Shortest path problem with uncertain arc lengths

AbstractUncertainty theory provides a new tool to deal with the shortest path problem with nondeterministic arc lengths. With help from the operational law of uncertainty theory, this paper gives the uncertainty distribution of the shortest path length. Also, it investigates solutions to the α-shortest path and the most shortest path in an uncertain network. It points out that there exists an equivalence relation between the α-shortest path in an uncertain network and the shortest path in a corresponding deterministic network, which leads to an effective algorithm to find the α-shortest path and the most shortest path. Roughly speaking, this algorithm can be broken down into two parts: constructing a deterministic network and then invoking the Dijkstra algorithm

An Efficient Approach for Solving Time-Dependent Shortest Path Problem under Fermatean Neutrosophic Environment

Efficiently determining optimal paths and calculating the least travel time within complex networks is of utmost importance in addressing transportation challenges. Several techniques have been developed to identify the most effective routes within graphs, with the Reversal Dijkstra algorithm serving as a notable variant of the classical Dijkstra’s algorithm. To accommodate uncertainty within the Reversal Dijkstra algorithm, Fermatean neutrosophic numbers are harnessed. The travel time associated with the edges, which represents the connection between two nodes, can be described using fermatean neutrosophic numbers. Furthermore, the edge weights in fermatean neutrosophic graphs can be subject to temporal variations, meaning they can change over time. In this study, an extended version of the Reversal Dijkstra algorithm is employed to discover the shortest path and compute the minimum travel time within a single-source time-dependent network, where the edges are weighted using fermatean neutrosophic representations. The proposed method is exemplified, and the outcomes affirm the effectiveness of the expanded algorithm. The primary aim of this article is to serve as a reference for forthcoming shortest path algorithms designed for time-dependent fuzzy graphs

Decomposition's Dantzig-Wolfe applied to fuzzy multicommodity flow problems

We present, in this paper, a method for solving linear programming problems with fuzzy costs based on the classical method of decomposition's Dantzig-Wolfe. Methods using decomposition techniques address problems that have a special structure in the set of constraints. An example of such a problem that has this structure is the fuzzy multicommodity flow problem. This problem can be modeled by a graph whose nodes represent points of supply, demand and passage of commodities, which travel on the arcs of the network. the objective is to determine the flow of each commodity on the arcs, in order to meet demand at minimal cost while respecting the capacity constraints of the arcs and the flow conservation constraints of the nodes. Using the theory of fuzzy sets, the proposed method aims to find the optimal solution, working with the problem in the fuzzy form during the resolution procedure. (c) 2012 Elsevier B.V. All rights reserved.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Univ Campinas UNICAMP, Sch Elect & Comp Engn, BR-13083852 Campinas, SP, BrazilUNIFESP, ICT, BR-12231280 Sao Jose Dos Campos, SP, BrazilUNIFESP, ICT, BR-12231280 Sao Jose Dos Campos, SP, BrazilWeb of Scienc

A New Algorithm for the Discrete Shortest Path Problem in a Network Based on Ideal Fuzzy Sets

A shortest path problem is a practical issue in networks for real-world situations. This paper addresses the fuzzy shortest path (FSP) problem to obtain the best fuzzy path among fuzzy paths sets. For this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (IFSs) in order to determine the fuzzy shortest path. Moreover, this algorithm is developed for a fuzzy network problem including three criteria, namely time, cost and quality risk. Several numerical examples are provided and experimental results are then compared against the fuzzy minimum algorithm with reference to the multi-labeling algorithm based on the similarity degree in order to demonstrate the suitability of the proposed algorithm. The computational results and statistical analyses indicate that the proposed algorithm performs well compared to the fuzzy minimum algorithm

Aplicação de Sistemas Baseados em Regras Fuzzy para o Roteamento em Redes Ópticas

