{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T02:02:26Z","timestamp":1772244146424,"version":"3.50.1"},"reference-count":45,"publisher":"ASME International","issue":"4","license":[{"start":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T00:00:00Z","timestamp":1737590400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.asme.org\/publications-submissions\/publishing-information\/legal-policies"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N000142212459"],"award-info":[{"award-number":["N000142212459"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["asmedigitalcollection.asme.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Many engineering design optimization problems are multi-objective, constrained, and contain uncertain parameters. For these problems, it is desirable to obtain solutions that are robustly optimum. A robust optimal solution is one which remains feasible and optimal despite perturbations in the uncertainty parameters. This article presents a scenario-generation-based method for solving multi-objective robust optimization (MORO) problems. The approach follows a sequential, single-level optimization problem workflow, with the uncertainty handled by a fixed sampling method. The proposed approach is applied to an unmanned surface vessel (USV) case study problem. The results obtained and subsequent performance analysis show that the proposed approach generally performs well.<\/jats:p>","DOI":"10.1115\/1.4067706","type":"journal-article","created":{"date-parts":[[2025,1,23]],"date-time":"2025-01-23T11:37:37Z","timestamp":1737632257000},"update-policy":"https:\/\/doi.org\/10.1115\/crossmarkpolicy-asme","source":"Crossref","is-referenced-by-count":0,"title":["On a Sampling-Based Method for Multi-Objective Robust Optimization"],"prefix":"10.1115","volume":"25","author":[{"given":"Elizabeth","family":"Jordan","sequence":"first","affiliation":[{"name":"University of Maryland Department of Mechanical Engineering, , , \u00a0","place":["College Park, MD, 20742"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arko","family":"Chatterjee","sequence":"additional","affiliation":[{"name":"University of Maryland Department of Mechanical Engineering, , , \u00a0","place":["College Park, MD, 20742"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruochen","family":"Yang","sequence":"additional","affiliation":[{"name":"University of Maryland Department of Mechanical Engineering, Center for Risk and Reliability, , , \u00a0","place":["College Park, MD, 20742"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katrina","family":"Groth","sequence":"additional","affiliation":[{"name":"University of Maryland Department of Mechanical Engineering, Center for Risk and Reliability, , , \u00a0","place":["College Park, MD, 20742"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shapour","family":"Azarm","sequence":"additional","affiliation":[{"name":"University of Maryland Department of Mechanical Engineering, , , \u00a0","place":["College Park, MD, 20742"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"33","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"key":"2026022720020676300_CIT0001","first-page":"1193","article-title":"Improving Multi-Objective Robust Optimization Under Interval Uncertainty Using Worst Possible Point Constraint Cuts","author":"Hu","year":"2009"},{"issue":"4","key":"2026022720020676300_CIT0002","doi-asserted-by":"publisher","first-page":"041012","DOI":"10.1115\/1.4040710","article-title":"Advanced Multi-Objective Robust Optimization Under Interval Uncertainty Using Kriging Model and Support Vector Machine","volume":"18","author":"Xie","year":"2018","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"issue":"2","key":"2026022720020676300_CIT0003","doi-asserted-by":"publisher","first-page":"580","DOI":"10.1108\/EC-09-2016-0320","article-title":"A Multi-objective Robust Optimization Approach for Engineering Design Under Interval Uncertainty","volume":"35","author":"Zhou","year":"2018","journal-title":"Eng. Comput."},{"issue":"2","key":"2026022720020676300_CIT0004","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1080\/09544828.2020.1858475","article-title":"An Improved Sequential Multi-Objective Robust Optimisation Approach Considering Interval Uncertainty Reduction Under Mixed Uncertainties","volume":"32","author":"Wei","year":"2021","journal-title":"J. Eng. Des."},{"issue":"2","key":"2026022720020676300_CIT0005","doi-asserted-by":"publisher","first-page":"021401","DOI":"10.1115\/1.4029026","article-title":"A New Hybrid Algorithm for Multi-objective Robust Optimization With Interval Uncertainty","volume":"137","author":"Cheng","year":"2015","journal-title":"ASME J. Mech. Des."},{"issue":"10","key":"2026022720020676300_CIT0006","doi-asserted-by":"publisher","first-page":"889","DOI":"10.1080\/03052150902853005","article-title":"Integrated Multi-Objective Robust Optimization and Sensitivity Analysis With Irreducible and Reducible Interval Uncertainty","volume":"41","author":"Li","year":"2009","journal-title":"Eng. Optim."},{"issue":"3","key":"2026022720020676300_CIT0007","doi-asserted-by":"publisher","first-page":"2094494","DOI":"10.1080\/23249935.2022.2094494","article-title":"Distributionally Robust Optimisation Model for Multi-Objective Hub Location Problem Via Considering Ambiguousness","volume":"19","author":"Yin","year":"2023","journal-title":"Transportmetrica A: Transp. Sci."