Abstract
The paper illustrates the method of the maximum flow value finding in a fuzzy weighted directed graph, which presented as a generalized network. The interest to such type of networks is explained by their wide practical implementation: they can deal with water distribution, money conversion, transportation of perishable goods or goods that can increase their value during transportation, like plants. At the same time the values of arc capacities of the considered networks can vary depending on the flow departure time, therefore, we turn to the dynamic networks. Network’s parameters are presented in a fuzzy form due to the impact of environment factors and human activity. Considered types of networks can be implemented in real roads during the process of transportation. The numerical example is given that operated data from geoinformation system “ObjectLand” that contains information about railway system of Russian Federation.
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References
Bozhenyuk, A.V., Gerasimenko, E.M., Kacprzyk, J., Rozenberg, I.N.: Flows in Networks Under Fuzzy Conditions. Studies in Fuzziness and Soft Computing, vol. 346. Springer International Publishing Switzerland (2017)
Kureichik, V., Gerasimenko, E.: Approach to the minimum cost flow determining in fuzzy terms considering vitality degree. In: Silhavy, R., Senkerik, R., Kominkova Oplatkova, Z., Prokopova, Z., Silhavy, P. (eds.). CSOC 2017, Artificial Intelligence Trends in Intelligent Systems, Advances in Intelligent Systems and Computing, vol. 573, pp, 200–210. Springer, Cham (2017)
Wayne, K.D.: Generalized maximum flow algorithm. Ph.D. dissertation, Cornell University, New York, January 1999
Murray, S.M.: An interior point approach to the generalized flow problem with costs and related problems. Ph.D. thesis, Stanford University (1993)
Radzik, T.: Faster algorithms for the generalized network flow problem. Math. Oper. Res. 23(1), 69–100 (1998)
Wayne, K.D., Fleischer, L.: Faster approximation algorithms for generalized flow. In: ACM Transactions on Algorithms (1998)
Eguchi, A., Fujishige, S., Takabatake, T.: A polynomial-time algorithm for the generalized independent-flow problem. J. Oper. Res. 47(1), 1–17 (2004)
Krumke, S.O., Zeck, C.: Generalized max flow in series–parallel graphs. Discret. Optim. 10(2), 155–162 (2013)
Groß, M., Skutella, M.: Generalized maximum flows over time. In: Solis-Oba, R., Persiano, G. (eds.) Approximation and Online Algorithms. WAOA 2011. Lecture Notes in Computer Science, vol. 7164. Springer, Heidelberg (2012)
ObjectLand/Geoinformation system. http://www.objectland.ru/
Acknowledgments
This work has been supported by the Russian Foundation for Basic Research, Projects 18-0700050, № 16-01-00090 a.
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Kureichik, V., Gerasimenko, E. (2019). Method of the Maximum Dynamic Flow Finding in the Fuzzy Graph with Gains. In: Abraham, A., Kovalev, S., Tarassov, V., Snasel, V., Sukhanov, A. (eds) Proceedings of the Third International Scientific Conference “Intelligent Information Technologies for Industry” (IITI’18). IITI'18 2018. Advances in Intelligent Systems and Computing, vol 874. Springer, Cham. https://doi.org/10.1007/978-3-030-01818-4_24
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DOI: https://doi.org/10.1007/978-3-030-01818-4_24
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