Em uma rede óptica transparente sem equipamentos para conversão de comprimentos de onda, o atendimento de uma requisição de conexão entre dois nós exige a determinação de uma entre as possíveis rotas que os interligam e a atribuição de um comprimento de onda específico, em que a informação será transmitida do nó origem ao nó destino. O processo de determinação de uma rota é importante, pois a escolha da rota influencia a eficiência na utilização de recursos e, consequentemente, o desempenho da rede. Nesse processo, geralmente é levado em consideração apenas um critério, quase sempre o número de enlaces das rotas. O uso de critérios adicionais, desde que adequadamente combinados, pode levar a uma melhoria no desempenho da rede. Para combinar critérios no processo de decisão de uma rota, é implementado neste trabalho um sistema baseado em regras fuzzy. Os resultados apresentados foram obtidos com um sistema fuzzy, que leva em consideração, além do número de enlaces das rotas, a quantidade de comprimentos de onda contínuos disponíveis em cada rota no momento em que ocorre uma requisição de conexão. É feita uma análise de desempenho de duas redes com topologias distintas: uma rede em malha regular com 16 nós e 32 enlaces e uma rede em malha irregular com 14 nós e 20 enlaces. Os parâmetros adotados nesta análise são a probabilidade de bloqueio de requisições de conexão e a utilização de recursos da rede

Multi-Core Parallel Routing

The recent increase in the amount of data (i.e., big data) led to higher data volumes to be transferred and processed over the network. Also, over the last years, the deployment of multi-core routers has grown rapidly. However, such big data transfers are not leveraging the powerful multi-core routers to the extent possible, particularly in the key function of routing. Our main goal is to find a way so we can use these cores more effectively and efficiently in routing the big data transfers. In this dissertation, we propose a novel approach to parallelize data transfers by leveraging the multi-core CPUs in the routers. Legacy routing protocols, e.g. OSPF for intra-domain routing, send data from source to destination on a shortest single path. We describe an end-to-end method to distribute data optimally on flows by using multiple paths. We generate new virtual topology substrates from the underlying router topology and perform shortest path routing on each substrate. With this framework, even though calculating shortest paths could be done with well-known techniques such as OSPF's Dijkstra implementation, finding optimal substrates so as to maximize the aggregate throughput over multiple end-to-end paths is still an NP-hard problem. We focus our efforts on solving the problem and design heuristics for substrate generation from a given router topology. Our heuristics' interim goal is to generate substrates in such a way that the shortest path between a source-destination pair on each substrate minimally overlaps with each other. Once these substrates are determined, we assign each substrate to a core in routers and employ a multi-path transport protocol, like MPTCP, to perform end-to-end parallel transfers

Algorithms for fuzzy graphs problems

Orientadores: Akebo Yamakami, Marcia Tomie TakahashiTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: A teoria de grafos é uma importante área da programação matemática, tendo um importante papel em áreas tais como engenharia e pesquisa operacional. Em particular, ela fornece ferramentas para tratar problemas de redes (tais como: alocação, caminho mínimo, fluxo máximo, etc.), que têm aplicações em diversas subáreas da engenharia (por exemplo: telecomunicações, transporte, manufatura, etc.). Estas aplicações podem, entretanto, possuir incertezas em seus parâmetros ou em sua estrutura. Baseado nisto, este trabalho trata de algumas importantes aplicações de problemas em grafos com incertezas em seus parâmetros ou estruturas e propõe algoritmos para encontrar suas soluções. As aplicações estudadas são: problemas de caminho mínimo, problemas de fluxo máximo, problemas de fluxo de custo mínimo e problemas de coloração de grafos. As incertezas são modeladas por meio da teoria dos conjuntos fuzzy, que tem sido aplicada com sucesso em problemas com incertezas e imprecisõesAbstract: The graph theory is an important area of mathematical programming, it has an important role in fields such as engineering and operational research. In particular, it provides the tools to tackle network problems (e.g. allocation, shortest path, maximum flow, etc), which have applications in several sub areas of engineering (e.g. telecommunications, transportation, manufacturing, etc). These applications can, however, possess uncertainties in their parameters or in their structure. Based on that, this work addresses some important applications of graph problems with uncertainties in their structure or parameters and proposes algorithms to find the solution to them. The applications studied are: shortest path problems, maximum flow problems, minimum cost flow problems and graph coloring problems. The uncertainties are modeled by means of the fuzzy sets theory, which has been successfully applied to problems with uncertainties and vaguenessDoutoradoAutomaçãoDoutor em Engenharia Elétric

