{"title":"带层次目标函数的旅行商问题","authors":"T. Dam, D. T. Nguyen, Q. Bui, T. Do","doi":"10.1109/KSE.2019.8919421","DOIUrl":null,"url":null,"abstract":"We address a novel variant of the wellknown Traveling Salesman Problem (TSP) called the Traveling Salesman Problem with Hierarchical Objective (TSPHO). In this problem, the customers are divided in to several groups with decreasing priority levels, i.e., the first group is more important than the second one and the second one is more important than the third one, and so on. The difference between TSPHO and the classical TSP lies in the objective function. The Hierarchical Objective does not minimize the total travel cost, but aims to minimize the completion time of the first group then the completion time of the second group, etc. A transformation of the TSPHO into an equivalent Asymmetric TSP is first proposed from which one can use efficient TSP solvers such as Concorde or Lin-Kernighan-Helsgaun (LKH) to solve the problem. A genetic algorithm is also developed as an alternative solution. Computational results show the performance of our methods.","PeriodicalId":439841,"journal":{"name":"2019 11th International Conference on Knowledge and Systems Engineering (KSE)","volume":"6 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the Traveling Salesman Problem with Hierarchical Objective Function\",\"authors\":\"T. Dam, D. T. Nguyen, Q. Bui, T. Do\",\"doi\":\"10.1109/KSE.2019.8919421\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We address a novel variant of the wellknown Traveling Salesman Problem (TSP) called the Traveling Salesman Problem with Hierarchical Objective (TSPHO). In this problem, the customers are divided in to several groups with decreasing priority levels, i.e., the first group is more important than the second one and the second one is more important than the third one, and so on. The difference between TSPHO and the classical TSP lies in the objective function. The Hierarchical Objective does not minimize the total travel cost, but aims to minimize the completion time of the first group then the completion time of the second group, etc. A transformation of the TSPHO into an equivalent Asymmetric TSP is first proposed from which one can use efficient TSP solvers such as Concorde or Lin-Kernighan-Helsgaun (LKH) to solve the problem. A genetic algorithm is also developed as an alternative solution. Computational results show the performance of our methods.\",\"PeriodicalId\":439841,\"journal\":{\"name\":\"2019 11th International Conference on Knowledge and Systems Engineering (KSE)\",\"volume\":\"6 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2019 11th International Conference on Knowledge and Systems Engineering (KSE)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/KSE.2019.8919421\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2019 11th International Conference on Knowledge and Systems Engineering (KSE)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/KSE.2019.8919421","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Traveling Salesman Problem with Hierarchical Objective Function
We address a novel variant of the wellknown Traveling Salesman Problem (TSP) called the Traveling Salesman Problem with Hierarchical Objective (TSPHO). In this problem, the customers are divided in to several groups with decreasing priority levels, i.e., the first group is more important than the second one and the second one is more important than the third one, and so on. The difference between TSPHO and the classical TSP lies in the objective function. The Hierarchical Objective does not minimize the total travel cost, but aims to minimize the completion time of the first group then the completion time of the second group, etc. A transformation of the TSPHO into an equivalent Asymmetric TSP is first proposed from which one can use efficient TSP solvers such as Concorde or Lin-Kernighan-Helsgaun (LKH) to solve the problem. A genetic algorithm is also developed as an alternative solution. Computational results show the performance of our methods.