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This paper proposes a methodology for the optimal design of series of sewer pipes including pumping stations. It employs a Shortest Path Algorithm to select the optimal combination of pipe diameters and invert elevations, as well as the optimal pumping features such as the number of pumps, location, and pumping head. The methodology is intended to be applied to the design of any sewer series. Although these are uncommon in real infrastructure, the study allows an analysis of the effect of pipe roughness, inflows, and pipe length on the total cost of the system and pumping features. The methodology was tested in theoretical series of 10 and 20 pipes as well as in a real series that is part of the sewer system of Bogotá, Colombia. The resulting designs suggested that using smooth pipes and reducing the pumping flow rate would decrease the cost of sewer systems in flat terrain. [ABSTRACT FROM AUTHOR]

The Shortest path problem is highly relevant in our daily lives, addressing uncertainties like traffic conditions and weather variations. To handle such uncertainties, we utilize Fuzzy Numbers. This paper focuses on Bipolar Neutrosophic Fuzzy Numbers, which have dual positive and negative aspects. They provide a robust framework for representing arc (node/edge) weights, signifying uncertain travel times between nodes. Importantly, these weights can change over time in bipolar neutrosophic fuzzy graphs. Our study introduces an extended Bellman-Ford Algorithm for identifying optimal paths and minimum times with time-dependent Bipolar Neutrosophic Fuzzy arc weights. We demonstrate its effectiveness through a step-by-step numerical example and conduct a comparative analysis to evaluate its efficiency. [ABSTRACT FROM AUTHOR]

The shortest path problem is a classic optimization problem in graph theory and computer technology. It involves identifying the shortest path between two nodes in a graph, where each edge has a numerical weight. In this paper, we put our effort into examining the use of the dynamic programming method to evaluate the shortest path (SP) between the two specified nodes in a multistage network where the parameter is a multi-value neutrosophic number (MVNN). Firstly, we propose an algorithm based on the forward and backward approach in an uncertain environment and also implement our approach in the Python-3 programming language. Furthermore, a numerical illustration has been provided to showcase the effectiveness and robustness of the novel model.

The Mobile Robot Path Problem looks to find the optimal shortest path from the starting point to the target point with collision-free for a mobile robot. This is a popular issue in robotics and in this paper the environment is considered as static and represented as a bidirectional grid map. Besides, the novel optimal method Dhouib-Matrix-SPP (DM-SPP) is applied to create the optimal shortest path for a mobile robot in a static environment. DM-SPP is a greedy method based on a column row navigation in the distance matrix and characterized by its rapidity to solve sparse graphs. The comparative analysis is conducted by applying DM-SPP on thirteen test cases and comparing its results to the results given by four metaheuristics the Max-Min Ant System, the Ant System with punitive measures, the A* and the Improved Hybrid A*. The outcomes acquired from different scenarios indicate that the proposed DM-SPP method can rapidly outperform the four predefined artificial intelligence methods.

The shortest path problem is a classic optimization problem in graph theory and computer technology. It involves identifying the shortest path between two nodes in a graph, where each edge has a numerical weight. In this paper, we put our effort into examining the use of the dynamic programming method to evaluate the shortest path (SP) between the two specified nodes in a multistage network where the parameter is a multi-value neutrosophic number (MVNN). Firstly, we propose an algorithm based on the forward and backward approach in an uncertain environment and also implement our approach in the Python-3 programming language. Furthermore, a numerical illustration has been provided to showcase the effectiveness and robustness of the novel model. [ABSTRACT FROM AUTHOR]

In the era of big data, using of data mining instead of data collection represents a new challenge for researchers and engineers. In the field of transportation, computing of the shortest path based on MapReduce using widely existing vehicle data is meaningful both in theory and practice. Therefore, this article proposes a simple shortest path approach to relieve urban traffic congestion. The objective is not to guarantee the optimality but to provide high-quality solutions in acceptable computational time. The proposed approach is based on partitioning of original graph into a set of subgraphs, and parallel solving of the shortest path for each subgraph in order to obtain a solution for the original graph. An iterative procedure is introduced to improve the accuracy. The experimental results show that proposed approach significantly reduces computational time. [ABSTRACT FROM AUTHOR]

