Hierarchical Chinese postman problem with fuzzy travel times

IF 1.9 4区数学 Q1 MATHEMATICS Iranian Journal of Fuzzy Systems Pub Date : 2021-10-01 DOI:10.22111/IJFS.2021.6257

O. C. S¨okmen, M. Yilmaz

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引用次数: 1

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.

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具有模糊行程时间的分层中国邮差问题

分层中国邮差问题(HCPP)是中国邮差问题(CPP)的一种，它的目标是根据它们的优先关系分类至少访问一次，并找到最短的行程。在HCPP中，如果构成成本的两个节点之间的行程时间值不清晰，则这种问题类型可以称为具有模糊行程时间的分层中国邮递员问题(HCPP- ftt)。在现实问题中，由于节点间的行程时间受各种因素的影响而不固定，因此本研究采用三角模糊数作为小样本问题的目标函数系数。采用不同的排序方法对模糊数进行去模糊化，并对得到的结果进行比较。采用CPLEX求解器GAMS 24.2.3软件对所形成的数学模型进行求解。此外，本研究还讨论了一个大尺度的现实问题。用梯形模糊数表示两个节点之间的行程时间的目标函数系数。由于问题的NP-hard性质，数学模型无法在适当的时间间隔内找到大尺寸问题的解。为此，本研究提出了基于贪心搜索(GS)算法的启发式方法和基于蚁群优化(ACO)的元启发式方法来解决现实问题。所提出的算法使用Matlab-2019b编程语言进行编码。利用所开发的算法，比较了不同排序方法的结果和求解次数。

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来源期刊

Iranian Journal of Fuzzy Systems 数学-数学

CiteScore

3.50

自引率

16.70%

发文量

期刊介绍： The two-monthly Iranian Journal of Fuzzy Systems (IJFS) aims to provide an international forum for refereed original research works in the theory and applications of fuzzy sets and systems in the areas of foundations, pure mathematics, artificial intelligence, control, robotics, data analysis, data mining, decision making, finance and management, information systems, operations research, pattern recognition and image processing, soft computing and uncertainty modeling. Manuscripts submitted to the IJFS must be original unpublished work and should not be in consideration for publication elsewhere.