{"title":"具有模糊行程时间的分层中国邮差问题","authors":"O. C. S¨okmen, M. Yilmaz","doi":"10.22111/IJFS.2021.6257","DOIUrl":null,"url":null,"abstract":"The hierarchical Chinese postman problem (HCPP), one of the kinds of Chinese postman problem (CPP), aims to visit at least once the arcs are classified according to their precedence relations and to find the shortest tour or tours. In HCPP, if the travel time values between two nodes constituting the cost are not crisp, this problem type can be said to be the hierarchical Chinese postman problem with fuzzy travel times (HCPP-FTT). In real-life problems, as the travel time between the nodes is not fixed due to various factors, in this study triangular fuzzy numbers are used at objective function coefficients of a small-size sample problem. Different ranking methods are used to defuzzify the fuzzy numbers and the acquired results are compared. The mathematical model formed is resolved using CPLEX solver GAMS 24.2.3 software. Besides, in this study, a large-size real-life problem was discussed. The objective function coefficients representing the travel time between the two nodes in the case study discussed were considered as trapezoidal fuzzy numbers. Due to the NP-hard nature of the problem, the mathematical model cannot find solutions in large size problems in the appropriate time interval. For this reason, in this study, the heuristic method based on the Greedy Search (GS) algorithm and the meta-heuristic method based on ant colony optimization (ACO) is proposed for the solution of the real-life problem. The proposed algorithms are coded using the Matlab-2019b programming language. Using the developed algorithms, the results of different ranking methods and solution times were compared.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Hierarchical Chinese postman problem with fuzzy travel times\",\"authors\":\"O. C. S¨okmen, M. Yilmaz\",\"doi\":\"10.22111/IJFS.2021.6257\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The hierarchical Chinese postman problem (HCPP), one of the kinds of Chinese postman problem (CPP), aims to visit at least once the arcs are classified according to their precedence relations and to find the shortest tour or tours. In HCPP, if the travel time values between two nodes constituting the cost are not crisp, this problem type can be said to be the hierarchical Chinese postman problem with fuzzy travel times (HCPP-FTT). In real-life problems, as the travel time between the nodes is not fixed due to various factors, in this study triangular fuzzy numbers are used at objective function coefficients of a small-size sample problem. Different ranking methods are used to defuzzify the fuzzy numbers and the acquired results are compared. The mathematical model formed is resolved using CPLEX solver GAMS 24.2.3 software. Besides, in this study, a large-size real-life problem was discussed. The objective function coefficients representing the travel time between the two nodes in the case study discussed were considered as trapezoidal fuzzy numbers. Due to the NP-hard nature of the problem, the mathematical model cannot find solutions in large size problems in the appropriate time interval. For this reason, in this study, the heuristic method based on the Greedy Search (GS) algorithm and the meta-heuristic method based on ant colony optimization (ACO) is proposed for the solution of the real-life problem. The proposed algorithms are coded using the Matlab-2019b programming language. Using the developed algorithms, the results of different ranking methods and solution times were compared.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2021-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.22111/IJFS.2021.6257\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.22111/IJFS.2021.6257","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
Hierarchical Chinese postman problem with fuzzy travel times
The hierarchical Chinese postman problem (HCPP), one of the kinds of Chinese postman problem (CPP), aims to visit at least once the arcs are classified according to their precedence relations and to find the shortest tour or tours. In HCPP, if the travel time values between two nodes constituting the cost are not crisp, this problem type can be said to be the hierarchical Chinese postman problem with fuzzy travel times (HCPP-FTT). In real-life problems, as the travel time between the nodes is not fixed due to various factors, in this study triangular fuzzy numbers are used at objective function coefficients of a small-size sample problem. Different ranking methods are used to defuzzify the fuzzy numbers and the acquired results are compared. The mathematical model formed is resolved using CPLEX solver GAMS 24.2.3 software. Besides, in this study, a large-size real-life problem was discussed. The objective function coefficients representing the travel time between the two nodes in the case study discussed were considered as trapezoidal fuzzy numbers. Due to the NP-hard nature of the problem, the mathematical model cannot find solutions in large size problems in the appropriate time interval. For this reason, in this study, the heuristic method based on the Greedy Search (GS) algorithm and the meta-heuristic method based on ant colony optimization (ACO) is proposed for the solution of the real-life problem. The proposed algorithms are coded using the Matlab-2019b programming language. Using the developed algorithms, the results of different ranking methods and solution times were compared.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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