M. Goerigk, R. Guillaume, A. Kasperski, Pawel Zieli'nski
{"title":"基于信念函数的鲁棒优化","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":"{\"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}","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}
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.