Shortest path problem (SPP) has various applications in areas such as telecommunications, transportation and emergency services, and postal services among others. As a result, several algorithms have been developed to solve the SPP and related problems. The current paper extends the TANYAKUMU labelling method for solving the Travelling salesman problem (TSP) to solve SPP in directed transportation networks. Numerical illustrations are used to prove the validity of the proposed method. The main contributions of this paper are as follows: (i) modification of TSP algorithm to solve single source SPP, (ii) the developed method numerically evaluated on four increasingly complex problems of sizes 11×11, 21×21, 23×23 and 26×26 and lastly (iii) the solutions obtained from solving these four problems are compared with those obtained by Minimum incoming weight label (MIWL) algorithm. The proposed algorithm computed the same shortest paths as the MIWL algorithm on all four problems.

We present a theoretical framework that links Fermat's principle of least time to optimal transport theory via a cost function that enforces local transport. The proposed cost function captures the physical constraints inherent in wave propagation; when paired with specific mass distributions, it yields shortest paths in the considered media through the optimal transport plans. In the discrete setting, our formulation results in physically significant optimal couplings, whose off-diagonal entries identify shortest paths in both directed and undirected graphs. For undirected graphs with positive edge weights, commonly used to parameterize seismic media, our method provides solutions to the Eikonal equation consistent with those from the Dijkstra algorithm. For directed negative-weight graphs, corresponding to transportation cost matrices with negative entries, our approach aligns with the Bellman–Ford algorithm but offers considerable computational advantages. We also highlight potential research directions. These include the use of sparse cost matrices to reduce the number of unknowns and constraints in the considered transportation problem, and solving specific classes of optimal transport problems through the Dijkstra algorithm to enhance computational efficiency. [ABSTRACT FROM AUTHOR]

We develop a projection recurrent neural network (RNN) to obtain the solution of the shortest path problem (SPP). Our focus on the paper is to give a compact single-layer structure RNN model to solve the SPP. To present the RNN model, we utilise a mixed linear complementarity problem (MLCP). Moreover, the developed RNN is proved to be globally stable. Finally, some numerical simulations are stated to show the performance of the presented approach. We compare the results with some other methods. [ABSTRACT FROM AUTHOR]

Shortest path problem (SPP) has various applications in areas such as telecommunications, transportation and emergency services, and postal services among others. As a result, several algorithms have been developed to solve the SPP and related problems. The current paper extends the TANYAKUMU labelling method for solving the Travelling salesman problem (TSP) to solve SPP in directed transportation networks. Numerical illustrations are used to prove the validity of the proposed method. The main contributions of this paper are as follows: (i) modification of TSP algorithm to solve single source SPP, (ii) the developed method numerically evaluated on four increasingly complex problems of sizes 11×11, 21×21, 23×23 and 26×26 and lastly (iii) the solutions obtained from solving these four problems are compared with those obtained by Minimum incoming weight label (MIWL) algorithm. The proposed algorithm computed the same shortest paths as the MIWL algorithm on all four problems. [ABSTRACT FROM AUTHOR]

