijnen, Jack, 2023. "Constrained optimization in Random Simulation : Efficient Global Optimization and Karush-Kuhn-Tucker Conditions (Revision of CentER DP 2022-022)," Other publications TiSEM ae1ec947-12e1-4bf7-89fb-7, Tilburg University, School of Economics and Management.
    3. Juergen Branke & Wen Zhang, 2019. "Identifying efficient solutions via simulation: myopic multi-objective budget allocation for the bi-objective case," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 831-865, September.
    4. Sridhar Bashyam & Michael C. Fu, 1998. "Optimization of (s, S) Inventory Systems with Random Lead Times and a Service Level Constraint," Management Science, INFORMS, vol. 44(12-Part-2), pages 243-256, December.
    5. Stephen E. Chick & Jürgen Branke & Christian Schmidt, 2010. "Sequential Sampling to Myopically Maximize the Expected Value of Information," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 71-80, February.
    6. Rojas Gonzalez, Sebastian & Jalali, Hamed & Van Nieuwenhuyse, Inneke, 2020. "A multiobjective stochastic simulation optimization algorithm," European Journal of Operational Research, Elsevier, vol. 284(1), pages 212-226.
    7. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    8. Justin Boesel & Barry L. Nelson & Seong-Hee Kim, 2003. "Using Ranking and Selection to “Clean Up” after Simulation Optimization," Operations Research, INFORMS, vol. 51(5), pages 814-825, October.
    9. Paul Feliot & Julien Bect & Emmanuel Vazquez, 2017. "A Bayesian approach to constrained single- and multi-objective optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 97-133, January.
    10. Xuefei Lu & Alessandro Rudi & Emanuele Borgonovo & Lorenzo Rosasco, 2020. "Faster Kriging: Facing High-Dimensional Simulators," Operations Research, INFORMS, vol. 68(1), pages 233-249, January.
    11. Weiwei Fan & L. Jeff Hong & Barry L. Nelson, 2016. "Indifference-Zone-Free Selection of the Best," Operations Research, INFORMS, vol. 64(6), pages 1499-1514, December.
    12. Loo Lee & Ek Chew & Suyan Teng & David Goldsman, 2010. "Finding the non-dominated Pareto set for multi-objective simulation models," IISE Transactions, Taylor & Francis Journals, vol. 42(9), pages 656-674.
    13. Teng, Suyan & Lee, Loo Hay & Chew, Ek Peng, 2010. "Integration of indifference-zone with multi-objective computing budget allocation," European Journal of Operational Research, Elsevier, vol. 203(2), pages 419-429, June.
    14. Binois, M. & Ginsbourger, D. & Roustant, O., 2015. "Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations," European Journal of Operational Research, Elsevier, vol. 243(2), pages 386-394.
    15. Kyle Cooper & Susan R. Hunter & Kalyani Nagaraj, 2020. "Biobjective Simulation Optimization on Integer Lattices Using the Epsilon-Constraint Method in a Retrospective Approximation Framework," INFORMS Journal on Computing, INFORMS, vol. 32(4), pages 1080-1100, October.
    16. Syberfeldt, Anna & Ng, Amos & John, Robert I. & Moore, Philip, 2010. "Evolutionary optimisation of noisy multi-objective problems using confidence-based dynamic resampling," European Journal of Operational Research, Elsevier, vol. 204(3), pages 533-544, August.
    17. Eric A. Applegate & Guy Feldman & Susan R. Hunter & Raghu Pasupathy, 2020. "Multi-objective ranking and selection: Optimal sampling laws and tractable approximations via SCORE," Journal of Simulation, Taylor & Francis Journals, vol. 14(1), pages 21-40, January.
    18. Peter I. Frazier, 2014. "A Fully Sequential Elimination Procedure for Indifference-Zone Ranking and Selection with Tight Bounds on Probability of Correct Selection," Operations Research, INFORMS, vol. 62(4), pages 926-942, August.
    19. Andradóttir, Sigrún & Lee, Judy S., 2021. "Pareto set estimation with guaranteed probability of correct selection," European Journal of Operational Research, Elsevier, vol. 292(1), pages 286-298.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rojas Gonzalez, Sebastian & Jalali, Hamed & Van Nieuwenhuyse, Inneke, 2020. "A multiobjective stochastic simulation optimization algorithm," European Journal of Operational Research, Elsevier, vol. 284(1), pages 212-226.