},{"key":"2026022720020676300_CIT0008","first-page":"0666","article-title":"A Distributionally Robust Approach to Black-Box Optimization","author":"Kapteyn","year":"2018"},{"issue":"2","key":"2026022720020676300_CIT0009","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10479-020-03813-3","article-title":"A Multi-Objective Distributionally Robust Model for Sustainable Last Mile Relief Network Design Problem","volume":"309","author":"Zhang","year":"2022","journal-title":"Ann. Oper. Res."},{"issue":"4","key":"2026022720020676300_CIT0010","doi-asserted-by":"publisher","first-page":"874","DOI":"10.1115\/1.2202884","article-title":"A New Deterministic Approach Using Sensitivity Region Measures for Multi-objective Robust and Feasibility Robust Design Optimization","volume":"128","author":"Li","year":"2006","journal-title":"ASME J. Mech. Des."},{"issue":"3","key":"2026022720020676300_CIT0011","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1016\/j.ejor.2013.09.036","article-title":"Recent Advances in Robust Optimization: An Overview","volume":"235","author":"Gabrel","year":"2014","journal-title":"Eur. J. Oper. Res."},{"key":"2026022720020676300_CIT0012","unstructured":"Li, M.\n          , 2007, \u201cRobust Optimization and Sensitivity Analysis With Multi-Objective Genetic Algorithms: Single- and Multi-Disciplinary Applications,\u201d Ph.D. dissertation, University of Maryland, College Park, College Park, MD."},{"key":"2026022720020676300_CIT0013","volume-title":"Multi-Objective Optimization Using Evolutionary Algorithms","author":"Deb","year":"2001","edition":"1st"},{"issue":"1","key":"2026022720020676300_CIT0014","doi-asserted-by":"publisher","first-page":"1502242","DOI":"10.1080\/23311916.2018.1502242","article-title":"A Review of Multi-Objective Optimization: Methods and Its Applications","volume":"5","author":"Gunantara","year":"2018","journal-title":"Cogent Eng."},{"key":"2026022720020676300_CIT0015","doi-asserted-by":"crossref","DOI":"10.1515\/9781400831050","volume-title":"Robust Optimization","author":"Ben-Tal","year":"2009"},{"issue":"5","key":"2026022720020676300_CIT0016","doi-asserted-by":"publisher","first-page":"051703","DOI":"10.1115\/1.4044918","article-title":"Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement","volume":"142","author":"Rudnick-Cohen","year":"2020","journal-title":"ASME J. Mech. Des."},{"issue":"6","key":"2026022720020676300_CIT0017","doi-asserted-by":"publisher","first-page":"061002","DOI":"10.1115\/1.4003918","article-title":"Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts","volume":"133","author":"Hu","year":"2011","journal-title":"ASME J. Mech. Des."},{"key":"2026022720020676300_CIT0018","unstructured":"Hu, W.\n          , 2012, \u201cApproximation Assisted Multiobjective and Collaborative Robust Optimization Under Interval Uncertainty,\u201d Ph.D. dissertation, University of Maryland, College Park, College Park, MD."},{"key":"2026022720020676300_CIT0019","article-title":"Single- and Multi-Objective Feasibility Robust Optimization Under Interval Uncertainty With Surrogate Modelling","author":"Kania","year":"2022"},{"issue":"1","key":"2026022720020676300_CIT0020","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/s00158-004-0450-8","article-title":"Multi-Objective Robust Optimization Using a Sensitivity Region Concept","volume":"29","author":"Gunawan","year":"2005","journal-title":"Struct. Multidiscipl. Optim."},{"issue":"4","key":"2026022720020676300_CIT0021","doi-asserted-by":"publisher","first-page":"041010","DOI":"10.1115\/1.4049996","article-title":"An Efficient Multi-objective Robust Optimization Method by Sequentially Searching From Nominal Pareto Solutions","volume":"21","author":"Xia","year":"2021","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"key":"2026022720020676300_CIT0022","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s10107-005-0678-0","article-title":"Ambiguous Chance Constrained Problems and Robust Optimization","volume":"107","author":"Erdo\u011fan","year":"2006","journal-title":"Math. Program."},{"issue":"6","key":"2026022720020676300_CIT0023","doi-asserted-by":"publisher","first-page":"352","DOI":"10.1016\/j.resconrec.2009.02.002","article-title":"SRCCP: A Stochastic Robust Chance-Constrained Programming Model for Municipal Solid Waste Management Under Uncertainty","volume":"53","author":"Xu","year":"2009","journal-title":"Resour. Conserv. Recycl."},{"key":"2026022720020676300_CIT0024","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.compchemeng.2015.01.003","article-title":"Optimal Robust Optimization Approximation for Chance Constrained Optimization Problem","volume":"74","author":"Li","year":"2015","journal-title":"Comput. Chem. Eng."},{"issue":"2","key":"2026022720020676300_CIT0025","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s10898-007-9244-z","article-title":"Global Optimization of Robust Chance Constrained Problems","volume":"43","author":"Parpas","year":"2009","journal-title":"J. Global Optim."