The realms of Intuitionistic Fuzzy Sets (IFSs), Pythagorean Fuzzy Sets (PFS), and qrung Orthopair Fuzzy Sets (q-ROFSs) have found extensive applications across various disciplines, notably in resolving real-world problems. However, limitations concerning membership and non-membership grades pose challenges to these theories. Efforts to mitigate these constraints have led to the introduction of a new concept, the Linear Diophantine Fuzzy Set (LDFS), with reference parameters. This study advances the shortest path (SP) problem for Linear Diophantine Fuzzy graphs. An innovative method for constructing direct network graphs within a Linear Diophantine Fuzzy (LDF) context is proposed. Distances or costs between nodes are encapsulated by Linear Diophantine Fuzzy numbers. The principal contribution of this investigation lies in proposing a novel approach to solving the Linear Fuzzy Diophantine Fuzzy shortest path problem using the Bellman-Ford algorithm for optimal solution attainment. Usage of the score function enables the comparison and identification of the minimum arc value between nodes. The proposed algorithm's validity is demonstrated through a numerical example, and a comparison with existing methodologies underscores the benefits of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The shortest path (SP) problem (SPP) has several applications in graph theory. It can be used to calculate the distance between the provided initial and final vertex in a network. In this paper, we employed the Fermatean neutrosophic number as the appropriate edge weight of the network to estimate the SP connecting the start and end vertex. This technique is highly useful in establishing the shortest path for the decision-maker under uncertainty. We also investigated its effectiveness in comparison to several existing methods. Finally, a few numerical tests were performed to demonstrate the validity and stability of this new technique, as well as to compare different types of shortest paths with different networks.

The most well-known subject in graph theory is the shortest path problem (SPP), which has real-world applications in several different fields of study, including transportation, emergency services, network communications, fire station services, etc. The arc weights of the applicable SP problems are typically represented by fuzzy numbers in real-world applications. In this paper, we discussed the process of finding the shortest distance in a connected graph network in which the arc weights are multi-valued neutrosophic numbers (MNNs). Moreover, here we compare our method with some of the existing results and illustrate one implementation of our method with the help of one numerical example.

The most well-known subject in graph theory is the shortest path problem (SPP), which has real-world applications in several different fields of study, including transportation, emergency services, network communications, fire station services, etc. The arc weights of the applicable SP problems are typically represented by fuzzy numbers in real-world applications. In this paper, we discussed the process of finding the shortest distance in a connected graph network in which the arc weights are multi-valued neutrosophic numbers (MNNs). Moreover, here we compare our method with some of the existing results and illustrate one implementation of our method with the help of one numerical example. [ABSTRACT FROM AUTHOR]

The shortest path (SP) problem (SPP) has several applications in graph theory. It can be used to calculate the distance between the provided initial and final vertex in a network. In this paper, we employed the Fermatean neutrosophic number as the appropriate edge weight of the network to estimate the SP connecting the start and end vertex. This technique is highly useful in establishing the shortest path for the decision-maker under uncertainty. We also investigated its effectiveness in comparison to several existing methods. Finally, a few numerical tests were performed to demonstrate the validity and stability of this new technique, as well as to compare different types of shortest paths with different networks. [ABSTRACT FROM AUTHOR]

The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes. It works well for crisp weights, but the problem arises when weights are vague and uncertain. Let us take an example of computer networks, where the chosen path might no longer be appropriate due to rapid changes in network conditions. The optimal path from among all possible courses is chosen in computer networks based on a variety of parameters. In this paper, we design a new variant of the Floyd-Warshall algorithm that identifies an All-Pair Shortest Path (APSP) in an uncertain situation of a network. In the proposed methodology, multiple criteria and their mutual association may involve the selection of any suitable path between any two node points, and the values of these criteria may change due to an uncertain environment. We use trapezoidal picture fuzzy addition, score, and accuracy functions to find APSP. We compute the time complexity of this algorithm and contrast it with the traditional Floyd-Warshall algorithm and fuzzy Floyd-Warshall algorithm. [ABSTRACT FROM AUTHOR]