    2. Weiwei Fan & L. Jeff Hong & Xiaowei Zhang, 2020. "Distributionally Robust Selection of the Best," Management Science, INFORMS, vol. 66(1), pages 190-208, January.
    3. Dawei Zhan & Huanlai Xing, 2020. "Expected improvement for expensive optimization: a review," Journal of Global Optimization, Springer, vol. 78(3), pages 507-544, November.
    4. Zhong, Ying & Du, Jianzhong & Li, Deng-Feng & Hu, Zhaolin, 2025. "Reference alternatives based knockout-tournament procedure for ranking and selection," European Journal of Operational Research, Elsevier, vol. 320(3), pages 628-641.
    5. Daniel Russo, 2020. "Simple Bayesian Algorithms for Best-Arm Identification," Operations Research, INFORMS, vol. 68(6), pages 1625-1647, November.
    6. Songhao Wang & Szu Hui Ng & William Benjamin Haskell, 2022. "A Multilevel Simulation Optimization Approach for Quantile Functions," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 569-585, January.
    7. Xuefei Lu & Alessandro Rudi & Emanuele Borgonovo & Lorenzo Rosasco, 2020. "Faster Kriging: Facing High-Dimensional Simulators," Operations Research, INFORMS, vol. 68(1), pages 233-249, January.
    8. Haihui Shen & L. Jeff Hong & Xiaowei Zhang, 2021. "Ranking and Selection with Covariates for Personalized Decision Making," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1500-1519, October.
    9. Rodriguez, Sergio & Ludkovski, Michael, 2020. "Probabilistic bisection with spatial metamodels," European Journal of Operational Research, Elsevier, vol. 286(2), pages 588-603.
    10. Zilong Wang & Marianthi Ierapetritou, 2018. "Surrogate-based feasibility analysis for black-box stochastic simulations with heteroscedastic noise," Journal of Global Optimization, Springer, vol. 71(4), pages 957-985, August.
    11. Juergen Branke & Wen Zhang, 2019. "Identifying efficient solutions via simulation: myopic multi-objective budget allocation for the bi-objective case," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 831-865, September.
    12. Michael Macgregor Perry & Hadi El-Amine, 2021. "Computational Efficiency in Multivariate Adversarial Risk Analysis Models," Papers 2110.12572, arXiv.org.
    13. Tsai, Shing Chih & Chen, Sin Ting, 2017. "A simulation-based multi-objective optimization framework: A case study on inventory management," Omega, Elsevier, vol. 70(C), pages 148-159.
    14. Kleijnen, Jack P.C., 2013. "Simulation-Optimization via Kriging and Bootstrapping : A Survey (Revision of CentER DP 2011-064)," Other publications TiSEM 6ac4e049-ad86-447f-aeec-a, Tilburg University, School of Economics and Management.
    15. L. Jeff Hong & Guangxin Jiang & Ying Zhong, 2022. "Solving Large-Scale Fixed-Budget Ranking and Selection Problems," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 2930-2949, November.
    16. Pedrielli, Giulia & Wang, Songhao & Ng, Szu Hui, 2020. "An extended Two-Stage Sequential Optimization approach: Properties and performance," European Journal of Operational Research, Elsevier, vol. 287(3), pages 929-945.
    17. Michael Perry & Hadi El-Amine, 2019. "Computational Efficiency in Multivariate Adversarial Risk Analysis Models," Decision Analysis, INFORMS, vol. 16(4), pages 314-332, December.
    18. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204, arXiv.org, revised May 2018.
    19. Lee, Mi Lim & Park, Chuljin & Park, Dong Uk, 2018. "Self-adjusting the tolerance level in a fully sequential feasibility check procedure," European Journal of Operational Research, Elsevier, vol. 271(2), pages 733-745.
    20. Mattila, V. & Virtanen, K., 2015. "Ranking and selection for multiple performance measures using incomplete preference information," European Journal of Operational Research, Elsevier, vol. 242(2), pages 568-579.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:322:y:2025:i:2:p:599-614. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.