Contribuições ao estudo de grafos fuzzy : teoria e algoritmos

Orientadores: Akebo YamakamiTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoDoutorad

Decompositions Dantzig-wolfe Applied To Fuzzy Multicommodity Flow Problems

We present, in this paper, a method for solving linear programming problems with fuzzy costs based on the classical method of decompositions Dantzig-Wolfe. Methods using decomposition techniques address problems that have a special structure in the set of constraints. An example of such a problem that has this structure is the fuzzy multicommodity flow problem. This problem can be modeled by a graph whose nodes represent points of supply, demand and passage of commodities, which travel on the arcs of the network. The objective is to determine the flow of each commodity on the arcs, in order to meet demand at minimal cost while respecting the capacity constraints of the arcs and the flow conservation constraints of the nodes. Using the theory of fuzzy sets, the proposed method aims to find the optimal solution, working with the problem in the fuzzy form during the resolution procedure. © 2012 Elsevier Ltd. All rights reserved.391233943407Bazaraa, M.S., Jarvis, J.J., Sherali, H.D., (2005) Linear Programming and Network Flows, , John Wiley & Sons New JerseyDubois, D., Prade, H., (1980) Fuzzy Sets and Systems: Theory and Applications, , Academic Press New YorkFord, L.R., Fulkerson, D.R., (1962) Flows in Networks, , Princeton University Press New JerseyGhatee, M., Hashemi, S.M., Some concepts of the fuzzy multicommodity flow problem and their application in fuzzy network design (2009) Mathematical and Computer Modelling, 49, pp. 1030-1043Hernandes, F., (2007) Algoritmos Para Problemas de Grafos Com Incertezas, , PhD thesis, FEEC, UNICAMP, Campinas, SPHernandes, F., Lamata, M.T., Verdegay, J.L., Yamakami, A., The shortest path problem on networks with fuzzy parameters (2007) Fuzzy Sets and Systems, 158 (14), pp. 1561-1570. , DOI 10.1016/j.fss.2007.02.022, PII S0165011407001066Hu, T.C., Multicommodity network flows (1962) Operations Research, 11, pp. 344-360Kaufmann, A., Gupta, M.M., (1988) Fuzzy Mathematical Models in Engineering and Management Science, , North Holland AmsterdamKlir, G., Yuan, B., (1995) Fuzzy Sets and Fuzzy Logic: Theory and Applications, , Prentice-Hall Upper Saddle River, NJOkada, S., Soper, T., A shortest path problem on a network with fuzzy arc lengths (2000) Fuzzy Sets and Systems, 109, pp. 129-140Okada, S., Fuzzy shortest path problems incorporating interactivity among paths (2004) Fuzzy Sets and Systems, 142 (3), pp. 335-357Pedrycz, W., Gomide, F., (2007) Fuzzy Systems Engineering Toward Human-centric Computing, , John Wiley and Sons Hoboken, NJTan, L.G., Sinclair, M.C., Wavelength assignment between the central nodes of the cost239 European optical network (1995) 11th UK Performance Engineering Workshop, pp. 235-247. , LiverpoolVerga, J., Ciappina, J.R., Yamakami, A., Algoritmo para a Resolução do Problema de Fluxo Multiproduto Fuzzy (2009) XLI Simpósio Brasileiro de Pesquisa Operacional, , Porto Seguro, BAZadeh, L., Fuzzy sets (1965) Journal of Information and Control, 8, pp. 338-353Zadeh, L., Fuzzy sets as a theory of possibility (1978) Journal of Fuzzy Sets and Systems, 1, pp. 3-28Zimmermann, H.-J., (1996) Fuzzy Set Theory - And Its Applications, , Kluwer Academic Publishers Bosto