Many spatial applications benefit from the fast answering to a seemingly simple spatial query: "Is a point of interest (POI) 'in-path' to the shortest path between a source and a destination?" In this context, an in-path POI is one that is either on the shortest path or can be reached within a bounded yet small detour from the shortest path. The fast answering of the in-path queries is contingent on being able to determine without having to actually compute the shortest paths during runtime. Thus, this requires a precomputation solution. The key contribution of the paper is the development of an in-path oracle that is based on precomputation of which pairs of sources and destinations are in-path with respect to the given POI. For a given road network with n nodes and m POIs, an O (m × n) -sized oracle is envisioned based on the reduction of the well-separated pairs (WSP) decomposition of the road network. Furthermore, an oracle can be indexed in a database using a B-tree that can answer queries at very high throughput. Experimental results on the real road network POI dataset illustrate the superiority of this technique compared to a baseline algorithm. The proposed approach can answer ≈ 1.5 million in-path queries per second compared to a few hundred per second using a suitable baseline approach. [ABSTRACT FROM AUTHOR]

Seamline detection is one of the most important issues in mosaicking high-resolution remote sensing images (HRRSIs). However, it is difficult to make a balance between efficiency and accuracy. On that account, a shortest matrix path-based dynamic programming (SMP-DP) algorithm is proposed to find the optimal seamline for HRRSI mosaicking. First, a pixel cost matrix defined by intensity difference, gradient similarity, and geometric difference is constructed in the overlapping area. Second, the least average path cost from the starting pixel to each pixel is calculated and the SMP-DP algorithm is applied to find the optimal path. Experimental results on HRRSI prove that the proposed method detects high-quality seamline and crosses much fewer objects with the highest computational efficiency, compared with the state-of-the-art method and commercial software. [ABSTRACT FROM AUTHOR]

Single-pair shortest pathfinding (SP) algorithms are used to identify the path with the minimum cost between two vertices in a given graph. However, their time complexity can rapidly increase as the graph size grows. In this paper, we propose a pattern-based blocking algorithm in a grid graph (PBGG) that iteratively blocks or reduces free space vertices that do not require exploration. The blocking process is based on the neighbors of each vertex and utilizes $3 \times 3$ binary pattern matching. The time complexity of blocking is $O(I\cdot \lceil \vert V\vert /C\rceil)$ , where $\vert V\vert $ is the number of vertices, $I$ is the maximum number of iterations, and $C$ is the number of parallelized cores. PBGG significantly reduces the total computation time when utilized to preprocess an input grid graph before applying existing SP algorithms. It also guarantees that if a minimum-cost path exists in the original graph, then the SP algorithms can find at least one path with the same minimum cost in the reduced graph. The proposed method is formulated by convolutions that can be easily implemented using machine learning platforms, such as PyTorch. Experimental results show that when PBGG can significantly reduce the total computation time when employed in conjunction with SP algorithms such as $\text{A}\ast $ and Jump Point Search. On average, PBGG reduces the total computation times by 71% for A and 41% for Jump Point Search, compared to the times taken by the SP algorithms alone.

In this paper, we consider an ambiguity-averse multistage network game between a user and an attacker. The arc costs are assumed to be random variables that satisfy prescribed first-order moment constraints for some subsets of arcs and individual probability constraints for some particular arcs. The user aims at minimizing its cumulative expected loss by traversing between two fixed nodes in the network, while the attacker's objective is to maximize the user's expected loss by selecting a distribution of arc costs from the family of admissible distributions. In contrast to most of the related studies, both the user and the attacker can dynamically adjust their decisions at particular nodes of the user's path. By observing the user's decisions, the attacker may reveal some additional distributional information associated with the arcs emanated from the current user's position. It is shown that the resulting multistage distributionally robust shortest path problem (DRSPP) admits a linear mixed-integer programming reformulation (MIP). In particular, we distinguish between acyclic and general graphs by introducing different forms of non-anticipativity constraints. Finally, we perform a numerical study, where the quality of adaptive decisions and computational tractability of the proposed MIP reformulation are explored with respect to several classes of synthetic network instances. [ABSTRACT FROM AUTHOR]