},{"issue":"1","key":"2026022720020676300_CIT0026","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.ejor.2014.03.013","article-title":"Minmax Robustness for Multi-objective Optimization Problems","volume":"239","author":"Ehrgott","year":"2014","journal-title":"Eur. J. Oper. Res."},{"issue":"1","key":"2026022720020676300_CIT0027","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/j.ejor.2021.03.068","article-title":"Multiobjective Optimization Under Uncertainty: A Multiobjective Robust (Relative) Regret Approach","volume":"296","author":"Groetzner","year":"2022","journal-title":"Eur. J. Oper. Res."},{"issue":"2","key":"2026022720020676300_CIT0028","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1016\/j.ejor.2018.08.020","article-title":"Dominance for Multi-objective Robust Optimization Concepts","volume":"273","author":"Botte","year":"2019","journal-title":"Eur. J. Oper. Res."},{"issue":"4","key":"2026022720020676300_CIT0029","doi-asserted-by":"publisher","first-page":"e2021WR030965","DOI":"10.1029\/2021WR030965","article-title":"Scenario-Based Multiobjective Robust Optimization and Decision-Making Framework for Optimal Operation of a Cascade Hydropower System Under Multiple Uncertainties","volume":"58","author":"Xu","year":"2022","journal-title":"Water Resour. Res."},{"issue":"1","key":"2026022720020676300_CIT0030","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1109\/JAS.2017.7510352","article-title":"Bad-Scenario-Set Robust Optimization Framework With Two Objectives for Uncertain Scheduling Systems","volume":"4","author":"Wang","year":"2017","journal-title":"IEEE\/CAA J. Autom. Sin."},{"issue":"10","key":"2026022720020676300_CIT0031","doi-asserted-by":"publisher","first-page":"101001","DOI":"10.1115\/1.4065793","article-title":"Risk-Based Design Optimization Via Scenario Generation and Genetic Programming Under Hybrid Uncertainties","volume":"24","author":"Li","year":"2024","journal-title":"ASME J. Comput. Inf. Sci. Eng."},{"key":"2026022720020676300_CIT0032","author":"MATLAB","year":"2022"},{"issue":"4","key":"2026022720020676300_CIT0033","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1198\/TECH.2009.08040","article-title":"Choosing the Sample Size of a Computer Experiment: A Practical Guide","volume":"51","author":"Loeppky","year":"2009","journal-title":"Technometrics"},{"issue":"5","key":"2026022720020676300_CIT0034","doi-asserted-by":"publisher","first-page":"051704","DOI":"10.1115\/1.4063661","article-title":"A Reliability-Based Optimization Framework for Planning Operational Profiles for Unmanned Systems","volume":"146","author":"Hazra","year":"2024","journal-title":"ASME J. Mech. Des."},{"key":"2026022720020676300_CIT0035","author":"Fossen","year":"2004"},{"key":"2026022720020676300_CIT0036","doi-asserted-by":"crossref","DOI":"10.1002\/9781119994138","volume-title":"Handbook of Marine Craft Hydrodynamics and Motion Control","author":"Fossen","year":"2011","edition":"1st"},{"key":"2026022720020676300_CIT0037","author":"PyTorch","year":"2024"},{"key":"2026022720020676300_CIT0038","author":"scikit learn","year":"2024"},{"key":"2026022720020676300_CIT0039","author":"BayesFusion, LLC","year":"2023"},{"key":"2026022720020676300_CIT0040","author":"MATLAB","year":"2022"},{"issue":"3","key":"2026022720020676300_CIT0041","doi-asserted-by":"publisher","first-page":"1109","DOI":"10.1137\/10079731X","article-title":"Direct Multisearch for Multiobjective Optimization","volume":"21","author":"Cust\u00f3dio","year":"2011","journal-title":"SIAM J. Optim."},{"key":"2026022720020676300_CIT0042","author":"MATLAB","year":"2022"},{"issue":"4","key":"2026022720020676300_CIT0043","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1137\/S1052623497325107","article-title":"An Interior Point Algorithm for Large-Scale Nonlinear Programming","volume":"9","author":"Byrd","year":"1999","journal-title":"SIAM J. Optim."},{"issue":"1","key":"2026022720020676300_CIT0044","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1007\/PL00011391","article-title":"A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming","volume":"89","author":"Byrd","year":"2000","journal-title":"Math. Program."},{"issue":"3","key":"2026022720020676300_CIT0045","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s10107-004-0560-5","article-title":"An Interior Algorithm for Nonlinear Optimization That Combines Line Search and Trust Region Steps","volume":"107","author":"Waltz","year":"2006","journal-title":"Math. Program."}],"container-title":["Journal of Computing and Information Science in Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/25\/4\/044501\/7428536\/jcise-24-1481.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article-pdf\/25\/4\/044501\/7428536\/jcise-24-1481.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T01:02:14Z","timestamp":1772240534000},"score":1,"resource":{"primary":{"URL":"https:\/\/asmedigitalcollection.asme.org\/computingengineering\/article\/25\/4\/044501\/1212231\/On-a-Sampling-Based-Method-for-Multi-Objective"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,28]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,4,1]]}},"URL":"https:\/\/doi.org\/10.1115\/1.4067706","relation":{},"ISSN":["1530-9827","1944-7078"],"issn-type":[{"value":"1530-9827","type":"print"},{"value":"1944-7078","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,28]]},"article-number":"044501"}}