Time-dependent stochastic shortest path(s) algorithms for a scheduled transportation network

Following on from our work concerning travellers’ preferences in public transportation networks (Wu and Hartley, 2004), we introduce the concept of stochasticity to our algorithms. Stochasticity greatly increases the complexity of the route finding problem, so greater algorithmic efficiency becomes imperative. Public transportation networks (buses, trains) have two important features: edges can only be traversed at certain points in time and the weights of these edges change in a day and have an uncertainty associated with them. These features determine that a public transportation network is a stochastic and time-dependent network. Finding multiple shortest paths in a both stochastic and time-dependent network is currently regarded as the most difficult task in the route finding problems (Loui, 1983). This paper discusses the use of k-shortest-paths (KSP) algorithms to find optimal route(s) through a network in which the edge weights are defined by probability distributions. A comprehensive review of shortest path(s) algorithms with probabilistic graphs was conducted

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

Intelligent algorithm for trapezoidal interval valued neutrosophic network analysis

The shortest path problem has been one of the most fundamental practical problems in network analysis. One of the good algorithms is Bellman-Ford, which has been applied in network, for the last some years. Due to complexity in the decision-making process, the decision makers face complications to express their view and judgment with an exact number for single valued membership degrees under neutrosophic environment. Though the interval number is a special situation of the neutrosophic, it did not solve the shortest path problems in an absolute manner. Hence, in this work, the authors have introduced the score function and accuracy function of trapezoidal interval valued neutrosophic numbers with their illustrative properties. These properties provide important theoretical base of the trapezoidal interval valued neutrosophic number. Also, they proposed an intelligent algorithm called trapezoidal interval valued neutrosophic version of Bellman’s algorithm to solve neutrosophic shortest path problem in network analysis. Further, comparative analysis has been made with the existing algorithm

Shortest path problem using Bellman algorithm under neutrosophic environment

An elongation of the single-valued neutrosophic set is an interval-valued neutrosophic set. It has been demonstrated to deal indeterminacy in a decision-making problem. Real-world problems have some kind of uncertainty in nature and among them; one of the influential problems is solving the shortest path problem (SPP) in interconnections

An approximation of balanced score in neutrosophic graphs with weak edge weights

Neutrosophic concept is known undirected graph theory to involve with complex logistic networks, not clearly given and unpredictable real life situations, where fuzzy logic malfunctions to model. The transportation objective is to ship all logistic nodes in the network. The logistic network mostly experiences in stable condition, but for some edges found to be volatile. The weight of these erratic edges may vary at random (bridge-lifting/bascule, ad hoc accident on road, traffic condition) In this article, we propose an approximation algorithm for solving minimum spanning tree (MST) of an undirected neutrosophic graphs (UNG), in which the edge weights represent neutrosophic values. The approximation upon the balanced score calculation is introduced for all known configurations in alternative MST. As the result, we further compute decisive threshold value for the weak weights amid minimum cost pre-computation. If the threshold triggers then the proper MST can direct the decision and avoid post-computation. The proposed algorithm is also related to other existing approaches and a numerical analysis is presented

p-Median problems in a fuzzy environment

In this paper a formulation for the fuzzy p-median model in a fuzzy environment is presented. The model allows to find optimal locations of p facilities and their related cost when data related to the node demands and the edge distances are imprecise and uncertain and also to know the degree of certainty of the solution. For the sake of illustration, the proposed model is applied in a reduced map of Kinshasa (Democratic Republic of Congo) obtaining results which are rather than realistic one

Spanning Tree Problem with Neutrosophic Edge Weights

Neutrosophic set and neutrosophic logic theory are renowned theories to deal with complex, not clearly explained and uncertain real life problems, in which classical fuzzy sets/models may fail to model properly. This paper introduces an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (abbr. UNWCG) where the arc/edge lengths are represented by a single valued neutrosophic numbers. To build the MST of UNWCG, a new algorithm based on matrix approach has been introduced. The proposed algorithm is compared to other existing methods and finally a numerical example is provided

SHORTEST PATH PROBLEM UNDER TRIANGULAR FUZZY NEUTROSOPHIC INFORMATION

In this paper, we develop a new approach to deal with neutrosphic shortest path problem in a network in which each edge weight (or length) is represented as triangular fuzzy neutrosophic number. The proposed algorithm also gives the shortest path length from source node to destination node using ranking function. Finally, an illustrative example is also included to demonstrate our proposed approach