Changeability analysis methods primarily assist with formulating a response to uncertain and new requirements from various system stakeholders and include asset management issues such as modelling lifecycle path dependency. Epoch-era networks proved to be an effective tool for managing the evolving requirements of a capability system, ensuring sustained value through life. Over the life of a system, stakeholders are faced with countless options to change their capability systems to sustain value, which is path dependent and can greatly impact the scope of decisions available later in life. This paper introduces and demonstrates the application of a revised epoch-era network approach to explore many potential lifecycle paths, along with utility vs. expense strategies, demonstrated through an example of a military frigate subject to evolving requirements. Results indicated the future limitations to sustaining value if the largest and most capable technology upgrades are selected too early in life. The two best lifecycle paths from different strategies were compared to understand the utility/expense trade-offs for the most optimal frigate upgrade trajectory. [ABSTRACT FROM AUTHOR]

Colonies of the arboreal turtle ant create networks of trails that link nests and food sources on the graph formed by branches and vines in the canopy of the tropical forest. Ants put down a volatile pheromone on the edges as they traverse them. At each vertex, the next edge to traverse is chosen using a decision rule based on the current pheromone level. There is a bidirectional flow of ants around the network. In a previous field study, it was observed that the trail networks approximately minimize the number of vertices, thus solving a variant of the popular shortest path problem without any central control and with minimal computational resources. We propose a biologically plausible model, based on a variant of the reinforced random walk on a graph, which explains this observation and suggests surprising algorithms for the shortest path problem and its variants. Through simulations and analysis, we show that when the rate of flow of ants does not change, the dynamics converges to the path with the minimum number of vertices, as observed in the field. The dynamics converges to the shortest path when the rate of flow increases with time, so the colony can solve the shortest path problem merely by increasing the flow rate. We also show that to guarantee convergence to the shortest path, bidirectional flow and a decision rule dividing the flow in proportion to the pheromone level are necessary, but convergence to approximately short paths is possible with other decision rules. [ABSTRACT FROM AUTHOR]

The shortest path problem has many different versions. In this manuscript, we proposed a muti-constrained optimization method to find the shortest path in a computer network. In general, a genetic algorithm is one of the common heuristic algorithms. In this paper, we employed the genetic algorithm to find the solution of the shortest path multi-constrained problem. The proposed algorithm finds the best route for network packets with minimum total cost, delay, and hop count constrained with limited bandwidth. The new algorithm was implemented on four different capacity networks with random network parameters, the results showed that the shortest path under constraints can be found in a reasonable time. The experimental results showed that the algorithm always found the shortest path with minimal constraints. [ABSTRACT FROM AUTHOR]

We present a theoretical framework that links Fermat’s principle of least time to optimal transport theory via a cost function that enforces local transport. The proposed cost function captures the physical constraints inherent in wave propagation; when paired with specific mass distributions, it yields shortest paths in the considered media through the optimal transport plans. In the discrete setting, our formulation results in physically significant optimal couplings, whose off-diagonal entries identify shortest paths in both directed and undirected graphs. For undirected graphs with positive edge weights, commonly used to parameterize seismic media, our method provides solutions to the Eikonal equation consistent with those from the Dijkstra algorithm. For directed negative-weight graphs, corresponding to transportation cost matrices with negative entries, our approach aligns with the Bellman–Ford algorithm but offers considerable computational advantages. We also highlight potential research directions. These include the use of sparse cost matrices to reduce the number of unknowns and constraints in the considered transportation problem, and solving specific classes of optimal transport problems through the Dijkstra algorithm to enhance computational efficiency.

Associated path detection is considered as the major concern of the traditional shortest path issue. The associated path is generally represented by the shortest distance among the source and destination. In the transportation network, distance or cost detection may identify this associated path. Specifically, it is very important to discover the shortest distance that has a minimum number of nodes, and it will give the most optimized result. In this paper, the Fuzzy based Pareto Optimal (FPO) approach is used to discover the shortest paths in a network graph. Initially, the FPO technique finds the shortest paths in a network by using set of rules. Then, the Lexicographical model uses a set of rules to rank the shortest distance based on minimum distance value. From the ranking results, the optimal shortest path is selected based on the proposed Ant Lion Optimization (ALO) algorithm. So, this paper achieves multi objectives like shortest path ranking and selection of the optimal shortest path. Time, distance or cost, convergence time, fitness function, and mean square error are the parameters used to relate the performance of the proposed technique with state-of-the-art techniques. Comparative results display the robustness and proficiency of the proposed system with several works. [ABSTRACT FROM AUTHOR]

