{"title":"Randomized Lagrangian heuristic based on Nash equilibrium for large scale single machine scheduling problem","authors":"Hanyu Gu, Y. Xi, Jiping Tao","doi":"10.1109/ISIC.2007.4450930","DOIUrl":null,"url":null,"abstract":"Lagrangian relaxation method for jobshop scheduling problems has been studied in the framework of combinatorial auction. In this paper a noncooperative game model is built for the Lagrangian relaxation method, and we prove that the equivalent continuous relaxation computed from the Lagrangian dual problem provides a mixed strategy Nash equilibrium for this game model. Based on this interpretation a randomized heuristic is exploited to get feasible schedules. Numerical experiments are carried out on a large scale single machine problem.","PeriodicalId":184867,"journal":{"name":"2007 IEEE 22nd International Symposium on Intelligent Control","volume":"57 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2007 IEEE 22nd International Symposium on Intelligent Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIC.2007.4450930","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
Lagrangian relaxation method for jobshop scheduling problems has been studied in the framework of combinatorial auction. In this paper a noncooperative game model is built for the Lagrangian relaxation method, and we prove that the equivalent continuous relaxation computed from the Lagrangian dual problem provides a mixed strategy Nash equilibrium for this game model. Based on this interpretation a randomized heuristic is exploited to get feasible schedules. Numerical experiments are carried out on a large scale single machine problem.