Trapezoidal Fuzzy Shortest Path (TFSP) Selection for Green Routing and Scheduling Problems

The routing of vehicles represents an important component of many distribution and transportation systems. Finding the shortest path is one of the fundamental and popular problems. In real life applications, like vehicle green routing and scheduling, transportation, etc. which are related to environmental issues the arc lengths could be uncertain due to the fluctuation with traffic conditions or weather conditions. Therefore finding the exact optimal path in such networks could be challenging. In this paper, we discuss and analyze different approaches for finding the Fuzzy Shortest Path. The shortest path is computed using the ranking methods based on i)Degree of Similarity ii) Acceptable Index, where the arc lengths are expressed as trapezoidal fuzzy numbers. The Decision makers can choose the best path among the various alternatives from the list of rankings by prioritizing the scheduling which facilitates Green Routing

A New Algorithm for Solving Shortest Path Problem on a Network with Imprecise Edge Weight

Nayeem and Pal (Shortest path problem on a network with imprecise edge weight, Fuzzy Optimization and Decision Making 4, 293-312, 2005) proposed a new algorithm for solving shortest path problem on a network with imprecise edge weight. In this paper the shortcomings of the existing algorithm, (Nayeem and Pal, 2005) are pointed out and to overcome these shortcomings a new algorithm is proposed. To show the advantages of the proposed algorithm over existing algorithm the numerical examples presented in (Nayeem and Pal, 2005) are solved using the proposed algorithm and obtained results are discussed

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

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

Qualitative Optimization : Development of a Methodology for Determining the Shortest Path of a Network with Interval-valued Arc Lengths

Industrial Engineering and Managemen

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

Multicriteria pathfinding in uncertain simulated environments

Dr. James Keller, Dissertation Supervisor.Includes vita.Field of study: Electrical and computer engineering."May 2018."Multicriteria decision-making problems arise in all aspects of daily life and form the basis upon which high-level models of thought and behavior are built. These problems present various alternatives to a decision-maker, who must evaluate the trade-offs between each one and choose a course of action. In a sequential decision-making problem, each choice can influence which alternatives are available for subsequent actions, requiring the decision-maker to plan ahead in order to satisfy a set of objectives. These problems become more difficult, but more realistic, when information is restricted, either through partial observability or by approximate representations. Pathfinding in partially observable environments is one significant context in which a decision-making agent must develop a plan of action that satisfies multiple criteria. In general, the partially observable multiobjective pathfinding problem requires an agent to navigate to certain goal locations in an environment with various attributes that may be partially hidden, while minimizing a set of objective functions. To solve these types of problems, we create agent models based on the concept of a mental map that represents the agent's most recent spatial knowledge of the environment, using fuzzy numbers to represent uncertainty. We develop a simulation framework that facilitates the creation and deployment of a wide variety of environment types, problem definitions, and agent models. This computational mental map (CMM) framework is shown to be suitable for studying various types of sequential multicriteria decision-making problems, such as the shortest path problem, the traveling salesman problem, and the traveling purchaser problem in multiobjective and partially observable configurations.Includes bibliographical references (pages 294-301)

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