This article studies the mean standard deviation (mean-std) Canadian traveller problem (CTP). Different from the canonical CTP, which aims at minimizing the traveller's expected travel time, while considering edge breakdown probabilities, we introduce the reliability version of CTP, which tries to find a routing policy with the minimal linear combination of the travel time's mean and standard deviation. With the recent development of internet-of-things (IoT) technology, the transportation network's edges' travel-time statistics, i.e., mean and standard deviation, as well as the traversal probabilities, are available to the end users. With those information, we propose a dual dynamic programming (DDP) method, which simultaneously estimates the first-order and the second-order moments of a given decision-list (DL) policy, and thereby makes improvements towards to the optimal one through the generalized policy iteration (GPI) scheme. We construct an open source benchmark environment to evaluate the performance of different mean-std CTP solutions, and show that the DDP method outperforms state of the arts in a range of transportation networks. [ABSTRACT FROM AUTHOR]

From the more than two hundred partial orders for fuzzy numbers proposed in the literature, only a few are total. In this article, we introduce the notion of admissible order for fuzzy numbers equipped with a partial order, i.e., a total order which refines the partial order. In particular, it is given special attention to the partial order proposed by Klir and Yuan in 1995. Moreover, we propose a method to construct admissible orders on fuzzy numbers in terms of linear orders defined for intervals considering a strictly increasing upper dense sequence, proving that this order is admissible for a given partial order. Finally, we use admissible orders to ranking the path costs in fuzzy weighted graphs. [ABSTRACT FROM AUTHOR]

This paper presents a new heuristic algorithm tailored to solve large instances of an NP-hard variant of the shortest path problem, denoted the cost-balanced path problem, recently proposed in the literature. The problem consists in finding the origin–destination path in a direct graph, having both negative and positive weights associated with the arcs, such that the total sum of the weights of the selected arcs is as close to zero as possible. At least to the authors' knowledge, there are no solution algorithms for facing this problem. The proposed algorithm integrates a constructive procedure and an improvement procedure, and it is validated thanks to the implementation of an iterated neighborhood search procedure. The reported numerical experimentation shows that the proposed algorithm is computationally very efficient. In particular, the proposed algorithm is most suitable in the case of large instances where it is possible to prove the existence of a perfectly balanced path and thus the optimality of the solution by finding a good percentage of optimal solutions in negligible computational time. [ABSTRACT FROM AUTHOR]

Traffic congestion is an inescapable problem that frustrates drivers in megacities. Although there is hardly a way to eliminate the congestion, it is possible to mitigate the impact through predictive methods. This paper develops a data-driven optimization approach for the dynamic shortest path problems (DSPP), considering traffic safety for urban navigations. The dynamic risk scores and travel times at different times and locations are estimated by the Safe Route Mapping (SRM) methodology and Long Short-Term Memory (LSTM) with Autoencoder, respectively, where possible variations in the future are considered. The DSPP is formulated as a mixed-integer linear programming problem under risk constraints to minimize the total travel cost, defined as the weighted sum of distance and travel time. To improve the efficiency of the DSPP, we design an improved tabu search with alternative initial-solution algorithms to accommodate various problem scales. Moreover, subgraph and self-adaptive insertion techniques are adopted as acceleration strategies to enhance computational efficiency further. Numerical experiments investigate the computational performance and the solution quality of our algorithm. The result shows satisfactory solution quality and computational efficiency with the proposed acceleration strategies compared to the CPLEX solver, a label-setting algorithm, and a state-of-the-art algorithm. Our algorithm can also compete with Google Maps regarding the travel cost in a real network in Manhattan, NY, USA, which is promising for Urban Navigations. [ABSTRACT FROM AUTHOR]

