M. Goerigk, R. Guillaume, A. Kasperski, Pawel Zieli'nski
{"title":"Robust optimization with belief functions","authors":"M. Goerigk, R. Guillaume, A. Kasperski, Pawel Zieli'nski","doi":"10.48550/arXiv.2303.05067","DOIUrl":null,"url":null,"abstract":"In this paper, an optimization problem with uncertain objective function coefficients is considered. The uncertainty is specified by providing a discrete scenario set, containing possible realizations of the objective function coefficients. The concept of belief function in the traditional and possibilistic setting is applied to define a set of admissible probability distributions over the scenario set. The generalized Hurwicz criterion is then used to compute a solution. In this paper, the complexity of the resulting problem is explored. Some exact and approximation methods of solving it are proposed.","PeriodicalId":13685,"journal":{"name":"Int. J. Approx. Reason.","volume":"24 1","pages":"108941"},"PeriodicalIF":0.0000,"publicationDate":"2023-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Approx. Reason.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2303.05067","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, an optimization problem with uncertain objective function coefficients is considered. The uncertainty is specified by providing a discrete scenario set, containing possible realizations of the objective function coefficients. The concept of belief function in the traditional and possibilistic setting is applied to define a set of admissible probability distributions over the scenario set. The generalized Hurwicz criterion is then used to compute a solution. In this paper, the complexity of the resulting problem is explored. Some exact and approximation methods of solving it are proposed.