This study investigates the analogy between the electric circuit and roadway traffic analyses based on the loop-wise route representation (LRR). These two seemingly different fields share common aspects in terms of primitive components, system behavior, and underlying principles. Considering this analogy, a novel topology optimization is proposed to solve a shortest path problem by introducing artificial loop variables, which are conceptually analogous to loop current in the electric circuit. Then, the loop-wise route optimization is formulated to minimize the travel cost in both symmetric and asymmetric networks. By virtue of using the LRR, the proposed method can guarantee the flow conservation at each node without imposing any constraint functions. To verify the proposed method, numerical experiments in 10 $\times10$ grid-type networks are conducted under various settings. These results show that the shortest path problems can be solved in a simpler form of unconstrained topology optimization. With further work, the proposed method could be applied to solve general vehicle routing problems such as traveling salesman problems in a more effective way.

The paper introduces the distributed framework for determining the shortest path of robots in the logistic applications, i.e. the warehouse with a swarm of robots cooperating in the Real- Time mode. The proposed solution uses the optimization routine to avoid the downtime and collisions between robots. The presented approach uses the reference model based on Dijkstra, Floyd- Warshall and Bellman-Ford algorithms, which search the path in the weighted undirected graph. Their application in the onboard robot’s computer requires the analysis of the time efficiency. Results of comparative simulations for the implemented algorithms are presented. For their evaluation the data sets reflecting actual processes were used. Outcomes of experiments have shown that the tested algorithms are applicable for the logistic purposes, however their ability to operate in the Real-Time requires the detailed analysis.

In the field of graph theory, the shortest path problem is one of the most significant problems. However, since varieties of indeterminated factors appear in complex networks, determining of the shortest path from one vertex to another in complex networks may be a lot more complicated than the cases in deterministic networks. To illustrate this problem, the model of uncertain random digraph will be proposed via chance theory, in which some arcs exist with degrees in probability measure and others exist with degrees in uncertain measure. The main focus of this paper is to investigate the main properties of the shortest path in uncertain random digraph. Methods and algorithms are designed to calculate the distribution of shortest path more efficiently. Besides, some numerical examples are presented to show the efficiency of these methods and algorithms. [ABSTRACT FROM AUTHOR]

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Copyright of Journal of Transportation & Logistics / Ulaştırma ve Lojistik Dergisi is the property of Journal of Transportation & Logistics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The construction of low-cost nanogrids could help speed up the electrification rate in remote communities in sub-Saharan Africa. One of the challenges in nanogrid design for these communities is the uncertainty in future load demand profiles impacting the cabling topology. We propose two new wiring design approaches for radial direct current power distribution systems. The first one is a modified minimum spanning tree (MST) algorithm and the second one is an adaptive shuffled frog leaping algorithm (SFLA). Their objective is to identify the optimal cable path and the lowest cost wiring characteristics to electrify rural areas with poor infrastructural development. A comparative study of computation burdens has shown the applicability limits relative to the SFLA based approach and encouraged the implementation of the MST as it is faster and does not imply any limitation regarding the number of dwellings to electrify, while providing low-cost wiring design option. The latter is applied to a village located in Kenya and demonstrated more than 25% savings on the entire system cabling cost compared to a classical wiring design based on shortest-path calculation. [ABSTRACT FROM AUTHOR]

Neutrosophic set (NS) is generalization of Intuitionistic Fuzzy Set (IFS) and Fuzzy Set (FS) where Neutrosophic Set(NS) is the collection of Membership, Non-Membership, Indeterminacy Membership of the constituent element. This paper includes the modified circle breaking techinque which is used to evaluate the Shortest Path Problem in which edge weight are protrayed in Single Valued Linear Heptagonal Neutrosophic Number (SVLHNN) and an numerical illustration is given for the efficiency of the given algorithm. [ABSTRACT FROM AUTHOR]